Change and Motion: Calculus Made Clear, 2nd Edition

Rated 5 out of 5 by from Really good way to review calculus I took calculus a long time ago at a far away university. I can remember how to calculate derivatives and integrals but I can't remember ever visualizing the concepts. Professor Starbird is excellent at teaching how to visualize calculus.
Date published: 2021-04-20
Rated 3 out of 5 by from overly verbose and unclear 9 minutes into this video, i have learned that the name of the driver of the professors imaginary car is xenos. In those 9 minutes i should have learned that Calculus is is used to calculate math over time, what the components used are, and how they are used. i would have been fine discovering a bit more about how newton invented calculus to calculate the movement of heavenly bodies, and how he used it to do this. instead it's xenos in his car. it doesn't help that the professor keeps stuttering, and changing up what he's saying. this makes the course seem unprofessional. now why would spend 2 hours on this course, when a 10 minute youtube video contains just as much useful information?
Date published: 2020-10-19
Rated 5 out of 5 by from A Survey, Not an Introduction I took this course to reacquaint myself with calculus which I studied many long years ago, but never used in my professional life. Plus this is an effort to work my way through TTC’s mathematics courses. And I have to say that I think Professor Starbird does an outstanding job of presenting his subject. He begins before the beginning, going all the way back to the 5th century BCE and Zeno to introduce some of the ideas of calculus and to help us realize that the “invention” of calculus by Newton and Liebniz was based on thoughts and ideas that had been around and being developed for a long time. The course shines in giving us the background and development of calculus both before and after Newton and Liebniz. But more importantly, it probably would help almost anyone with modest mathematical background understand the basic concepts of calculus. It would not help anyone I think actually solve problems or to be able to even set up problems, perhaps excepting the most basic. And herein lies the one problem I see in this course. Many times the demonstrations of problems involves passing by the fairly simple algebraic manipulation of equations, meaning that anyone who is not able to make the connections from one place to another may become a bit puzzled at best. That is, the course does not put heavy emphasis on actually using math, but often assumes a knowledge that is higher than what I think the target audience is expected to possess. To be fair, the real target audience may well be people like myself with a solid background that has atrophied (and many of the reviews indicate that this may well be the case). Some reviews have not liked Dr. Starbird’s presentation skills. It is true that he often stutters or stammers a bit as he is transitioning from one topic to another or when he is bending down to begin using his computer to set up a demonstration, but I find it much more realistic that reading from a teleprompter and not at all disconcerting. And he does have a quiet, gentle sense of humor. How can one not like his stuffed owl and passel of woodmice as he demonstrates the use of calculus in population change? And my favorite, his commentary and analysis of why calculus is better than sliced bread made me chuckle internally, even if not rolling on the floor laughing. Get this course if you are interested in the whys and wherefores of calculus, but not if your objective is to actually learn the subject. Most highly recommend if you fall into the first category and many who are in the second and wish to prepare for a rigorous course.
Date published: 2020-09-12
Rated 5 out of 5 by from An Interesting Refresher Course I bought this course last week. It has fulfilled ally expectations. I wanted to refresh my memory of Calculus, which I studied at University some 60years ago, and which I had not used for the last 50 years!
Date published: 2020-09-04
Rated 1 out of 5 by from Not a good review I took Calculus over 50 years ago, so I was hoping for a refresher course. This was not it. Lots of repetitive examples barely touching the real math. The content of this entire course should have been covered in 5 lectures, and it wouldn't have been nearly as boring.
Date published: 2020-07-06
Rated 4 out of 5 by from For the Non-mathematician If you are a student and plan to study calculus, this course is not for you. Rather, Professor Bruce Edwards’s—the professor pictured in the catalogue—many courses on calculus and precalculus will brace you for staying up all night and studying for a test and memorizing proofs. (Professor Edwards’s pre-calculus course may have gotten lesser reviews because the subject matter is so difficult to teach and learn.) Professor Starbird offers a calculus survey for people intrigued by the noun, which is used widely as a power synonym for measurement. At the end of Professor Starbird’s 24 lectures, even if you are like many who don’t get algebra or poetry, you will understand the beauty, elegance, and power of calculus. Professor Starbird is a little nuts, with so much activity going on in that extraordinary mind; but he tries harder than anybody, putting his full heart into what he does, and he is one truly fantastic teacher. Even if you don’t want to learn about calculus, you can buy this course to sharpen your teaching skills. He appears to use his children’s or grandchildren’s toys as props. (When trying to make sense of Professor Kung’s course on music and math, differential equations popped up, and though I taught the subject in my youth, I was fortunate to have Professor Starbird’s million-word illustrations by using toy animals.) His teaching ploy of trying to recreate calculus tangibly in the real world is his strength. After blowing up my mind on this subject 37 years ago, it still amazes me how far one can apply calculus. The four stars I award the course factors in some distractions, and the warning that the real calculus course is found under Bruce Edwards. But if you are able to realize the essence of calculus without going crazy, this would be a five-star course for you. You will no longer misuse the term calculus. (Another point of view: on a Miami bus bench where are you can find the most fascinating conversation, in front of the thrift store I had just bought a math textbook, a man told me he had bought Professor Starbird’s course on calculus from TTC and that he really enjoyed it, finally grasping all that that gigantic noun signifies, dissolves, and transmutes.) Calculus is one really cool set of only two tools; and if math is not your thing, and there are many extraordinarily talented people who cannot make heads or tails of mathematics, after this fine course you will understand the power of calculus.
Date published: 2020-06-28
Rated 3 out of 5 by from Confused I viewed the first two lectures and I have to review the second lecture again because i really didn't understand it.
Date published: 2020-05-16
Rated 4 out of 5 by from Great for basic understanding of Calculus I read many of the reviews> I agree w/ almost all of the good ones and bad ones. The overview he presents would be a great help before taking a Cal class. I had to go back over the material numerous times to understand it 100%. His latter lectures were breezed through quickly w/out adequate detail to get to 100%. So I agree he could have developed some of the basics/formulas a little better at times. Overall. It was worth my time and I will now start over to see how well it all fits together.
Date published: 2020-05-16
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Change and Motion: Calculus Made Clear, 2nd Edition
Course Trailer
Two Ideas, Vast Implications
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.

