Change and Motion: Calculus Made Clear, 2nd Edition

Course No. 177
Professor Michael Starbird, Ph.D.
The University of Texas at Austin
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Course No. 177
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Course Overview

One of the greatest achievements of the human mind is calculus. It justly deserves a place in the pantheon of our accomplishments with Shakespeare's plays, Beethoven's symphonies, and Einstein's theory of relativity.

In fact, most of the differences in the way we experience life now and the way we experienced it at the beginning of the 17th century emerged because of technical advances that rely on calculus. Calculus is a beautiful idea exposing the rational workings of the world; it is part of our intellectual heritage.

The True Genius of Calculus Is Simple

Calculus, separately invented by Newton and Leibniz, is one of the most fruitful strategies for analyzing our world ever devised. Calculus has made it possible to build bridges that span miles of river, travel to the moon, and predict patterns of population change.

Yet for all its computational power, calculus is the exploration of just two ideas—the derivative and the integral—both of which arise from a commonsense analysis of motion. All a 1,300-page calculus textbook holds, Professor Michael Starbird asserts, are those two basic ideas and 1,298 pages of examples, variations, and applications.

Many of us exclude ourselves from the profound insights of calculus because we didn't continue in mathematics. This great achievement remains a closed door. But Professor Starbird can open that door and make calculus accessible to all.

Why You Didn't Get It the First Time

Professor Starbird is committed to correcting the bewildering way that the beauty of calculus was hidden from many of us in school.

He firmly believes that calculus does not require a complicated vocabulary or notation to understand it. Indeed, the purpose of these lectures is to explain clearly the concepts of calculus and to help you see that "calculus is a crowning intellectual achievement of humanity that all intelligent people can appreciate, enjoy, and understand."

He adds: "The deep concepts of calculus can be understood without the technical background traditionally required in calculus courses. Indeed, frequently the technicalities in calculus courses completely submerge the striking, salient insights that compose the true significance of the subject.

"In this course, the concepts and insights at the heart of calculus take center stage. The central ideas are absolutely meaningful and understandable to all intelligent people—regardless of the level or age of their previous mathematical experience. Historical events and everyday action form the foundation for this excursion through calculus."

Two Simple Ideas

After the introduction, the course begins with a discussion of a car driving down a road. As Professor Starbird discusses speed and position, the two foundational concepts of calculus arise naturally, and their relationship to each other becomes clear and convincing.

Professor Starbird presents and explores the fundamental ideas, then shows how they can be understood and applied in many settings.

Expanding the Insight

Calculus originated in our desire to understand motion, which is change in position over time. Professor Starbird then explains how calculus has created powerful insight into everything that changes over time. Thus, the fundamental insight of calculus unites the way we see economics, astronomy, population growth, engineering, and even baseball. Calculus is the mathematical structure that lies at the core of a world of seemingly unrelated issues.

As you follow the intellectual development of calculus, your appreciation of its inner workings will deepen, and your skill in seeing how calculus can solve problems will increase. You will examine the relationships between algebra, geometry, trigonometry, and calculus. You will graduate from considering the linear motion of a car on a straight road to motion on a two-dimensional plane or even the motion of a flying object in three-dimensional space.

Designed for Nonmathematicians

Every step is in English rather than "mathese." Formulas are important, certainly, but the course takes the approach that every equation is in fact also a sentence that can be understood, and solved, in English.

This course is crafted to make the key concepts and triumphs of calculus accessible to nonmathematicians. It requires only a basic acquaintance with beginning high-school level algebra and geometry. This series is not designed as a college calculus course; rather, it will help you see calculus around you in the everyday world.

