Understanding Multivariable Calculus: Problems, Solutions, and Tips

Course No. 1023
Professor Bruce H. Edwards, Ph.D.
University of Florida
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Course No. 1023
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Course Overview

Calculus offers some of the most astounding advances in all of mathematics—reaching far beyond the two-dimensional applications learned in first-year calculus. We do not live on a sheet of paper, and in order to understand and solve rich, real-world problems of more than one variable, we need multivariable calculus, where the full depth and power of calculus is revealed.

Whether calculating the volume of odd-shaped objects, predicting the outcome of a large number of trials in statistics, or even predicting the weather, we depend in myriad ways on calculus in three dimensions. Once we grasp the fundamentals of multivariable calculus, we see how these concepts unfold into new laws, entire new fields of physics, and new ways of approaching once-impossible problems.

With multivariable calculus, we get

  • new tools for optimization, taking into account as many variables as needed;
  • vector fields that give us a peek into the workings of fluids, from hydraulic pistons to ocean currents and the weather;
  • new coordinate systems that enable us to solve integrals whose solutions in Cartesian coordinates may be difficult to work with; and
  • mathematical definitions of planes and surfaces in space, from which entire fields of mathematics such as topology and differential geometry arise.

Understanding Multivariable Calculus: Problems, Solutions, and Tips, taught by award-winning Professor Bruce H. Edwards of the University of Florida, brings the basic concepts of calculus together in a much deeper and more powerful way. This course is the next step for students and professionals to expand their knowledge for work or study in many quantitative fields, as well as an eye-opening intellectual exercise for teachers, retired professionals, and anyone else who wants to understand the amazing applications of 3-D calculus.

Designed for anyone familiar with basic calculus, Understanding Multivariable Calculus follows, but does not essentially require knowledge of, Calculus II. The few topics introduced in Calculus II that do carry over, such as vector calculus, are here briefly reintroduced, but with a new emphasis on three dimensions.

Your main focus throughout the 36 comprehensive lectures is on deepening and generalizing fundamental tools of integration and differentiation to functions of more than one variable. Under the expert guidance of Professor Edwards, you’ll embark on an exhilarating journey through the concepts of multivariable calculus, enlivened with real-world examples and beautiful animated graphics that lift calculus out of the textbook and into our three-dimensional world.

A New Look at Old Problems

How do you integrate over a region of the xy plane that can’t be defined by just one standard y = f(x) function? Multivariable calculus is full of hidden surprises, containing the answers to many such questions. In Understanding Multivariable Calculus, Professor Edwards unveils powerful new tools in every lecture to solve old problems in a few steps, turn impossible integrals into simple ones, and yield exact answers where even calculators can only approximate.

With these new tools, you will be able to

  • integrate volumes and surface areas directly with double and triple integrals;
  • define easily differentiable parametric equations for a function using vectors; and
  • utilize polar, cylindrical, and spherical coordinates to evaluate double and triple integrals whose solutions are difficult in standard Cartesian coordinates.

Professor Edwards leads you through these new techniques with a clarity and enthusiasm for the subject that make even the most challenging material accessible and enjoyable. With graphics animated with state-of-the-art software that brings three-dimensional surfaces and volumes to life, as well as an accompanying illustrated workbook, this course will provide anyone who is intrigued about math a chance to better understand the full potential of one of the crowning mathematical achievements of humankind.

About Your Professor

Dr. Bruce H. Edwards is Professor of Mathematics at the University of Florida. He earned his Ph.D. in Mathematics from Dartmouth College. He has been honored with numerous Teacher of the Year awards as well as awards for his work in mathematics education for the state of Florida.

