Change and Motion: Calculus Made Clear, 2nd Edition

Rated 2 out of 5 by from I wouldn't advise it I was not too impressed with this. Starbird gets hyper-repetetive on many simple concepts to the point of frustration and then he glosses over more complicated conclusions that he presents, which further obfuscates the watcher. I even counted and average of 5 verbal stutters from him before most ahh, umm, ahh ummm uhhh transitions. But he definitely cherishes his lame jokes, and so he seems to feel, should you. Ugggh, no thanks.
Date published: 2019-11-12
Rated 3 out of 5 by from Adequate. Clear explanations and examples but not inspiring.
Date published: 2019-11-06
Rated 1 out of 5 by from Worst Course Ever!! I'm just sorry I purchased courses ahead of time so it probably can't be returned. This course does NOTHING to base the results of applying Calculus to a core of practiced skills which must be mastered. The Professor talks about the grandeur of what is accomplished with Calculus, but doesn't provide basic applications which if made crystal clear bring the student along for the ride. If you want to get a person curious and started in meaningful mastery of Calculus, this is just not the way to get there.
Date published: 2019-01-02
Rated 5 out of 5 by from Great Introduction to Calculus This course is a great introduction to calculus. Good preparation for the more Dvanced calculus courses offered by The Great Courses.
Date published: 2018-11-24
Rated 3 out of 5 by from Change and Motion: Calculus Made Clear, 2nd Editio I like Dr. Starbird's teaching. This program is a bit too complicated trying to get the Calculus to the point. I give the course 3/5 stars...
Date published: 2018-08-21
Rated 2 out of 5 by from The speaker is undoubtedly knowledgeable but his halting presentation style makes viewing a painful experience.
Date published: 2018-07-26
Rated 4 out of 5 by from Easy to understand The course just arrived last week and I'm only up to lesson #8, however, Professor Starbird has done a very good job of giving you the most rudimentary understanding of what calculus is trying to accomplish. It's been 40 years since I took a calculus course but I can sense rejuvenated brain cells springing to life. My only minor criticism would be the professor is sometimes not very smooth in presenting the material.
Date published: 2018-02-23
Rated 5 out of 5 by from Now I understand! When I studied pre-calculus in high school, I never understood the basic concepts. Now, after 50 years (I am 67 years old) I finally understand! Thank you, Professor Starbird. Great job!
Date published: 2018-02-16
Rated 2 out of 5 by from Sooooo Chatty It may turn out to be great, but I have not made it through the second lecture. There is a limit to how much I need to hear about the course; what I NEED is to get to the actual material.
Date published: 2017-12-09
Rated 5 out of 5 by from Clear is the key word If you are expecting number kruching you'll be disappointed. But if you want to know the why and how excellent course. Wish I had had it in college
Date published: 2017-05-02
Rated 5 out of 5 by from Conceptual Overview of Calculus Professor Starbird has a passion for math and his aim is to provide an overview of calculus concepts to non-mathematicians. The first half of the course provides an overview of the two fundamental concepts of calculus, i.e., the derivative and the integral, and how they are related via the Fundamental Theorem of Calculus. The second half of the course shows some of the applications of these concepts, e.g., optimization, economics, calculating volumes, etc. In my experience, if you’ve taken a calculus course, then this course will add some conceptual understanding to the formula-based instruction you likely received. However, if you haven’t taken a calculus course, you will gain a conceptual understanding that is foundational to this subject, but you will not be able to apply these methods without further study. If you desire to learn the mechanics of calculating a derivative or integral, definitely check out Professor Bruce Edwards' course, "Understanding Calculus." I do think these courses complement each other very nicely.
Date published: 2017-03-31
Rated 5 out of 5 by from Clear explanation of topic My college calculus course was a disappointment. When I had a question I was shut down with "it's intuitively obvious!" Dr. Starbird is a wonderful teacher with a firm grasp of the subject matter and a clear delivery. His kindness and concern for the student's struggles is refreshing.
Date published: 2017-02-11
Rated 4 out of 5 by from Excellent Overview I earned a Masters degree in math many years ago. So my motivation for purchasing this course was to refresh my memory about a subject (calculus) that I was already familiar with. The videos not only refreshed my memory on the basic concepts, but also provided many new insights. I especially liked the historical references in the course.