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24 lectures
 |  Average 31 minutes each
  • 1
    Two Ideas, Vast Implications
    Calculus is a subject of enormous importance and historical impact. It provides a dynamic view of the world and is an invaluable tool for measuring change. Calculus is applicable in many situations, from the trajectory of a baseball to changes in the Dow Jones average or elephant populations. Yet, at its core, calculus is the study of two ideas about motion and change. x
  • 2
    Stop Sign Crime—The First Idea of Calculus—The Derivative
    The example of a car moving down a straight road is a simple and effective way to study motion. An everyday scenario that involves running a stop sign and the use of a camera illustrates the first fundamental idea of calculus: the derivative. x
  • 3
    Another Car, Another Crime—The Second Idea of Calculus—The Integral
    You are kidnapped and driven away in a car. You can't see out the window, but you are able to shoot a videotape of the speedometer. The process by which you can use information about speed to compute the exact location of the car at the end of one hour is the second idea of calculus: the integral. x
  • 4
    The Fundamental Theorem of Calculus
    The moving car scenario illustrates the Fundamental Theorem of Calculus. This states that the derivative and the integral are two sides of the same coin. The insight of calculus, the Fundamental Theorem creates a method for finding a value that would otherwise be hard or impossible to get, even with a computer. x
  • 5
    Visualizing the Derivative—Slopes
    Change is so fundamental to our vision of the world that we view it as the driving force in our understanding of physics, biology, economics—virtually anything. Graphs are a way to visualize the derivative's ability to analyze and quantify change. x
  • 6
    Derivatives the Easy Way—Symbol Pushing
    The derivative lets us understand how a change in one variable affects a dependent quantity. We have studied this relationship with respect to time. But the derivative can be abstracted to many other dependencies, such as that of the area of a circle on the length of its radius, or supply or demand on price. x
  • 7
    Abstracting the Derivative—Circles and Belts
    One of the most useful ways to consider derivatives is to view them algebraically. We can find the derivative of a function expressed algebraically by using a mechanical process, bypassing the infinite process of taking derivatives at each point. x
  • 8
    Circles, Pyramids, Cones, and Spheres
    The description of moving objects is one of the most direct applications of calculus. Analyzing the trajectories and speeds of projectiles has an illustrious history. This includes Galileo's famous experiments in Pisa and Newton's theories that allow us to compute the path and speed of projectiles, from baseballs to planets. x
  • 9
    Archimedes and the Tractrix
    Optimization problems—for example, maximizing the area that can be enclosed by a certain amount of fencing—often bring students to tears. But they illustrate questions of enormous importance in the real world. The strategy for solving these problems involves an intriguing application of derivatives. x
  • 10
    The Integral and the Fundamental Theorem
    Formulas for areas and volumes can be deduced by dividing such objects as cones and spheres into thin pieces. Ancient examples of this method were precursors to the modern idea of the integral. x
  • 11
    Abstracting the Integral—Pyramids and Dams
    Archimedes devised an ingenious method that foreshadowed the idea of the integral in that it involved slicing a sphere into thin sections. Integrals provide effective techniques for computing volumes of solids and areas of surfaces. The image of an onion is useful in investigating how a solid ball can be viewed as layers of surfaces. x
  • 12
    Buffon’s Needle or π from Breadsticks
    The integral involves breaking intervals of change into small pieces and then adding them up. We use Leibniz's notation for the integral because the long S shape reminds us that the definition of the integral involves sums. x
  • 13
    Achilles, Tortoises, Limits, and Continuity
    The integral's strategy of adding up little pieces solves a variety of problems, such as finding the volume of a pyramid or the total pressure on the face of a dam. x
  • 14
    Calculators and Approximations
    The Fundamental Theorem links the integral and the derivative. It shortcuts the integral's infinite process of summing and replaces it by a single subtraction. x
  • 15
    The Best of All Possible Worlds—Optimization
    Calculus is useful in many branches of mathematics. The 18th-century French scientist Georges Louis Leclerc Compte de Buffon used calculus and breadsticks to perform an experiment in probability. His experiment showed how random events can ultimately lead to an exact number. x
  • 16
    Economics and Architecture
    Zeno's Arrow Paradox concerns itself with the fact that an arrow traveling to a target must cover half the total distance, then half the remaining distance, etc. How does it ever get there? The concept of limit solves the problem. x
  • 17
    Galileo, Newton, and Baseball
    The real numbers in toto constitute a smooth, seamless continuum. Viewing the world as continuous in time and space allows us to make mathematical models that are helpful and predictive. x
  • 18
    Getting off the Line—Motion in Space
    Zeno's Arrow Paradox shows us that an infinite addition problem (1/2 + 1/4 + 1/8 + . . .) can result in a single number: 1. Similarly, it is possible to approximate values such as π or the square root of 2 by adding up the first few hundred terms of infinite sum. Calculators use this method when we push the "sin" or square root keys. x
  • 19
    Mountain Slopes and Tangent Planes
    We have seen how to analyze change and dependency according to one varying quantity. But many processes and things in nature vary according to several features. The steepness of a mountain slope is one example. To describe these real-world situations, we must use planes instead of lines to capture the philosophy of the derivative. x
  • 20
    Several Variables—Volumes Galore
    After developing the ideas of calculus for cars moving in a straight line, we have gained enough expertise to apply the same reasoning to anything moving in space—from mosquitoes to planets. x
  • 21
    The Fundamental Theorem Extended
    Calculus plays a central role in describing much of physics. It is integral to the description of planetary motion, mechanics, fluid dynamics, waves, thermodynamics, electricity, optics, and more. It can describe the physics of sound, but can't explain why we enjoy Bach. x
  • 22
    Fields of Arrows—Differential Equations
    Many money matters are prime examples of rates of change. The difference between getting rich and going broke is often determined by our ability to predict future trends. The perspective and methods of calculus are helpful tools in attempts to decide such questions as what production levels of a good will maximize profit. x
  • 23
    Owls, Rats, Waves, and Guitars
    Whether looking at people or pachyderms, the models for predicting future populations all involve the rates of population change. Calculus is well suited to this task. However, the discrete version of the Verhulst Model is an example of chaotic behavior—an application for which calculus may not be appropriate. x
  • 24
    Calculus Everywhere
    There are limits to the realms of applicability of calculus, but it would be difficult to exaggerate its importance and influence in our lives. When considered in all of its aspects, calculus truly has been—and will continue to be—one of the most effective and influential strategies for analyzing our world that has ever been devised. x

