Understanding Calculus: Problems, Solutions, and Tips

Course No. 1007
Professor Bruce H. Edwards, Ph.D.
University of Florida
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Course No. 1007
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Course Overview

Calculus is the greatest mathematical breakthrough since the pioneering discoveries of the ancient Greeks. Without it, we wouldn't have spaceflight, skyscrapers, jet planes, economic modeling, accurate weather forecasting, modern medical technologies, or any of the countless other achievements we take for granted in today's world.

Indeed, calculus is so versatile and its techniques so diverse that it trains you to view problems, no matter how difficult, as solvable until proved otherwise. And the habit of turning a problem over in your mind, choosing an approach, and then working through a solution teaches you to think clearly—which is why the study of calculus is so crucial for improving your cognitive skills and why it is a prerequisite for admission to most top universities.

Understanding Calculus: Problems, Solutions, and Tips

immerses you in the unrivaled learning adventure of this mathematical field in 36 half-hour lectures that cover all the major topics of a full-year calculus course in high school at the College Board Advanced Placement AB level or a first-semester course in college. With crystal-clear explanations of the beautiful ideas of calculus, frequent study tips, pitfalls to avoid, and—best of all—hundreds of examples and practice problems that are specifically designed to explain and reinforce major concepts, this course will be your sure and steady guide to conquering calculus.

Your teacher for this intensively illustrated DVD set is Professor Bruce H. Edwards, an award-winning instructor at the University of Florida and the coauthor of a best-selling series of calculus textbooks.

Accomplish Mathematical Wonders

Calculus is one of the most powerful and astonishing tools ever invented, yet it is a skill that can be learned by anyone with an understanding of high school mathematics.

Among its many uses, calculus teaches you to

  • analyze a multitude of situations involving change, whether it's an accelerating rocket, the growth of a bacterial colony, or fluctuating stock prices;
  • calculate optimum values, such as the greatest volume for a box with a given surface area or the highest feasible profit from the sales of an item;
  • measure complex shapes—for example, the volume of a doughnut-shaped object called a torus or the area of a plot of land bounded by a river.
Learn about Precalculus and Limits . . .

Solving many types of calculus problems usually requires employing precalculus—algebra and trigonometry—to work out a solution. For this reason, Professor Edwards devotes the first few lectures to reviewing key topics in precalculus, then he covers some basic concepts such as limits and continuity before moving on to the two simple, yet brilliant ideas behind calculus—the derivative and the integral.

Despite the apparent differences between the derivative and integral, you discover that they are inextricably linked by the surprising fundamental theorem of calculus. Throughout the course, you will discover that simplicity is one of the hallmarks of the essential ideas of calculus.

. . . the Power of the Derivative . . .

The derivative is the foundation of differential calculus, which you study through Lecture 17, exploring its many applications in science, engineering, business, and other fields.

You start with a classic problem that illustrates one of the core ideas of calculus: Can you find the tangent line to a curve at a given point? This is the same as asking if the rate of change of the curve can be measured at that point—with a host of potential applications in situations where a quantity is changing, such as the speed of an accelerating vehicle. The answer is: Yes, and with amazing simplicity! After learning the steps involved, you have solved your first calculus problem.

You then

  • study a variety of ways to find derivatives, including the power rule, the constant multiple rule, the quotient rule, the chain rule, and implicit differentiation;
  • learn how to find extrema—the absolute maximum and minimum values of functions, using derivatives; and
  • apply derivatives to solve a variety of real-world problems.
. . . and the Importance of the Integral

Next, you are introduced to the integral, using a classic problem in which you are asked to find the area of a plot of land bounded by curves. To solve this problem, calculus provides us with the integral—a powerful tool that allows us to calculate areas, volumes, and other characteristics of complex shapes. The balance of the course is devoted to integral calculus and its applications. You study

  • arc length and surface area—two applications of calculus that are at the heart of engineering;
  • integration by substitution—a method that enables you to convert a difficult problem into one that's easier to solve; and
  • the formulas for continuous compound interest, radioactive decay, and a host of other real-world applications.

A Calculus Course for All

Understanding Calculus is well suited for anyone who wants to take the leap into one of history's greatest intellectual achievements, whether for the first time or for review. Those who will benefit include these learners:

  • Any student now studying calculus who would like personal coaching from a professor who has spent years honing his explanations for the areas that are most challenging to students. This course is specifically designed to cover all the major topics of a full-year calculus course in high school at the College Board Advanced Placement AB level or a first-semester course in college.
  • Parents of students studying calculus, a subject with which they often give up trying to help their high-school-age children—at a critical turning point in their educational careers.
  • Those who have already taken calculus and who need a thorough review.
  • Anyone who didn't understand calculus on the first try and wants a lucid, in-depth presentation, with lots of interesting, well-explained practice problems.