Date published: 2017-01-06
Rated 5 out of 5 by from Finally! Calculus made understandable! Years and years of math course and I learned nothing. Professor Starbird FINALLY made calculus intelligible. Thank you! And as a bonus, this got me excited about looking at other Great Courses. I've been hooked ever since.
Date published: 2016-10-10
Rated 5 out of 5 by from A Great Course The lecture series definitely clarify Calculus and its applications.
Date published: 2016-10-08
Rated 5 out of 5 by from A Great Introduction to the Concepts of Calculus Why would a retiree like me, who's never used calculus in his life (but studied a bit of it in graduate business school), take a course like this? Well, I had two reasons: (1) I had previously taken Professor Starbird's Probability and Statistics courses and had enjoyed his clear teaching style and wonderful examples in those courses very much, and (2) my interest in science has shown me that many scientists and philosophers have found it remarkable that the natural world is so amenable to the tools of calculus. So, with virtually no background in the subject, I trusted that the professor could give me a clear understanding of the concepts of calculus, and he delivered. It was a very stimulating course, and you don't have to be a mathematician or engineer (I'm not) to get a lot of benefit from this course, but simply must possess an inquiring mind. Among the highlights of the course, at least for me, were: (1) the clear explanations of the derivative and the integral and concrete examples supporting both "sides" of calculus, (2) Archimedes ingeniously using a kind of pre-calculus to calculate the volume of a sphere, (3) optimizing in economics by finding the derivative where it's zero to locate maxima and minima for profits, costs, etc., and (4) the marvelous calculus that outfielders intuitively perform when they judge the velocity, height, and arc of a fly ball and run right to the spot where the ball comes down. Professor Starbird's verbal comments are also very insightful. He says the integral represents "the accumulation of change to a net effect" (Lecture 21), and in his final lecture he says: "that the story of calculus is the story of the intellectual conquest of infinity." I liked that.
Date published: 2016-09-01
Rated 5 out of 5 by from Surprisingly engaging I thought sure this was going to be difficult to understand, but it was wonderful. I loved the instructor's wry humor and he does every thing he can to make this topic interesting. I've not completed the course yet, but I look forward to doing so.
Date published: 2016-08-03
Rated 5 out of 5 by from Calculus I have a BS in Math and never heard calculus explained so well. The professor makes calculus not only understandable, but shows how it effects our everyday lives. We may not use calculus to solve problems every day, but we use the tools and ideas of calculus in making many decisions every day, Anyone, whether student or curious individual, can benefit greatly from this course.
Date published: 2016-08-01
Rated 5 out of 5 by from Math Is Fun I've loved math all my 74 years. Starbird presents math in a way that is understandable, and fun, to persons of all levels of math knowledge and intuition. The owls eating the wood rats is hilarious. ... Thanks Michael, Al
Date published: 2016-06-09
Rated 4 out of 5 by from "Great Courses" is a "great find" for me! This course is an excellent value. The instructor is engaging and presents material in a very simple and straight forward way. My only complaint is that I could not download the course using my windows 10 system. Streaming is working fine but I would like to be able to use the course when I am in an area where streaming is not available.
Date published: 2016-02-01
Rated 4 out of 5 by from Calculus Made Clear, 2nd Edition I purchased this for my new bride. We are both abt 70, and she is a retired high school mathematics teacher. She is once again tutoring students (loves to do that!) and wanted a refresher on Calc. She is thrilled by the explainations offered by the Prof. I am a retired engineering manager, and during our courtship would exchange off-color text messages written in code, based on Calc. When a good thing in her life was getting even better, she would relay that as the 2nd derivative of ABCD was positive. How nerdy is that?!! Her children and students could not understand them when she left her phone on a table; thus a big success for us. Now, after getting halfway through this course she is speaking to me in calc codes. Doesn't get much funnier than that; or more weird. We are expecting to hear or see that soon on The Big Bang. Your course deserves 6 stars out of 5.