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Your professor

Michael Starbird

About Your Professor

Michael Starbird, Ph.D.
The University of Texas at Austin
Dr. Michael Starbird is Professor of Mathematics and University Distinguished Teaching Professor at The University of Texas at Austin, where he has been teaching since 1974. He received his B.A. from Pomona College in 1970 and his Ph.D. in Mathematics from the University of Wisconsin-Madison in 1974. Professor Starbird's textbook, The Heart of Mathematics: An Invitation to Effective Thinking, coauthored with Edward B. Burger,...
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Reviews

Change and Motion: Calculus Made Clear, 2nd Edition is rated 4.2 out of 5 by 101.
Rated 5 out of 5 by from A well done refresher While not minimizing the difficulty of the material Prof. Starbird's course is an enjoyable presentation of a difficult subject. He mixes the nuts and bolts of calculus with interesting real world examples. Perhaps someone who has never taken calculus would struggle to completely understand the material but this IS calculus after all so no apologies for it being difficult even as a refresher some 40 years later for me. Good job. Will definitely look into other courses by this professor.
Date published: 2014-01-30
Rated 5 out of 5 by from Change and Motion : Calculus made clear Apparently here in NC the public high schools have changed to longer classes and are in the habit of totally dropping key subjects such as Math and English for whole semesters. It beats me as to how this can be a better system but, anyway, the reason I bought this course was to teach our grandson in the evenings in those "down" semesters. We typically went through 2 lectures each evening (one evening per week) and I have to say this course is excellent. It logically explains the origin of the Calculus and the practical applications. Professor Starbird is the sort of professor I wish I'd had to teach me calculus long ago. I know that our grandson is now well versed in this subject whether or not the NC system ever gets around to teaching it to him.
Date published: 2014-01-30
Rated 3 out of 5 by from Completed and glad Am 40 years from my last calculus course and pushed to finish this one. Have completed several of his other courses but at times lost his thread in this one. The basic concepts and importance do however come through in the end.
Date published: 2013-04-28
Rated 2 out of 5 by from A little slow. There was some good information in the part that I watched, but I couldn't sit through it. I think it may be that I didn't have the math background.
Date published: 2013-04-21
Rated 5 out of 5 by from Aptly Named Course Calculus Made Clear couldn't be a better title for this course. Professor Starbird clarifies the science of calculus in a way that I had never experienced before. I happen to teach on an adjunct basis at a large university, primarily courses in quantitative business applications and economics, and took two years of college calculus, but even I found that although I can solve your basic 2nd year calculus textbook problems,I didn't really have a full appreciation until being enlightened by Professor Starbird. This course should be required for all beginning calculus students so they understand why they are doing what they're doing and putting the applications into their proper perspective. What an eye-opener it would be for them and how much easier the course content would be if they were to understand the big picture the way that Professor Starbird presents it. A huge thumbs up and a thank you from me.
Date published: 2013-02-05
Rated 1 out of 5 by from I thought my calculus Prof in college was bad.... With all due respect, this course is dreadful. Professor Starbird mixes metaphors, as if maths isn't confusing enough. Doesn't explain notation/symbols--as if they don't matter. (They do.) Often childish to lighten the tiresome verbiage—only adding to the superfluous baggage of circumlocutory explanation. I took calculus in college and was constantly amazed at how sharp professors weren’t able to successfully use real-world examples to convey the utility of the maths they were trying to teach. Professor Starbird falls into this category of a teacher who uses presumably “simple” (ie, childish) scenarios. Not good. He says the same thing twice, or three times (which means the course could be at least half as long). Professor Starbird’s lectures were motivating in one respect—I motioned myself to the DVD player and changed to a different Teaching Company lecture series. Sitting through this course was like having surgery without the benefit of anesthesia. Painful and disappointing.
Date published: 2013-01-07