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36 lectures
 |  Average 30 minutes each
  • 1
    A Visual Introduction to 3-D Calculus
    Review key concepts from basic calculus, then immediately jump into three dimensions with a brief overview of what you’ll be learning. Apply distance and midpoint formulas to three-dimensional objects in your very first of many extrapolations from two-dimensional to multidimensional calculus, and observe some of the new curiosities unique to functions of more than one variable. x
  • 2
    Functions of Several Variables
    What makes a function “multivariable?” Begin with definitions, and then see how these new functions behave as you apply familiar concepts of minimum and maximum values. Use graphics and other tools to observe their interactions with the xy-plane, and discover how simple functions such as y=x are interpreted differently in three-dimensional space. x
  • 3
    Limits, Continuity, and Partial Derivatives
    Apply fundamental definitions of calculus to multivariable functions, starting with their limits. See how these limits become complicated as you approach them, no longer just from the left or right, but from any direction and along any path. Use this to derive the definition of a versatile new tool: the partial derivative. x
  • 4
    Partial Derivatives—One Variable at a Time
    Deep in the realm of partial derivatives, you’ll discover the new dimensions of second partial derivatives: differentiate either twice with respect to x or y, or with respect once each to x and y. Consider Laplace’s equation to see what makes a function “harmonic.” x
  • 5
    Total Differentials and Chain Rules
    Complete your introduction to partial derivatives as you combine the differential and chain rule from elementary calculus and learn how to generalize them to functions of more than one variable. See how the so-called total differential can be used to approximate ?z over small intervals without calculating the exact values. x
  • 6
    Extrema of Functions of Two Variables
    The ability to find extreme values for optimization is one of the most powerful consequences of differentiation. Begin by defining the Extreme Value theorem for multivariable functions and use it to identify relative extrema using a “second partials test”—which you may recognize as a logical extension of the “second derivative test” used in Calculus I. x
  • 7
    Applications to Optimization Problems
    Continue the exploration of multivariable optimization by using the Extreme Value theorem on closed and bounded regions. Find absolute minimum and maximum values across bounded regions of a function, and apply these concepts to a real-world problem: attempting to minimize the cost of a water line’s construction. x
  • 8
    Linear Models and Least Squares Regression
    Apply techniques of optimization to curve-fitting as you explore an essential statistical tool yielded by multivariable calculus. Begin with the Least Squares Regression Line that yields the best fit to a set of points. Then, apply it to a real-life problem by using regression to approximate the annual change of a man’s systolic blood pressure. x
  • 9
    Vectors and the Dot Product in Space
    Begin your study of vectors in three-dimensional space as you extrapolate vector notation and formulas for magnitude from the familiar equations for two dimensions. Then, equip yourself with an essential new means of notation as you learn to derive the parametric equations of a line parallel to a direction vector. x
  • 10
    The Cross Product of Two Vectors in Space
    Take the cross product of two vectors by finding the determinant of a 3x3 matrix, yielding a third vector perpendicular to both. Explore the properties of this new vector using intuitive geometric examples. Then, combine it with the dot product from Lecture 9 to define the triple scalar product, and use it to evaluate the volume of a parallelepiped. x
  • 11
    Lines and Planes in Space
    Turn fully to lines and entire planes in three-dimensional space. Begin by defining a plane using the tools you’ve acquired so far, then learn about projections of one vector onto another. Find the angle between two planes, then use vector projections to find the distance between a point and a plane. x
  • 12
    Curved Surfaces in Space