Date published: 2016-01-31
Rated 5 out of 5 by from Very enjoyable and entertaining too. Prof. Starbird was entertaining as he presented the lectures via streaming download; the disks and other material arrived shortly after I completed the course online. He was correct, in that, previous high school and college calculus courses only taught the mechanics of using derivatives and the integral functions, and I never had any problems doing so, but I had a serious concern that I may have missed something along the way in my career that could help me to understand why I did these thing. Prof. Starbird filled in some blanks that I had.
Date published: 2016-01-28
Rated 4 out of 5 by from A GOOD PLACE TO CATCH UP I think this is a very good course. I think it will present all the required information to prepare the student for the required expectations. However I think I should have asked for some local advise from someone who knows my background in math. It seems like I should have started with a course a little more primary. This course seems like a rather mid subject course. I intend to continue with this course and then explore what other courses are available in Calculus. This is a subject that I have wanted ever since I wasn't able to acquire it in 1955 at U of I. Clifford (Gene) Dawdy
Date published: 2016-01-22
Rated 4 out of 5 by from My review of "Change and Motion: Calculus Made Clear" by Michael P. Starbird: Professor Starbird does a good job of connecting calculus to real-world applications. He is very knowledgeable and knows how the subject is used in areas such as physics, economics, business, biology, and so on. This makes the course meaningful and enjoyable.
Date published: 2015-05-23
Rated 5 out of 5 by from Great Course, Well Presented As one of those people who faked my way through calculus by learning enough of the mechanics to get good grades, I really appreciated the way this course was presented. The focus on understanding the underlying concepts in the math did slow the pace a bit, but just enough to give you a chance to internalize the ideas. This course could work equally well as a review, or as an intro. I think this series of lectures is also a great way to gain an understanding of calculus even if you might need to brush up on your algebra, geometry, and trigonometry.
Date published: 2015-05-20
Rated 5 out of 5 by from Change and Motion: Calculus Made Clear 1st edition I purchased the course several years ago and--without having previously studied calculus--watched it two or three times without getting much out of it. According to Starbird, the presenter, it was a "conceptual approach", which is exactly what thought I wanted. I am a mathematical layman and not interested in the practical applications of calculus, but I merely wanted to know more about the subject in general. The video didn't help much. Then I took two courses in calculus. The courses emphasized techniques and algorithms, and skimmed over the concepts. A few years later when I returned to the Starbird videos, having had that good dose of calc vocabulary and technique, the whole thing made sense. I highly recommend the video series as long as the viewer does some pencil and paper calculus as well.
Date published: 2015-03-29
Rated 4 out of 5 by from Nice review of my calculus from many years ago in college.
Date published: 2015-03-16
Rated 5 out of 5 by from Great teacher I took this course because I hated calculus in college. I really needed to see if I could finally understand it and be able to utilize it. I am only part way through the course but I understand everything so far. That is a credit to our very qualified instructor. His lectures are very well presented in a way that is interesting, relevant and easy to understand.
Date published: 2015-03-14
Rated 5 out of 5 by from Change and Motion: Calculus Made Clear, 2nd Editio Wish it was this understandable when I took it in College. Professor does a great job making it easy to understand and retain....
Date published: 2015-02-26
Rated 5 out of 5 by from Finally, a course that makes sense of Calculus! I've been trying to make sense of calculus text books, and have watched other calculus courses. But I still didn't understand why you'd want to take a limit, what the derivative was, or how integral calculus differed. This course is just what I needed! This course provides an overview and higher level explanations that helped me understand why calculus is used, what kinds of problems it solves, exactly why taking the limit is important, and why you'd use integral calculus. You won't be able to solve calculus problems after this course, but you will understand the high level view. Now, I can turn back to the textbooks and make sense of those problems and how to work them. I wish I had taken this course before trying to make sense of working problems, but I'm glad I did get a chance to watch all of these lectures. This is a great course for people who need the conceptual understanding first, and then can later get down to the nitty-gritty of problem-solving. I have the other calculus course on problem solving through great courses, so now I'm going back to that one as I'm confident I'll be able to make sense of it now. I found this course enjoyable as well as informative. Hard to believe I used to hate math so much. My love of science has brought on the desire to learn math now in my 50's, whereas when I was younger I really detested it. Math is fascinating and I'm grateful for these courses!
Date published: 2014-11-30
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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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