Rated 5 out of 5 by from Just right The course makes calculus a breeze - the professor explains ideas of calculus and how they lead to development of specific formulas and relationships. The examples are fun, yet develop a deep understanding of the subject. It is not an extensive problem solving course in a tactical sense - don't expect to learn stuff like integration by substitution or chain rule, but the course will enable you to see the big picture and arm you with a strategic approach to problem solving: you will be able to understand the physical nature of the problem and properly analyze it. You will also find that much of the stuff in calculus textbooks and reference books becomes a breeze, because you start to intuitively understand the physical essence of relationships described by the theorems and the formulas. I only wish there was a sequel to this course, going into more advanced subjects - Gauss theorem, del operator and so forth.
Date published: 2012-05-04
Rated 4 out of 5 by from Great low-stress explanation of Calculus... I'm a big fan of Dr. Starbird's Teaching Company courses and feel that this is his best. In this course, he manages in only 12 hours of lectures to give a fine explanation of what Calculus is, and how it can be used. With this overview of Calculus, Dr. Starbird is able to reduce the mystery, confusion, and fear levels that new students sometimes have, as they approach the subject for the first time. He does this with patience, kindness, and humor, as well as with many fine examples and wonderful graphics that make Calculus much easier to understand and swallow. This is the course to watch, if you are going to be taking Calculus at school or at College for the first time, in a few months. You can quickly learn about all the important concepts of Calculus in a relaxing and low-stress environment on your own - with no problems to work, no homework or reading, and no tests to take. After this course, you will be much more able to understand what you would be taught in a real Calculus class, and be much more ready to do well in that class. This course is also useful for those of us who have already taken Calculus, but didn't quite get what it was all about. I do so wish that I'd been able to watch this course before I took Calculus the first time.
Date published: 2012-03-09
Rated 5 out of 5 by from Good Overview Course This was one of the first courses I bought from TTC, and i now own over 30. On first viewing I found the concepts understandable and the presentation inviting and intriguing despite some of the negative reviews regarding Dr. Starbird's lecturing style. I can forgive his few stumbles and hesitations. He tries to inject some lightness and humor into the material to give it some life, although he might have gone too far with the stuffed animals towards the end. I have had to watch the lectures several times to acquire the full understanding of the concepts, but what I discovered was most interesting about his lectures was how much information he has packed into the first 12 lectures. I realized this after viewing several actual college calculus courses online. I discovered that many of the college courses took 10 - 20 1 hour lectures to convey what Dr. Starbird did in 6 half hour lectures, and in some cases, his material made more sense. This gave me a renewed appreciation for this course than what I had originally formed on the first viewing. Be reminded, this course is not intended to make one proficient in solving real calculus problems. It is an overview of the subject, and I think a good one. It provides an awareness of what calculus is and what it is good for. If you want a truly functional understanding of calculus you should look toward the course by Dr. Edwards. I plan to get that one next. I bought his PreCalculus course and enjoyed and benefited from it a lot.
Date published: 2012-02-25
Rated 3 out of 5 by from An overview for the non-mathematician For a person wanting to have a basic understanding of the principals of calculus, this is an excellent introduction. Dr. Starbird is enthusiastic in his treatment of calculus and clearly wants his TTC "students" to appreciate the subject. He illustrates calculus principals with everyday examples that do not require algebraic or trigonometric manipulation. The lectures can be viewed without any work on the part of the student other than listening. However, this course does not compare in scope or content with the calculus course presented by Dr. Bruce Edwards. The Edwards course requires strict attention to the lectures and work with pen and paper during the lecutures. Both courses have value, but for different learners.
Date published: 2011-11-08
Rated 1 out of 5 by from Boooring! Returned. Perhaps I am not being "fair" by comparing professor Starbird to professor Benjamin, but my personal bias is that anyone who is selected to teach a course to thousands via DVD, should at least SHOW ENTHUSIASM toward his subject... If you have not viewed any math courses by prof. Benjamin, you are denying yourself a great experience, in my opinion. During my college days, there were too many professors who taught a course because they had to, not because they wanted to, and it showed.