The plentiful graphs, equations, and other visual aids in these lectures are clear and well-designed, allowing you to follow each step of Professor Edwards's presentation in detail. The accompanying workbook includes lecture summaries, sample problems and worked-out solutions, tips, and pitfalls; lists of formulas and theorems; a trigonometry review sheet; a glossary; and a removable study sheet to use for quick and easy reference during the lectures.

The Ideal Calculus Teacher

Professor Edwards is the ideal calculus teacher—friendly, animated, encouraging, and witty, but also focused on presenting the material in an organized and understandable way. For anyone who feels intimidated by calculus, there is a distinct joy in being able to calculate a derivative after just a few lessons. It's easier than one might have supposed, and it opens an amazing new world of insight.

As an educator who has been honored repeatedly, both for his teaching and for his textbooks, Professor Edwards is a fount of valuable advice. He offers frequent tips for success, including guidance for those preparing for the Advanced Placement Calculus AB exam, for which he has served as a grader and for which this course is excellent preparation. Among his suggestions are these:

  • Graphing calculators: While some calculus teachers prefer that their students not use graphing calculators, the Advanced Placement exam requires them. Professor Edwards points out the strengths of graphing calculators as well as the weaknesses—for example, that in certain situations they can fool you.
  • Memorization: Always memorize what your teacher assigns. However, no one can memorize all the formulas in calculus. A good approach is to commit to memory the idea behind a technique—for example, that the disk method of computing the volume of a solid involves slicing it into innumerable disks.

Ever since its inception in the 17th century, calculus has spawned a continuing flood of new ideas and techniques for solving problems. It's easy to be overwhelmed by the richness of this subject, which is why many beginning students find themselves struggling.

Through Professor Edwards's exceptional teaching in Understanding Calculus, you will come away with a deep appreciation for the extraordinary power of calculus, a grasp of which methods apply to different types of problems, and, with practice, a facility for unlocking the secrets of the ceaselessly changing world around us.