33 min
Stop Sign Crime-The First Idea of Calculus-The Derivative
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.

31 min
Another Car, Another Crime-The Second Idea of Calculus-The Integral
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.

31 min
The Fundamental Theorem of Calculus
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.

31 min
Visualizing the Derivative-Slopes
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.

31 min
Derivatives the Easy Way-Symbol Pushing
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.

31 min
Abstracting the Derivative-Circles and Belts
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.

32 min
Circles, Pyramids, Cones, and Spheres
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.

31 min
Archimedes and the Tractrix
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.

31 min
The Integral and the Fundamental Theorem
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.

29 min
Abstracting the Integral-Pyramids and Dams
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.

30 min
Buffon's Needle or ? from Breadsticks
12: Buffon's Needle or ? 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....

32 min
Achilles, Tortoises, Limits, and Continuity
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.

31 min
Calculators and Approximations
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.

32 min
The Best of All Possible Worlds-Optimization
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.

31 min
Economics and Architecture
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.

30 min
Galileo, Newton, and Baseball
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....

31 min
Getting off the Line-Motion in Space
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 ? 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.

30 min
Mountain Slopes and Tangent Planes
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.

31 min
Several Variables-Volumes Galore
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.

31 min
The Fundamental Theorem Extended
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.

31 min
Fields of Arrows-Differential Equations
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.

32 min
Owls, Rats, Waves, and Guitars
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.

32 min
Calculus Everywhere
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.

32 min
Michael Starbird

The geometrical insights that I most like are those where different ideas come together unexpectedly to reveal some sort of a relationship that was not obvious at first


University of Wisconsin, Madison


The University of Texas at Austin

About Michael Starbird

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, won a 2001 Robert W. Hamilton Book Award. Professors Starbird and Burger also collaborated on Coincidences, Chaos, and All That Math Jazz: Making Light of Weighty Ideas, published in 2005. Professor Starbird has won many teaching awards, including the Mathematical Association of America's 2007 Deborah and Franklin Tepper Haimo National Award for Distinguished College or University Teaching of Mathematics, which is the association's most prestigious teaching award. It is awarded nationally to 3 people from its membership of 27,000. Professor Starbird is interested in bringing authentic understanding of significant ideas in mathematics to people who are not necessarily mathematically oriented. He has developed and taught an acclaimed class that presents higher-level mathematics to liberal arts students.

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