Date published: 2011-10-26
Rated 4 out of 5 by from Good, not Great I used this course to supplement my college coursework. While the course is short on mathematical mechanics (probably because it would be far too tedious), I did find that the course allowed me to develop a good understanding of the general concepts of Calculus,
Date published: 2011-09-18
Rated 3 out of 5 by from An OK course Good, but not as clear as I think Prof. Starbird would like to think.
Date published: 2011-07-15
Rated 2 out of 5 by from For neophytes only If you have any prior knowledge of calculus (or just understand mathematical concepts without too much trouble), then you'll find this course tedious. Long after you've gotten the point, the instructor continues to hammer the concepts home. I found it baffling that what takes five minutes to understand was drawn out into a 30-minute lecture. However, I do have a basic understanding of math. Also, pastel pinks and blues are the theme. Filmed in the '80s?
Date published: 2011-06-14
Rated 5 out of 5 by from Valuable It's hard to make math lectures enjoyable (spoken from experience), but Dr. Starbird manages fine. I like his overview approach. There's no way anybody is going to be able to compress the typical two-inch-thick calculus book into a couple dozen lectures, and he doesn't try. Rather, he focuses on the key aspects and shows how they connect. His examples are helpful.
Date published: 2011-05-18
Rated 4 out of 5 by from helpful but not for remedials Professor Starbird’s enthusiasm was infectious and I did get some of what he was saying but could not master the subject sufficiently. I think that he is a good teacher for the mathematically inclined, those people who have a mystical affinity for the subject. I give him 68% and the course 60%. However he is the best Maths teacher I have ever had and he shone a light on the subject and I do understand it better as a result of viewing these lectures even though I sometimes thought my brain was going to suffer meltdown. On the down side, I found the course hard going and Calculus has not been made all that clear to me by the end of it. Neither frequent use of the pause button nor rerunning of sections and even entire lectures over and over again helped my understanding enough to really get the maths at all times. It seemed that the Prof. speeded up as he reached the difficult bits and did not spoon feed at those stages to a necessary extreme degree. Sometimes I was not only confounded by the mathematics but could not understand the verbal describing either, especially the last 2/5ths of Lecture 14 and the 2nd Path example of Lecture 21, both of which I found incomprehensible. That was very discouraging and frustrating. As well, I was hugely frustrated and disappointed that I could not achieve an understanding of the ‘guitar string’ section of the end 5 minutes of Lecture 23. A much more detailed explanation of the equations was needed. He has a halting, stammering delivery oftentimes and repeats words but that was merely an annoyance and a drain on my concentration and attention span but not the cause of my difficulties, which are probably due to my stupidity and lack of aptitude for mathematics. I took Advanced Maths and Applied Maths at A level in 1958 and failed them both.
Date published: 2011-03-26
Rated 3 out of 5 by from Much is left desired The course is a very high-level overview of two concepts of calculus. Professor is stumbling and mumbling through the course. I am surprised TTC could not find anyone better to talk about calculus.
Date published: 2011-03-24
Rated 1 out of 5 by from poor editing I was distracted by the poor editing of the course,to the point of giving up. I felt as if I was in a classroom , watching all the little errors and hesitations. I read many reviews stating how well this course was, and perhaps if I had already taken calculus courses before, I may have felt the same way. I found myself replaying the first eight lessons trying to understand, however his lecturing missteps kept jarring me to distraction. May I suggest watching a lecture by a pro such as Brian Tracy for the editing of a series such as this, because I am reluctant to spend this much money for quality such as this.
Date published: 2011-02-14
Rated 4 out of 5 by from This is a "theory" course This course is NOT a nuts & bolts class in calculus. Frankly, I enjoyed it much more after I taught myself calculus out of several workbooks from Amazon. Still, I adore Prof. Starbird & find him hilarious to watch. He DOES get one to think about the Big Picture of what is going on when working out a calculus problem. His examples are good and he keeps you interested. Now that I think of it, I should watch these lectures yet again. And he really is funny:. 'Remember the derivative? We studied it back in Lecture 6 & you all understood it & you loved it..Well, now we're going to look at the ANTI-derivative.' I just love this man.