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36 lectures
 |  Average 30 minutes each
  • 1
    A Preview of Calculus
    Calculus is the mathematics of change, a field with many important applications in science, engineering, medicine, business, and other disciplines. Begin by surveying the goals of the course. Then get your feet wet by investigating the classic tangent line problem, which illustrates the concept of limits. x
  • 2
    Review—Graphs, Models, and Functions
    In the first of two review lectures on precalculus, examine graphs of equations and properties such as symmetry and intercepts. Also explore the use of equations to model real life and begin your study of functions, which Professor Edwards calls the most important concept in mathematics. x
  • 3
    Review—Functions and Trigonometry
    Continue your review of precalculus by looking at different types of functions and how they can be identified by their distinctive shapes when graphed. Then review trigonometric functions, using both the right triangle definition as well as the unit circle definition, which measures angles in radians rather than degrees. x
  • 4
    Finding Limits
    Jump into real calculus by going deeper into the concept of limits introduced in Lecture 1. Learn the informal, working definition of limits and how to determine a limit in three different ways: numerically, graphically, and analytically. Also discover how to recognize when a given function does not have a limit. x
  • 5
    An Introduction to Continuity
    Broadly speaking, a function is continuous if there is no interruption in the curve when its graph is drawn. Explore the three conditions that must be met for continuity—along with applications of associated ideas, such as the greatest integer function and the intermediate value theorem. x
  • 6
    Infinite Limits and Limits at Infinity
    Infinite limits describe the behavior of functions that increase or decrease without bound, in which the asymptote is the specific value that the function approaches without ever reaching it. Learn how to analyze these functions, and try some examples from relativity theory and biology. x
  • 7
    The Derivative and the Tangent Line Problem
    Building on what you have learned about limits and continuity, investigate derivatives, which are the foundation of differential calculus. Develop the formula for defining a derivative, and survey the history of the concept and its different forms of notation. x
  • 8
    Basic Differentiation Rules
    Practice several techniques that make finding derivatives relatively easy: the power rule, the constant multiple rule, sum and difference rules, plus a shortcut to use when sine and cosine functions are involved. Then see how derivatives are the key to determining the rate of change in problems involving objects in motion. x
  • 9
    Product and Quotient Rules
    Learn the formulas for finding derivatives of products and quotients of functions. Then use the quotient rule to derive formulas for the trigonometric functions not covered in the previous lecture. Also investigate higher-order derivatives, differential equations, and horizontal tangents. x
  • 10
    The Chain Rule
    Discover one of the most useful of the differentiation rules, the chain rule, which allows you to find the derivative of a composite of two functions. Explore different examples of this technique, including a problem from physics that involves the motion of a pendulum. x
  • 11
    Implicit Differentiation and Related Rates
    Conquer the final strategy for finding derivatives: implicit differentiation, used when it's difficult to solve a function for y. Apply this rule to problems in related rates—for example, the rate at which a camera must move to track the space shuttle at a specified time after launch. x
  • 12
    Extrema on an Interval
    Having covered the rules for finding derivatives, embark on the first of five lectures dealing with applications of these techniques. Derivatives can be used to find the absolute maximum and minimum values of functions, known as extrema, a vital tool for analyzing many real-life situations. x
  • 13
    Increasing and Decreasing Functions
    Use the first derivative to determine where graphs are increasing or decreasing. Next, investigate Rolle's theorem and the mean value theorem, one of whose consequences is that during a car trip, your actual speed must correspond to your average speed during at least one point of your journey. x
  • 14
    Concavity and Points of Inflection
    What does the second derivative reveal about a graph? It describes how the curve bends—whether it is concave upward or downward. You determine concavity much as you found the intervals where a graph was increasing or decreasing, except this time you use the second derivative. x
  • 15
    Curve Sketching and Linear Approximations
    By using calculus, you can be certain that you have discovered all the properties of the graph of a function. After learning how this is done, focus on the tangent line to a graph, which is a convenient approximation for values of the function that lie close to the point of tangency. x
  • 16
    Applications—Optimization Problems, Part 1
    Attack real-life problems in optimization, which requires finding the relative extrema of different functions by differentiation. Calculate the optimum size for a box, and the largest area that can be enclosed by a circle and a square made from a given length of wire. x
  • 17
    Applications—Optimization Problems, Part 2
    Conclude your investigation of differential calculus with additional problems in optimization. For success with such word problems, Professor Edwards stresses the importance of first framing the problem with precalculus, reducing the equation to one independent variable, and then using calculus to find and verify the answer. x
  • 18
    Antiderivatives and Basic Integration Rules
    Up until now, you've calculated a derivative based on a given function. Discover how to reverse the procedure and determine the function based on the derivative. This approach is known as obtaining the antiderivative, or integration. Also learn the notation for integration. x