    Beginning with the equation of a sphere, apply what you’ve learned to curved surfaces by generating cylinders, ellipsoids, and other so-called quadric surfaces. Discover the recognizable parabolas and other 2D shapes that lay hidden in new vector equations, and observe surfaces of revolution in three-dimensional space. x
  • 13
    Vector-Valued Functions in Space
    Consolidate your mastery of space by defining vector-valued functions and their derivatives, along with various formulas relating to arc length. Immediately apply these definitions to position, velocity, and acceleration vectors, and differentiate them using a surprisingly simple method that makes vectors one of the most formidable tools in multivariable calculus. x
  • 14
    Kepler’s Laws—The Calculus of Orbits
    Blast off into orbit to examine Johannes Kepler’s laws of planetary motion. Then apply vector-valued functions to Newton’s second law of motion and his law of gravitation, and see how Newton was able to take laws Kepler had derived from observation and prove them using calculus. x
  • 15
    Directional Derivatives and Gradients
    Continue to build on your knowledge of multivariable differentiation with gradient vectors and use them to determine directional derivatives. Discover a unique property of the gradient vector and its relationships with level curves and surfaces that will make it indispensable in evaluating relationships between surfaces in upcoming lectures. x
  • 16
    Tangent Planes and Normal Vectors to a Surface
    Utilize the gradient to find normal vectors to a surface, and see how these vectors interplay with standard functions to determine the tangent plane to a surface at a given point. Start with tangent planes to level surfaces, and see how your result compares with the error formula from the total differential. x
  • 17
    Lagrange Multipliers—Constrained Optimization
    It’s the ultimate tool yielded by multivariable differentiation: the method of Lagrange multipliers. Use this intuitive theorem and some simple algebra to optimize functions subject not just to boundaries, but to constraints given by multivariable functions. Apply this tool to a real-world cost-optimization example of constructing a box. x
  • 18
    Applications of Lagrange Multipliers
    How useful is the Lagrange multiplier method in elementary problems? Observe the beautiful simplicity of Lagrange multipliers firsthand as you reexamine an optimization problem from Lecture 7 using this new tool. Next, explore one of the many uses of constrained optimization in the world of physics by deriving Snell’s Law of Refraction. x
  • 19
    Iterated integrals and Area in the Plane
    With your toolset of multivariable differentiation finally complete, it’s time to explore the other side of calculus in three dimensions: integration. Start off with iterated integrals, an intuitive and simple approach that merely adds an extra step and a slight twist to one-dimensional integration. x
  • 20
    Double Integrals and Volume
    In taking the next step in learning to integrate multivariable functions, you’ll find that the double integral has many of the same properties as its one-dimensional counterpart. Evaluate these integrals over a region R bounded by variable constraints, and extrapolate the single variable formula for the average value of a function to multiple variables. x
  • 21
    Double Integrals in Polar Coordinates
    Explore integration from a whole new perspective, first by transforming Cartesian functions f(x.y) into polar coordinates defined by r and ?. After getting familiar with surfaces defined by this new coordinate system, see how these coordinates can be used to derive simple and elegant solutions from integrals whose solutions in Cartesian coordinates may be arduous to derive. x
  • 22
    Centers of Mass for Variable Density
    With these new methods of evaluating integrals over a region, we can apply these concepts to the realm of physics. Continuing from the previous lecture, learn the formulas for mass and moments of mass for a planar lamina of variable density, and find the center of mass for these regions. x
  • 23
    Surface Area of a Solid
    Bring another fundamental idea of calculus into three dimensions by expanding arc lengths into surface areas. Begin by reviewing arc length and surfaces of revolution, and then conclude with the formulas for surface area and the differential of surface area over a region. x
  • 24