Date published: 2010-11-11
Rated 5 out of 5 by from Don't expect to be a mathematician after this I tooks calculus many years ago. So I decided to buy this video courses for fun. After going to the video, I find it to be very informative and enjoyable. The professor have a likeable demeanor. I would recommend this for anyone who want to have an idea of what calculus is. However, don't expect to be a mathematician after the video lectures. I remember that the actual mechanics of calculus was very difficult. I had to used everything that I learned from algebra, geometry, trigonometry and other maths, that I don't even remember what it was called, to arrived at the equation for you to apply the derivative or integration. It was very difficult and you had to spend hours to come up with the equation just to apply the derivative or integration. Thus the actual mechanics was very tedious. The mathematical equations that is used on this video are very simple. I guess they are trying to teach the non-mathematically incline people about the concept of Calculus. In fact the concept of calculus is very simple. Two words can sum it up: Derivative & Integration. But the mathematic behind it is what hard. If you apply calculus to a problem that is mathematically simple, then calculus is simple. And that is exactly what this video lecture use to portray calculus. But real life problems are mathematically complicated thus the calculus related to that problem is very complicated. So what I am trying to say is that enjopy this video but don't expect to be a mathematician after watching the video. It is like watching a video on playing golf & it rules and expect to be Tiger Woods.
Date published: 2010-10-10
Rated 5 out of 5 by from Excellent course to learn calculus with! I like to write evaluations that I feel will be useful in helping the reader determine whether a course is for them or not. If you are not the mathematically inclined type, please read the whole evaluation. Mathematics was my strong point in high school with grades of 90+, and I was 17 when I started University. I am not telling you this to tell you how smart I was, but let me continue the story. I was able to get the right answers, but I didn’t really “get” it. As long as I was given a formula I was able to solve the various maximum, minimum, derivative or integration questions; but in hindsight I really did not understand what the formulae were telling me nor did I appreciate how much that understanding would have helped me. When I got to University I found myself lost in the mathematical lexicon and started failing miserably. Oh how mathematicians can take simple concepts and make them so complicated with their terminology. Soon I was neither understanding the math or even interested in learning more. I decided to quit university until I found out what did interest me. Truly, if I had Professor Starbird as an instructor for the mathematics courses in high school and university, my life would have turned out very differently. He would have had a profound effect on my life. It has been 30 years since I last looked at calculus. I never did go back to university. Professor Starbird’s “Change and Motion: Calculus Made Clear” was very brain friendly, with repeated listening that is. Either I got smarter or Professor Starbird was the catalyst that forged understanding in my brain cells. I am certain of the later, and doubtful of the former! There were a number of lectures that I watched 2-3 times before it sunk in, and I will give professor Starbird full credit for the fact that the material did sink in. I am not sure if it is fair for me to lend my opinion on whether this course is for non-mathematicians because I am comfortable with mathematics. My opinion though would be that this is certainly a course to take. You need to be patient with yourself. Repeat each lecture as often as you need to until you get it, and you don’t need to get 100% of it either before proceeding, just get 80%. I agree that this course makes calculus accessible to all and that the beauty of calculus was hidden from me in school. You can be assured that there is no complicated vocabulary or mathematical notation (except for one frame out of hundreds) but that is not to say the professor does not use mathematical notation. You have to. The professor starts with a common sense analysis of motion using a car driving down the road and goes from there to explain deep concepts of calculus without the traditional technical background that clouded the insights and significance of the subject when it was first taught to me. The two main concepts of calculus arise naturally and their relationship