  • 19
    The Area Problem and the Definite Integral
    One of the classic problems of integral calculus is finding areas bounded by curves. This was solved for simple curves by the ancient Greeks. See how a more powerful method was later developed that produces a number called the definite integral, and learn the relevant notation. x
  • 20
    The Fundamental Theorem of Calculus, Part 1
    The two essential ideas of this course—derivatives and integrals—are connected by the fundamental theorem of calculus, one of the most important theorems in mathematics. Get an intuitive grasp of this deep relationship by working several problems and surveying a proof. x
  • 21
    The Fundamental Theorem of Calculus, Part 2
    Try examples using the second fundamental theorem of calculus, which allows you to let the upper limit of integration be a variable. In the process, explore more relationships between differentiation and integration, and discover how they are almost inverses of each other. x
  • 22
    Integration by Substitution
    Investigate a straightforward technique for finding antiderivatives, called integration by substitution. Based on the chain rule, it enables you to convert a difficult problem into one that's easier to solve by using the variable u to represent a more complicated expression. x
  • 23
    Numerical Integration
    When calculating a definite integral, the first step of finding the antiderivative can be difficult or even impossible. Learn the trapezoid rule, one of several techniques that yield a close approximation to the definite integral. Then do a problem involving a plot of land bounded by a river. x
  • 24
    Natural Logarithmic Function—Differentiation
    Review the properties of logarithms in base 10. Then see how the so-called natural base for logarithms, e, has important uses in calculus and is one of the most significant numbers in mathematics. Learn how such natural logarithms help to simplify derivative calculations. x
  • 25
    Natural Logarithmic Function—Integration
    Continue your investigation of logarithms by looking at some of the consequences of the integral formula developed in the previous lecture. Next, change gears and review inverse functions at the precalculus level, preparing the way for a deeper exploration of the subject in coming lectures. x
  • 26
    Exponential Function
    The inverse of the natural logarithmic function is the exponential function, perhaps the most important function in all of calculus. Discover that this function has an amazing property: It is its own derivative! Also see the connection between the exponential function and the bell-shaped curve in probability. x
  • 27
    Bases other than e
    Extend the use of the logarithmic and exponential functions to bases other than e, exploiting this approach to solve a problem in radioactive decay. Also learn to find the derivatives of such functions, and see how e emerges in other mathematical contexts, including the formula for continuous compound interest. x
  • 28
    Inverse Trigonometric Functions
    Turn to the last set of functions you will need in your study of calculus, inverse trigonometric functions. Practice using some of the formulas for differentiating these functions. Then do an entertaining problem involving how fast the rotating light on a police car sweeps across a wall and whether you can evade it. x
  • 29
    Area of a Region between 2 Curves
    Revisit the area problem and discover how to find the area of a region bounded by two curves. First imagine that the region is divided into representative rectangles. Then add up an infinite number of these rectangles, which corresponds to a definite integral. x
  • 30
    Volume—The Disk Method
    Learn how to calculate the volume of a solid of revolution—an object that is symmetrical around its axis of rotation. As in the area problem in the previous lecture, you imagine adding up an infinite number of slices—in this case, of disks rather than rectangles—which yields a definite integral. x
  • 31
    Volume—The Shell Method
    Apply the shell method for measuring volumes, comparing it with the disk method on the same shape. Then find the volume of a doughnut-shaped object called a torus, along with the volume for a figure called Gabriel's Horn, which is infinitely long but has finite volume. x
  • 32
    Applications—Arc Length and Surface Area
    Investigate two applications of calculus that are at the heart of engineering: measuring arc length and surface area. One of your problems is to determine the length of a cable hung between two towers, a shape known as a catenary. Then examine a peculiar paradox of Gabriel's Horn. x
  • 33
    Basic Integration Rules
    Review integration formulas studied so far, and see how to apply them in various examples. Then explore cases in which a calculator gives different answers from the ones obtained by hand calculation, learning why this occurs. Finally, Professor Edwards gives advice on how to succeed in introductory calculus. x
  • 34
    Other Techniques of Integration
    Closing your study of integration techniques, explore a powerful method for finding antiderivatives: integration by parts, which is based on the product rule for derivatives. Use this technique to calculate area and volume. Then focus on integrals involving products of trigonometric functions. x
  • 35
    Differential Equations and Slope Fields
    Explore slope fields as a method for getting a picture of possible solutions to a differential equation without having to solve it, examining several problems of the type that appear on the Advanced Placement exam. Also look at a solution technique for differential equations called separation of variables. x
  • 36
    Applications of Differential Equations
    Use your calculus skills in three applications of differential equations: first, calculate the radioactive decay of a quantity of plutonium; second, determine the initial population of a colony of fruit flies; and third, solve one of Professor Edwards's favorite problems by using Newton's law of cooling to predict the cooling time for a cup of coffee. x

