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Change and Motion: Calculus Made Clear, 2nd Edition

Conquer calculus-one of the most powerful and useful of all mathematical skills-with this simple and brilliant guide taught by an award-winning mathematician.
Change and Motion: Calculus Made Clear, 2nd Edition is rated 4.2 out of 5 by 121.
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Rated 5 out of 5 by from Excellent Introduction to Calc! I really enjoyed this course. Starbird is a fun guy and his excitement for math is contageous. This is great for those who just need to refresh their calc memory as well those who are just getting into calc and want a good overview of the subject. Really great lecture series! Thanks!
Date published: 2024-04-09
Rated 5 out of 5 by from Excellent Professor Starbird; This is a short story, and a commendation, I am now 83, in 1960 I went to a private college for electronics, and found that algebra and Trigonometry really had uses, and loved it. When they gave a course in calculus, it was a brick wall for me, I dropped out of college (not because of Calculus), later I became a flight instructor, and taught students how to figure average speed (ground speed). About the time I retired calculus came to mind. There was a book in cartoon form that promised to teach calculus in an easy way; no dice, it still wouldn't come. This year your course came to me, and Voila' the idea of calculus became clear after only two lectures, Derivative and Integral. If text books spent more time on the very basics, like you present them, we might have many more brilliant mathematicians. Thank you so much, Griffin McCullar
Date published: 2023-05-22
Rated 1 out of 5 by from Extremely Disappointing. Why is this course called Calculus Made Clear? It is not made clear at all. The professor uses terminology without introducing those concepts and what they mean e.g. In Lecture 2, he begins using the terms Average Velocity and Instantaneous Velocity without ever explaining what that means nor why he is talking about it and proceeds to use those concepts in calculations as if I am suppose to know what is going on. He uses the term Position Function without ever explaining what that means, what is a function anyway? He immediately assembles data into value charts and then says as Delta T gets smaller... Why are we assembling data into a chart, what do those values mean, what exactly is Delta and how can it be a value if it is getting smaller and smaller? What does that even mean? He presents equations where p(t)-Δt plus p(t)-Δt-1 etc. etc. as if I'm supposed to know what that all means. I suppose he's saying that if we measure where the car is at different points in time from an origin point that tells us how fast it's going and if we further measure how fast it's going at different points we can calculate the car's position and velocity in general and at points as of yet undetermined (I guess?) In Lecture 3 he uses graphs with "Step" type representations without any explanation of what it is nor why we are using it and just breezes on through as though I'm suppose to know what's going on. In Lecture 4 he introduces curves on a graph as a visual representation of where the car is and how fast it is moving between any point (I think) and then applies to the graph a Tangent Line without telling me what that is and why we are using it. I understand that there is a proportional relationship between the result of one calculation and another so that the value of one can be obtained by referencing its opposite but I don't understand what's going on and why we're doing it. He extends the lines drawn into a parabola and says "and if we plot this point on the tangent line that gives us the Derivative Curve" or some such without explain what he is doing and WHY he is doing it: it's all just supposed to make sense I guess... He use yet more messy equations with t in parenthesis and Δ this and Δ that and if the Derivative is t² then the Integral will be 2t(p) or something without explaining what it means and why I am learning it. All the 5-Star reviews I have read describe this course as a great "refresher" for those who took Calculus 50 years ago etc. Perhaps it should be marketed as such
Date published: 2023-05-06
Rated 5 out of 5 by from Enjoyed a smooth ride on the calculus highway Liked the punt at the end of chapter 20. With a loaf of sliced bread in a tray, Professor Starbird fittingly stated: Calculus is the best thing since sliced bread.
Date published: 2023-04-05
Rated 5 out of 5 by from A winner Engaging lecturer, clear, and nails the subject. A+.
Date published: 2022-10-03
Rated 4 out of 5 by from Good course I bought this course as an adjunct to Bruce Edwards calculus productions. While Prof. Starbird lacks Prof. Edwards smoothness of presentation and absolute competence, he did teach me some things that were lacking in my understanding of calculus, and I enjoyed his demonstrations. I would recommend this course for the absolute beginner in calculus and Bruce Edwards for the more experienced.
Date published: 2022-10-01
Rated 5 out of 5 by from Very fine course!! I've studied some calculus on my own, but this video course really clears up the whole subject--I watch some lessons two or three times and get more out of each viewing--the instructor is outstanding!!
Date published: 2022-05-21
Rated 5 out of 5 by from Very well explained! I am an old retired nephrologist, but was a physics major as an undergraduate. It was fun to go through the basic concepts of calculus, and remember why calculus is so important. Doctor Starbird did an excellent job of walking through the maze of calculus without getting lost.
Date published: 2021-10-12
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Calculus has had a notorious reputation for being difficult to understand, but the 24 lectures of Change and Motion: Calculus Made Clear are crafted to make the key concepts and triumphs of this field accessible to non-mathematicians. This course teaches you how to grasp the power and beauty of calculus without the technical background traditionally required in calculus courses. Follow award-winning Professor Michael Starbird as he takes you through derivatives and integrals-the two concepts that serve as the foundation for all of calculus. As you investigate the field's intellectual development, your appreciation of its inner workings and your skill in seeing how it can solve a variety of problems will deepen.


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


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, 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.

By This Professor

Change and Motion: Calculus Made Clear, 2nd Edition
Meaning from Data: Statistics Made Clear
What Are the Chances? Probability Made Clear
Change and Motion: Calculus Made Clear, 2nd Edition


Two Ideas, Vast Implications

01: 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

02: 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

03: 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

04: 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

05: 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

06: 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

07: 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

08: 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

09: 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