does become clear. I thoroughly enjoyed the interjection of historical events throughout the lectures that humanized the evolution of calculus. His everyday examples of things that change over time give calculus the practical meaning that my brain craves. I finally had an understanding of its inner workings. The geometry link with calculus gave me a lot of eureka moments. The 2 dimensional and 3 dimensional objects used in the explanations very much appealed to my visual learning side, and like the saying goes, a picture is indeed worth a thousand words. I am amazed at how simple the process of derivation is, or integration and the fact that those simple processes – mathematically created formulas that define real world motion – actually work! Such a direct relationship between mathematics and the physical world amazes me. Professor Starbird made what I failed to be taught in high school, learnable. I found myself pressing the pause button so as to give me time to review screens/frames of calculations so that I could be sure I understood it. Pencil and paper came in handy as well. I didn’t mind if I didn’t understand everything in a lecture on the first viewing. That is a fact of life and learning -- that we don’t always get it the first time. I had to be patient with my learning abilities, not with Dr. Starbird’s teaching abilities. Usually by the 3rd review of the material with numerous pauses, I got it. I found his demeanour enjoyable; I appreciate the variety of teaching styles that I have seen in all the TTC courses I have taken. How boring it would be if everyone taught exactly the same way. I look forward to watching my next Starbird course!
Date published: 2010-06-30
Rated 1 out of 5 by from Not Engaging My daughter and I began watching this DVD and after the second lecture decided we could no longer get through this series of lectures. Michael Starbird's presentation is not fluent and his stumbling is a distraction. We have watched his DVD on probability and feel the same way. I would not buy another DVD with him as a lecturer.
Date published: 2010-06-08
Rated 5 out of 5 by from A fine treatment of Newton and Leibniz Why is that car speeding down the road? To help Professor Michael Starbird explain calculus, of course! He uses this practical example, and others such as a buzzing mosquito and the predator-prey balance between spotted owls and wood rats, to make his points clear. His purpose: to tell us that the “Derivative” shows how fast things are changing and that the “Integral” is a dynamic way of combining parts to get something whole. Even a math neophyte like myself clearly understood these concepts. Professor Starbird peppers his lectures with historical anecdotes and mercifully uses complex algebra sparingly, instead focusing on clear logically worded explanations. The DVD format, showing Professor Starbird in a simulated classroom was necessary, although the brick wall outside the classroom window hinted at claustrophobia. Animations were easy to follow but the course outline was sometimes too concise and ambiguous. Oftentimes, the transcript was needed to figure out what the professor had exactly said. This course is recommended to anyone with an interest in calculus, as long as they can remember high school algebra..
Date published: 2010-06-04
Rated 5 out of 5 by from Excellent introduction As a mechanical engineering student at UT back in the 90's, I took calculus and struggled with it. I learned it well enough but never fully grasped it. After watching this course I felt I had a much better grasp of not just the how but the why, and what it all meant. I thoroughly enjoyed the presentation by this professor. Calculus is a hard subject but Dr. Starbird's exposition on the subject makes it clear and attainable by the rest of us mere non-mathemetician mortals.
Date published: 2010-03-16
Rated 5 out of 5 by from Exceptional Visual Presentation of Calculus I thoroughly enjoyed this course and would recommend it to anyone curious to know the reasoning behind the algebraic processes learned in a traditional calculus course. The lecture on Mamikon and visual calculus was of particular interest to me. I would say that the middle lectures (volume and integrals) were the strongest part of the course. If there is one thing I can fault this course on, I would agree with a reviewer on this site who said that the last few lectures focused more on applications of calculus rather than the mathematics behind it. Still, the early and middle lectures more than make up for it in terms of density of ideas, good visual aids, and well timed examples to illustrate the concepts taught. I will probably try out some other courses taught by Professor Starbird.
Date published: 2010-01-26