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Your professor

Bruce H. Edwards

About Your Professor

Bruce H. Edwards, Ph.D.
University of Florida
Dr. Bruce H. Edwards is Professor of Mathematics at the University of Florida. Professor Edwards received his B.S. in Mathematics from Stanford University and his Ph.D. in Mathematics from Dartmouth College. After his years at Stanford, he taught mathematics at a university near Bogot·, Colombia, as a Peace Corps volunteer. Professor Edwards has won many teaching awards at the University of Florida, including Teacher of...
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Understanding Calculus: Problems, Solutions, and Tips is rated 4.9 out of 5 by 80.
Rated 5 out of 5 by from Fantastic review prior to grad school I purchased this course as a review, prior to entering a masters degree program in environmental engineering at Johns Hopkins. I am extremely glad that I did so - 3 out of 4 courses so far have required calculus, and this course got me back up to speed better than anything else I tried, including several "review" books (useless) and "tutorials" on the internet (also useless). I last took calculus 25 years ago, so most of my knowledge is essentially gone, having barely used it in my field. This course and the accompanying workbook got me 90% of the way there. It would be great if Professor Edwards could put together a similar course on differential equations, as well as a continuation of this course (a Calculus 2). I HIGHLY recommend this course for anyone else in my position.
Date published: 2013-02-18
Rated 5 out of 5 by from Continuation I would like to say that I love the Great course entitled "Understanding Calculus: Problems, Solutions, and Tips" by Dr. Bruce Edwards. He takes the student through the rudiments of Calculus in a very understandable manner. If there is one flaw in an otherwise great course, I would have to say that this one does not cover enough material. Consequently, I would like to suggest a course entitled Mathematical Analysis by Dr. Edwards. It could begin with basic set theory and then end with the Beta and Gamma functions. It would provide an effective continuation from "Calculus." I cannot think of a better professor to teach it than the great Dr. Edwards.
Date published: 2012-11-28
Rated 5 out of 5 by from Excelent Course & Excelent Teacher Professor Edwards is an excellent teacher and you really learn Calculus from his exposition. Nevertheless I you are a bit rusty with precalculus I recomend you listening to his course on the matter also from TTC . He presents the course material with such gusto that motivates the student to pay attention mindfully and cheerfully. I wish my math teachers where like him. I was studying Calculus probably at the same time as professor Edwards while pursuing my BS in Chemistry in San Antonio, Texas, (1965-1969) and the book we used was a dreadful delta – epsilontics “cryptology text” –a least it seemed so to me- by authors Johnson and Kiokemeister. Our teacher, a retired Colonel, seldom turned his face from the blackboard to make eye contact with the class and the same happened with my other teachers in more advanced mathematics courses. Because I enjoy science I have, by my own, continued reviewing and learning more during the years but there is nothing as a structured class by good professor: just think of learning/reviewing piano by your own or doing it with a master that gives you structure, techniques and insights. I would surely welcome a course with Analytic Geometry, Vector Functions, Parametric Equations and Several Variables. My thanks goes to Dr. Bruce Edwards and to the Teaching Company for this adventure. A Calculus Lover
Date published: 2012-11-26
Rated 5 out of 5 by from Oh WOW! THANK You! I just want to THANK you for such an awesome video! My girl just turned 16 and started college calculus after homeschooling and doing the Saxon Advanced Math courses. She thought she was ready, and tested as ready by the college, but it was her first math that she "couldn't get". She withdrew to retake it later and I ordered this course. Today was the first time she's sat down with the first DVD - I required two hours a week but four hours later she was still watching!!! She LOVES this presentation and she truly 'got" it!! She's especially excited about the comparisons that make sense to her (such as the teacher using his cell phone plan to show greatest integer function), and his way of speaking and manner of presenting that tell her this teacher enjoys his subject so she can too. I know she will finish this DVD series and then she will be better able to tackle the calculus course during the summer. I am so grateful!! Mostly, for her joy at watching - I won't have to battle at all to get her to do this "homework" she's enjoying it too much!.
Date published: 2012-11-18
Rated 5 out of 5 by from Absolutely spectacular! Best class I've ever taken Wow, this class is an absolute winner. Professor Edwards is one of the best teachers I've ever seen. He begins with examples, and then uses those to explain the concepts. His explanations are clear and direct. Let me say a word about the graphics. They are excellent, and compliment the lectures extremely well. The workbook contains many problems which help in understanding the concepts. Every single problem has a full solution in the back, not just an answer. This also helps tremendously in understanding. I give this class my highest recommendation. As others have written, hopefully he will be back for more calculus (such as multivariate), and other math classes. This is certainly the best of the best in the catalog. Excellent job to everyone involved!
Date published: 2012-11-12
Rated 5 out of 5 by from Wonderful course on Calculus It has been 35 years since I studied calculus in high school. This course was just what I needed to get back into the subject (with the goal of being able to enjoy some of the other math courses from the TC). If everyone in high school could have a teacher like this, math most certainly would be more popular. Professor Edwards obviously enjoys math, but it seems he loves teaching even more. He manages to keep the course interesting from start to finish, and his way of presenting should appeal to a very broad range of students. I highly recommend Professor Edwards' other course on precalculus topics also. As the Prof points out several times himself, the precalculus topics are often the hardest part of calculus problems. Mastering those first will definitely help with this course.
Date published: 2012-11-09