    Triple Integrals and Applications
    Explore integration from a whole new perspective, first by transforming Cartesian functions f(x.y) into polar coordinates defined by r and ?. After getting familiar with surfaces defined by this new coordinate system, see how these coordinates can be used to derive simple and elegant solutions from integrals whose solutions in Cartesian coordinates may be arduous to derive. x
  • 25
    Triple Integrals in Cylindrical Coordinates
    Just as you applied polar coordinates to double integrals, you can now explore their immediate extension into volumes with cylindrical coordinates—moving from a surface defined by (r,?) to a cylindrical volume with an extra parameter defined by (r,?,z). Use these conversions to simplify problems. x
  • 26
    Triple Integrals in Spherical Coordinates
    Similar to the shift from rectangular coordinates to cylindrical coordinates, you will now see how spherical coordinates often yield more useful information in a more concise format than other coordinate systems—and are essential in evaluating triple integrals over a spherical surface. x
  • 27
    Vector Fields—Velocity, Gravity, Electricity
    In your introduction to vector fields, you will learn how these creations are essential in describing gravitational and electric fields. Learn the definition of a conservative vector field using the now-familiar gradient vector, and calculate the potential of a conservative vector field on a plane. x
  • 28
    Curl, Divergence, Line Integrals
    Use the gradient vector to find the curl and divergence of a field—curious properties that describe the rotation and movement of a particle in these fields. Then explore a new, exotic type of integral, the line integral, used to evaluate a density function over a curved path. x
  • 29
    More Line Integrals and Work by a Force Field
    One of the most important applications of the line integral is its ability to calculate work done on an object as it moves along a path in a force field. Learn how vector fields make the orientation of a path significant. x
  • 30
    Fundamental Theorem of Line Integrals
    Generalize the fundamental theorem of calculus as you explore the key properties of curves in space as they weave through vector fields in three dimensions. Then find out what makes a curve smooth, piecewise-smooth, simple, and closed. Next, manipulate curves to reveal new, simpler methods of evaluating some line integrals. x
  • 31
    Green’s Theorem—Boundaries and Regions
    Using one of the most important theorems in multivariable calculus, observe how a line integral can be equivalent to an often more-workable area integral. From this, you will then see why the line integral around a closed curve is equal to zero in a conservative vector field. x
  • 32
    Applications of Green’s Theorem
    With the full power of Green’s theorem at your disposal, transform difficult line integrals quickly and efficiently into more approachable double integrals. Then, learn an alternative form of Green’s theorem that generalizes to some important upcoming theorems. x
  • 33
    Parametric Surfaces in Space
    Extend your understanding of surfaces by defining them in terms of parametric equations. Learn to graph parametric surfaces and to calculate surface area. x
  • 34
    Surface Integrals and Flux Integrals
    Discover a key new integral, the surface integral, and a special case known as the flux integral. Evaluate the surface integral as a double integral and continue your study of fluid mechanics by utilizing this integral to evaluate flux in a vector field. x
  • 35
    Divergence Theorem—Boundaries and Solids
    Another hallmark of multivariable calculus, the Divergence theorem, combines flux and triple integrals, just as Green’s theorem combines line and double integrals. Discover the divergence of a fluid, and call upon the gradient vector to define how a surface integral over a boundary can give the volume of a solid. x
  • 36
    Stokes’s Theorem and Maxwell's Equations
    Complete your journey by developing Stokes’s theorem, the third capstone relationship between the new integrals of multivariable calculus, seeing how a line integral equates to a surface integral. Conclude with connections to Maxwell’s famous equations for electric and magnetic fields—a set of equations that gave birth to the entire field of classical electrodynamics. x