Rated 3 out of 5 by from good material hobbled by poor presentation The content of the course is, as a vehicle for visualizing the power of calculus, well constructed. Unfortunately Prof. Starbird crashes the vehicle on the way to the classroom. Especially in an area such as math, the learning process flows when the the professor's timing and presentation gives the student small nooks of time to integrate (sorry for the pun) the material . This professor stutters, repeatedly repeats phrases prior to establishing their context (did I mention repeatedly?), loses his train of thought, and, most damaging, mis-states himself and uses those little nooks of time to correct his thoughts. The students are robbed of the time during the lecture where they would cement their comprehension of the presentation. It is only the value of the content, the way Prof. Starbird tries to connect the concepts of calculus to workaday physics, that kept me from hanging up on this series. I agree with the previous reviewer that a level II calculus course could appeal to your customers. If TTC produces that course, I would suggest re-shooting this course with a different professor, whomsoever you would choose to do the level II. Out of about 40 courses viewed so far, the two I've seen with this professor were the only two that have left me with the feeling that TTC could have done better.
Date published: 2010-01-03
Rated 5 out of 5 by from Superb Topic, Superb Presentation When I was in college more than two decades ago, I took three semesters of calculus and a semester of differential equations. I learned the material well enough and enjoyed doing so, but I unfortunately haven’t really used calculus much since then. I decided it was time for a refresher, and thought I’d start with this TTC course, though I didn’t really expect much, since I anticipated that this course would be really watered down. To my great surprise and delight, I found this course to be superb. Michael Starbird covers nearly all of the fundamental ideas of calculus, he provides good examples, his graphics are excellent, and he brings in an appropriate amount of historical context. More generally, he succeeds in showing why the development of calculus represents a huge intellectual accomplishment for humankind and an incredibly powerful tool for modeling applications. His delivery could perhaps be a bit smoother sometimes, but I like his humility and his sense of humor, and I think he explains things quite clearly almost all of the time, so I think he’s a very effective lecturer. It’s quite evident that Starbird has put a great deal of thought and care into developing this course. The only real way I can think of to improve this course is to add another 12+ lectures to allow more in-depth coverage of the more advanced topics which are currently just touched on in the last third of the course (calculus of variations, Stokes’ theorem, Green’s theorem, Gauss’ theorem, etc.). A dream-come-true would be for TTC to develop a “Part 2” for this course which focuses on these advanced topics, along with a separate course on differential equations. Meanwhile, I highly recommend this course to anyone interested in learning the key concepts of calculus for the first time, or wishing to review these concepts. The only people who wouldn’t benefit from this course are those who don’t like math (but then why are you reading this review?) and people who already have an advanced knowledge of calculus. Bravo and thank you to Michael Starbird and TTC for this superb course!
Date published: 2009-09-04
Rated 5 out of 5 by from Great Intro to Calculus I took calculus a long time ago, and wanted to refresh my knowledge. This course was perfect for that. The presentation was clear, and it helped me understand why calculus was so important that it had to be invented twice. If you are looking to improve your calculating skills, this course is not for you, but if you are looking for a clear and concise overview, look no further.
Date published: 2009-08-28
Rated 5 out of 5 by from A Plus I have purchased about 15 Teaching Company courses and have experienced many excellent instructors, but I believe Professor Starbird has to be the most outstanding teacher I have ever had including elementary school through college. I studied Calculus as an engineering student over 50 years ago and although I used it as a tool to solve a few specific problems I never had as clear an understanding as is delivered by Professor Starbird. He presents the subject in extremely clear and simple terms with a very pleasant and unassuming and sometimes amusing manner. It is truly a joy to grasp what to most is such a forbidding and fearful subject.
Date published: 2009-06-12
Rated 4 out of 5 by from My daughter loved it My daughter claims this course augmented her high school math studies and made a significant difference in her grades. She is now at a top-tier university and looks back fondly on this course.
Date published: 2009-06-07
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