Rated 5 out of 5 by from I actually like calculus! As someone in their mid-30s who recently transitioned into a career in finance and risk managment, I initially used this course to brush up on calculus as part of my preparation for the Financial Risk Manager (FRM) exam. The course was a tremendous help, and I am happy to say that I passed the FRM exam in part because of Professor Edwards' course. I remember high school calculus as being dry, difficult, and intimidating to the point that I didn't pursue any additional math classes in university. But after starting this course, I was surprised to find that I actually like calculus. Professor Edward's lectures helped me gain confidence in a subject that I had long since given up on understanding and appreciating. Professor Edwards is one of those rare teachers that can communicate difficult, but truly beautiful, subject matter to his students.
Date published: 2012-09-28
Rated 5 out of 5 by from Spectacular... a Masterpiece ! Clear, accessible, comprehensive, and, with the inclusion of the workbook and a little 'sweat equity', no one with a reasonably solid foundation in elementary Algebra need ever fear Calculus again. Professor Edwards has performed a genuine service to the world with this masterpiece!
Date published: 2012-08-15
Rated 5 out of 5 by from Solid Overview of Elementary Calculus I am a computer science major, and calculus is not exactly the most relevant part of math in my area. Thus I had forgotten most of the calculus I had studied during my college years. Since integration and differentiation can seem a bit forbidding after a few years, the plan was to review the basics, get back up to speed, and restore my self-confidence. I am happy to say that the course did just that. Like many other reviewers, I was pleasantly surprised to see all my "implicit" calculus skills gush out. When I was struggling, Dr. Edwards' was there to the rescue. People who think the topic of this course is restricted to the "concepts" that lay at the foundations of calculus (whatever that might mean), or prefer to sit back and listen passively, are in for a surprise. Edwards is not afraid of proofs and formulas, and his method is example-driven throughout the course. He starts all his discussions with an example, and I frequently paused the tape to see if I could solve the problems myself before he does. Also, based on his experience as a teacher and a textbook-writer, Edwards is quite familiar with "common pitfalls" in calculus, and takes his time to draw the attention of the audience to them. Those who have previous experience with calculus know that it can be pretty dry and austere, so I, for one, greatly benefited from the cheerful enthusiasm of Dr. Edwards in his delivery. Prior to starting this course, my intuition told me that any TTC offering whose title starts with "Understanding..." delivers on its promise. Within the bounds of a math course for the general public, I think Dr. Edwards reaffirms that intuition. Highly recommended.
Date published: 2012-05-23
Rated 5 out of 5 by from Ode to Edwards "The Chain Rule, One thing to rule them all, One thing to find them, One thing to bring them all, And in a matrix bind them." I highly recommend this course to anyone going into mathematics, science, or engineering. I used this course as a review before going into third semester calculus. Magically it all came back to me while watching the course. Professor Edwards does a great job with his use of technology. He also has a way to keep you engaged and interested. Great examples, great professor, great course.
Date published: 2012-03-09
Rated 5 out of 5 by from Understanding Calculus: Problems, Solutions, and T An excellent, thorough, detailed, practical and logical introduction to calculus for students who intend to use it as a tool. I strongly recommend this course for high school students and graduates BEFORE they take the calculus series for credit. It will help you review what you've learned and understand why you learned it and how it will be useful. Then it will get you started in calculus. You'll quickly see that calculus is not the bogey you've probably feared it is.
Date published: 2011-10-05
Rated 5 out of 5 by from Unbelievably Great I took Calculus in college many years. Really got nothing out of it and never used the knowledge. But Professor Edwards takes the theory and turns it into something useful. Something I could have used over my professional career. I recommend this course for any pre Calculus student. It will help the student see the big picture, so as his college professor slogs though all the theory the student may be able to see the light at the end of the tunnel. I would also recommend this course for anyone who wants to brush up on calculus. I only wish Professor Edwards had taught Calculus at the college I attended. He is one of my favorite Great Courses professors.
Date published: 2011-09-22
Rated 5 out of 5 by from An excellent course! With these lectures and a textbook, my ninth grade son learned calculus and got a top mark on the Advanced Placement calculus exam this spring. He didn't need to attend math classes or meet with a tutor. I don't know anything about calculus at all, but I can say that my son enjoyed and benefited from this course.
Date published: 2011-07-29
Rated 5 out of 5 by from Great Course--What A Blessing! I taught myself calculus out of books. Well, first I had to teach myself advanced algebra, then trig, and THEN I got to calculus. I did this because I was tired of not knowing enough math to really study various sciences. In high school, I decided I was bad at math. In Biz Ad. graduate school, however, I got As in business math. I found out I loved it! After many years as a CPA, I had to retire due to a disability so I picked up math again (as described above). When you teach yourself, you end up with gaps, holes & blind spots. And that is why THIS course and its excellent instructor are such a blessing to me. I'd never watched an instructor go through calculus problems before & Prof. Edwards made everything understandable. Plus, it all looked like a breeze when HE did it! Then I hit the problem book. I found some of the problems quite--stimulating. Still, I could always re-watch the lecture to figure out how to do them. ( And frankly I was amazed at how much I really HAD taught myself.) I've just ordered Prof. Edward's PreCalculus course-- which would have been nice to take PRIOR to this one. However, it didn't exist at the time I ordered this course & began watching it/ working it. Better late than never, though! I found most of my mistakes/confusion arose in areas covered in Precalculus, not Calculus. (Example: inverse trig functions. WHAT is up with inverse trig functions? Slippery little devils...) Anyway, I am very glad to have this excellent set of DVDs in my math arsenal & I do not care that PreCalculus is coming after Calculus. It's all good. And it's all forgettable, too, so I can take a refresher course whenever I need it. I really dig the workbook concept. I hope TTC offers workbooks with other courses--Prof. Hazen's 'Joy of Science' & Norwieci's (sp?) 'Joy of Biology' or whatever would be enhanced by workbooks. Also, if TTC ever takes my advice & offers a real college-level survey course in physics, a workbook would be great to have. They ensure you've got the concepts down.