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Your professor

Bruce H. Edwards

About Your Professor

Bruce H. Edwards, Ph.D.
University of Florida
Dr. Bruce H. Edwards is Professor of Mathematics at the University of Florida. Professor Edwards received his B.S. in Mathematics from Stanford University and his Ph.D. in Mathematics from Dartmouth College. After his years at Stanford, he taught mathematics at a university near Bogot·, Colombia, as a Peace Corps volunteer. Professor Edwards has won many teaching awards at the University of Florida, including Teacher of...
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Reviews

Understanding Multivariable Calculus: Problems, Solutions, and Tips is rated 4.9 out of 5 by 34.
Rated 5 out of 5 by from Multivariable Calculus Sorted. A wonderfully supreme course masterly taught and presented. The animations, graphics, video clips and visuals were magnificent. One of your best courses ever. Very highly recommended.
Date published: 2017-10-09
Rated 4 out of 5 by from Great lecture sequence and examples I purchased mainly as a review/refresher course. The professors presentation is well done with practical (real world) examples. My only minor gripe would be that more time should be devoted to "Physics" concepts like Maxwell's Equations.
Date published: 2017-06-19
Rated 5 out of 5 by from Bruce Edward's teaching. I have purchased Edward's pre-Calculus course as well as one of his calculus courses. His coverage is excellent and his presentations are excellent. In addition, his pedagogy (overall) is superb. I have one complaint. To wit, he refuses to call the natural logarithm by its proper name of "ln" - pronounced "lin". He correctly states that mathematicians and scientists almost always use logs to the base 10 or e, when logarithms can be taken to ANY real number base, except zero or one. He correctly refers to base 10 logarithms as "log", and logarithms to other bases as (for instance) "log to the base 4" of some real number. The base 10 is special and omnipresent so it is proper to refer to them as simply "logs". Well, the base e is also special, and he should be verbally calling logarithms to the base e as "lin" - referring to their mathematics abbreviation, ln. Edwards is the best math teacher I have ever run across. Please tell him I said this, and further add that if he were just a LITTLE bit better, he might be able to teach at Florida State. (He'll like that!) James H. Bentley, PhD
Date published: 2017-02-10
Rated 5 out of 5 by from Good Overview I needed to refresh some topics from my sophomore calculus course, especially div, curl, Green's Theorem, etc., and Prof. Edwards course was perfect for that purpose. The presentation is top-notch, topics are nicely explained, examples and exercises are straightforward. The emphasis is on understanding basic concepts and facility with calculations, not theory per se. In that respect, it would not be a substitute for a 2nd year calculus course, which would spend additional time on proofs, theory, and properties of operators, etc. But theory and proofs can come later - if you want. The exercises in the accompanying study book are generally easy - just what you need to verify your understanding, without getting mired down with the intricacies of very hard problems. Overall, this is a great introductory/refresher course in applying the concepts of multivariate calculus and is well worth the price. I would love to have had this DVD during the summer before my sophomore year in college - with the basic calculations/techniques in place, I would then have been able to better focus on the nuances of theory. Unfortunately, DVDs and the Internet didn't exist back then, but at least today's students have access to this wonderful resource.
Date published: 2016-11-27
Rated 5 out of 5 by from Tough Topic - Terrificallly Taught Going back to school in engineering. This is an advanced topic with many complexities but Prof Edwards does and excellent job explaining the material very clearly and in an organized fashion. Makes it possible for me to keep up with the subject even though has been a long time since I had last covered the topic. Highly recommend this presentation and teacher.
Date published: 2016-06-01
Rated 5 out of 5 by from I liked very much the application on Maxwell’s eq. After completing the 3 courses of calculus given by Professor Edwards, I would like to say that these are the best courses on calculus that I had ever taken. This last course has fantastic visual aids that facilitate the understanding of calculus in 3D. I would strongly suggest to the Teaching Company to get a Lineal Algebra course (by Professor Edwards) to complement these math courses.
Date published: 2016-05-18
Rated 5 out of 5 by from Third is challenging and a charm This is my third TTC calculus course taught by Dr. Edwards. The third is challenging and a charm! Why a charm? This course solidifies fundamental precalculus and elementary calculus skills. Dr. Edwards, once again, emphasizes the necessity for expertise in these fundamentals to understand and enjoy higher mathematics. For me, use of these skills became second nature in understanding and completing these lectures. Calculus III is challenging. This is not a "sit and listen" course; rather it is a course that requires time and engagement. For each lecture, I spent one hour or more to complete the lecture with notes and review of concepts. Without that commitment, the course would be a waste of time. As other reviewers have written, this course requires fundamental knowledge of algebra, trigonometry and elementary calculus. Don't purchase this course if you do not have these skills!. Finally, Dr. Edwards is the consummate teacher. His presentations are clear; he makes complex concepts understandable by taking small bits of a problem and bringing them together into a whole (Integration!). I am a medical school professor, and I learn continually from other professors like Dr. Edwards. He has deep knowledge of his subject, speaks well, has poise, and presents himself with elegant dress and appearance. Dr. Edwards is a role model for students and for teachers.