Date published: 2011-07-13
Rated 5 out of 5 by from A TOUR DE FORCE OF CALCULUS I have listened to many TC courses. Prof Edwards is one of the best. He simplifies a difficult subject. I reviewed this course with my teenage son who had no difficulties understanding the subject. My son got a 5 in AP Calculus after listening to this course and going through the accompanying queston booklet.
Date published: 2011-06-24
Rated 5 out of 5 by from Bravo, Professor Edwards! After 50-years away from higher mathematics, I decided to refurbish some old mental skills. When I completed Lesson Three, I thought: "I will never finish this course as my fundamental algebra, trigonometry and pre-calculus is inadequate to continue." I persisted. Not only did I finish the course, but honed other math skills as well. Professor Edwards is a supurb teacher; he is clear, enthusiastic, well-paced and has excellent presentation skills. What will I do with this? I plan to tutor high school physics---using calculus. I recommend that the Teaching Company develop--with Professor Edwards-- a Pre-calculus course, as well as Calculus II and Calculus III. These courses will correlate with texts of the same subjects written by Dr. Edwards.
Date published: 2011-03-18
Rated 5 out of 5 by from Logically arranged and well presented This course progresses well through the basic calculus topics. Each lecture covers the topic clearly, recapping methods from previous lectures and showing how they apply to the current topic. Professor Edwards' bright manner and presentation is refreshing and holds ones attention throughout the lecture. The diagrams are well done and the development of the problem on the 'blackboard' is easy to follow. Bear in mind that if you don't get it first time you can always repeat that part of the lecture by 're-winding' back to the start of that section or replay the entire lecture. If I have trouble with a lecture or two I push on to the end of the disc for an overview and replay the entire disc for deeper study. An excellent course for first time learners or those who have forgotten and want to refresh their memory.
Date published: 2011-02-17
Rated 5 out of 5 by from A Must-Have for Calculus Students I've just started Calc I as an independent study. I've watched the first 4 lectures and Prof. Edwards completely hits the mark. He's covered everything in my text. My text is much easier to understand because I've already seen and heard the material. I enjoy Prof. Edward's teaching style. He really loves calculus and his enthusiasm is contagious.
Date published: 2011-02-14
Rated 5 out of 5 by from Highly Recommended I undertook to take Calculus 2 after a 25 year break from taking math in school. To recover my completely-forgotten Calc 1, I ordered this DVD set. I wanted to wait until I was well into Calc 2 before writing this review so I could accurately relate its effectiveness. I am VERY pleased with how well this course prepared me for Calc 2. There is nothing we have covered so far that I was not well prepped for by Dr. Edwards' course. The course's workbook is decent and contains problems that well test one's understanding of the material. I would recommend that you check out a calculus textbook from your library to have more practice problems on hand (the workbook has an average of 10 per unit). Even the things not directly covered by this DVD set--e.g. L'Hopital's rule--are easily and quickly absorbed after completing this course. I got this course at a greatly reduced price, but for someone in my shoes the course is easily worth the full price. Compare the full cost to the cost of enrolling in Calc 1 and purchasing a textbook. Not only is Dr. Edwards' course cheaper, but it offers several advantages: 1) You know you won't get a turkey for an instructor (yes, Edwards is something of a math geek, but his quirks--i.e. his fondness for the word "duh" and his coining of the term "compactify"--are endearing after a while). 2) You can re-watch lectures over and over again until you get it. Dr. Edwards has a good sense of how much time to spend on what. Once or twice during the course I wished he'd elaborated a little further, but I was always able to understand eventually through re-watching and doing the exercises. (Oh yes; the workbook not only contains answers in the back but explanations as well.) Just outstanding. I couldn't be more pleased with this course.
Date published: 2011-01-30
Rated 5 out of 5 by from Outstanding Calculus Course This is one of the best courses from the Teaching Company. It is a full treatment of Calculus I and a great review for those of us who are a bit rusty and I believe would be great for newcomers as well. Dr. Edwards comes across as someone who truly loves math and teaching and this really enhances the learning experience with him. I look forward to more advanced calculus and differential equations courses from him. I hope more people are inspired by courses like this to appreciate the beauty of mathematics and see the doors it can open in your life.
Date published: 2010-12-25
Rated 5 out of 5 by from Excellent Calculus Course! More Please!! This is the real deal, not an overview, but a hands on detailed course on calculus. I loved it, probably the best course I have watched from the Teaching Company. Very clear presentation and good use of examples. I particularly like the way that he doesn't labour the routine algebra of the examples, but focuses instead on the calculus principles. Prof. Edwards is the sort of teacher who makes a difficult subject such as Calculus accessible to anyone with a basic maths background. I hope Prof. Edwards (and the Teaching Company) will produce a "Calculus II" and Calculus III course, The overview courses are interesting, but this sort of course if far better.
Date published: 2010-10-18
Rated 5 out of 5 by from Excellent Course I wanted a course that covered the basics and then developed the more difficult concepts of Calculus in a step by step, easy to understand manner. This course achieved that. Prof Edwards explained the mathematics well and used appropriate problems to further develop understanding. The pace of the lectures was good for me and there was also appropiate revision. I think the course would be ideal for students who want to learn Calculus using self paced lessons. The lectures cover most of the material you would encounter in High School and first Year University courses. I would recommend Prof Starbird's series on Calculus as an adjunct, as it covers more of the history, ideas and concepts in Calculus; whereas Prof Edwards focuses on the problems and solution you would encounter in School.
Date published: 2010-10-11
Rated 5 out of 5 by from Best! Best! Best! Before I received the CD's I had used Prof. Edwards textbooks on Precalculus, Applied Calculus, and his Calculus for math majors. I bought the CD's based on my experience with his textbooks. He is a great author and no less a lecturer. As a math major I would have liked more theory and discussion of traditional proofs. This man is a teacher in his bones. It comes through in this writing style which is clear, lucid, and totally suited to his target audience - not overly rigorous, but certainly not dumbed down. His style of lecturing is fantastic. He doesn't dare you to learn calculus. Rather, he invites you take a journey with him where he will act as your guide. The CD's are a great resource and Prof Edwards lecture style is very enjoyable. However, to get the full impact of his teaching you should also use his "Applied Calculus" and "Calculus". I personally will buy any of materials sight unseen.
Date published: 2010-09-04
Rated 3 out of 5 by from Professor, get your hands dirty. Use the BOARD. I was very excited when I ordered this course. But when viewing the lessons I was thoroughly disappointed. Why? This set is a series of lectures with slides of fully worked out problems whizzing by now and then. In my experience of taking math courses the best ones are where after reviewing the theory the teacher works out sample problems on the board - step by step. Here the Good Doctor, with a remote control in hand, talks and clicks to change slides. Sorry, if you want to really UNDERSTAND and learn Calculus, you AND the teacher needs to solve problem after problem, step by step. This course does not do that. An opportunity missed.
Date published: 2010-08-21
Rated 5 out of 5 by from Calculus CAN be FUN Even though I don’t have anything to do with calculus in my professional life I ordered this course as a refresher of what I had learned in high school and college in the remote past, as a purely intellectual diversion, that is. Having had an excellent math teacher in high school I never held a grudge against math, so investing 18 hours into something I did not really need meant that my expectations (in the prescriptive sense) were high. And what a treat it was! Professor Edwards’ enthusiasm for his subject, his almost boyish joy while lecturing, were truly contagious and made the lectures fly by in no time. He gave roughly equal time to the differential and integral calculus which seems in order, even if the integral lectures did appear to be somewhat “denser”. The course emphasizes applications rather than rigorous proofs of theorems, although theorems are introduced and made plausible. This worked fine for me but I can easily imagine that with Professor Edwards as teacher I would have enjoyed a more theorem-oriented approach as well. Throughout the course Professor Edwards makes excellent use of the visual, almost all examples are accompanied by graphs which greatly facilitate understanding the concepts and applying them. A superb course. I emphatically support other reviewers’ pleas for more from Professor Edwards, like a follow-up course on advanced calculus.
Date published: 2010-08-13
Rated 3 out of 5 by from Disappointing.. These lectures fit a strange niche. At times it leaps too far with concepts that a beginner calculus student would get lost and thus frustrated, but if you are already familiar with calculus then these videos may be too elementary. I am not sure who to recommend these to. I may look back and realize they are better than I thought but only after I learn from another source which defeats the purpose of buying these in the first place.
Date published: 2010-08-03
Rated 5 out of 5 by from Another excellent instructor from the teaching co. The only complaint I have was the workbook did not contain enough problems to work out.
Date published: 2010-07-29
Rated 5 out of 5 by from For a better understanding Professor Edwards made calculus clear and easy to understand if you do the practice exercise he has for each lecture. This was especially true near the end of the series when he skipped some of the steps that gets the problem from here to there because he assumes you know those steps after doing the practice exercises. As Professor Edwards said Calulus is not a spectator sport. It also helps that if certain methods do not come to mind during the lecture you can replay the DVD that explains the method you are not clear on. This is not a course most people will do in two weeks because of the practice exercises. If you want to understand calculus this is a great place to start.
Date published: 2010-07-17
Rated 5 out of 5 by from Can't wait for Part II This is one of the best courses I have taken at the Teaching Company, and I have taken many. It is also the first Math course that dares attack the nuts and bolts of the subject right from Lesson 1, rather than remain at the level of a "general overview" (as for example Prof. Starbird's course on the same subject, which was excellent in its own way, and would be a good introduction to this course). I wish the Teaching Company would offer more courses based on that philosophy in all the sciences (Maths, Physics, Chemistry etc) Prof. Edwards is a living proof that a good teacher can address a difficult subject such as Calculus and make it crystal clear to someone who has no background in the subject (such as myself). I sincerely hope Prof. Edwards (and the Teaching Company) can be convinced to offer a "Calculus II" course, where the second part of his Calculus Textbook would be covered.
Date published: 2010-06-12
Rated 5 out of 5 by from Great Course I just received this course today, and I'm enjoying it. Starbird's course seems to discuss the theories and ideas of calculus, this one actually works and displays problems, discusses graphing calculators, and takes things one step at a time. For someone wanting refresher, or wanting to be able to work calculus problems, this is great.
Date published: 2010-05-22
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