Date published: 2016-03-04
Rated 5 out of 5 by from A Class Act Professor Edwards is one of the great teachers of my autodidact career: a sharp intellect; a sharp sense of humor; and yes, a sharp dresser. In short, a class act. I've been lucky to have had a few teachers in various disciplines who successfully balanced tough demands on students with elegant presentation of material, but never (until The Great Courses) in mathematics. Perhaps like many otherwise strong students in middle school and high school, I had my early enthusiasm for mathematics quelled to the point of boredom by constant exposure to the New Math as taught in a program with the acronym "SSMCIS" (which students and teachers pronounced as "SMIX"). By the time we reached high school and were studying calculus, even the teachers quietly despised the SSMCIS textbooks — which began the study of calculus with a detailed and perplexing account of continuity — and after some equally quiet rioting, swapped the New Math books for the old Thomas calculus text instead. For many decades after high school, I pondered the problem of re-treading my knowledge of mathematics — not for any practical purpose but for the sake of grasping its essentials — and only recently found a satisfying solution in The Great Courses mathematics series. Kudos, again, to the brilliant Bruce Edwards, as well as to the ever patient and methodical James Sellers, the impressive Edward Burger and Arthur Benjamin, and the engaging Michael Starbird.
Date published: 2016-01-22
Rated 5 out of 5 by from Excellent Comprehensive Calculus III Course I bought this course as a supplement for a Calc III course that I was going to take online. It ended up being a lot more than a supplement. It basically replaced it. I just looked at the lecture topic for the week and popped in the right DVD. If your school offers credit by exam for Calc III, then it is entirely realistic that you could complete this course over a summer and test out in the fall. If you are considering Calc III, this probably goes without saying. But this is certainly not a "from scratch" math class. You could probably keep up after a first semester Calculus class, but you really should have the full single variable curriculum under your belt before you dive into this. Long story short, this course covers everything that you need for college Calc III course, either as a supplement or a full replacement, and it covers it very well.
Date published: 2016-01-03
Rated 5 out of 5 by from Can't recommend any more!!:) Thanks great courses and Prof. Edward for this awesome material. I developed some great concepts from this course. I will be coming back to purchase more. Thanks again.
Date published: 2015-06-09
Rated 5 out of 5 by from Calculus III challenge The college I attended when I took calculus used Larson, Edwards, and Hostetler text. You will never find a better text for Calculus I, II, or III. This video follows the text very closely. If you did not have a good classroom instructor, want to review calculus since you have been away for a while, or if you are curious what calculus is about and whether you should try to take a class, this video was made for you. This is an advanced course. So If you had trouble with Calc I and II, you might want to hold off.
Date published: 2015-03-07
Rated 5 out of 5 by from Another winner This course is closer to a true college course than any other I have seen here. As long as you are comfortable with vectors, derivatives and integrals it is quite doable, especially with such an accomplished teacher. Having had a similar course 49 years ago(!), ostensibly there was little new. However, in my analytical career, only 20% of what is covered here was actually used. (After all, how many times do you need the equation of a plane?) Having said that, it was thoroughly enjoyable to be reacquainted with some wonderful mathematical ideas! Mathematicians often use the word "elegant" to describe the concepts they love so much, and the coverage within this Dr. Edwards course fits that adjective. On a practical note, the area of a region using Green's theorem became a computer program I wrote to evaluate the square footage of my home. [The appraiser shorted me by 100 square ft]. Oh well, I suspect he never learned Green's theorem......
Date published: 2015-02-21
Rated 5 out of 5 by from An Excellent Course and Review Having recently taken and done well in multivariable calculus, I was very happy to find an excellent and detailed review of the course material to help reinforce and to remember important concepts, theories, and formulas. We all have a tendency to forget and this course will bridge that gap for anyone searching for that review, learning about multivariable calculus for the first time, and/or wanting to study advanced math for sheer enjoyment and knowledge.
Date published: 2015-01-25
Rated 5 out of 5 by from Genius educator. Fantastic course! I had thought about purchasing this course for over a year but I thought the price was a bit steep, and the content might be over my head since I have not taken a calculus course in many years. So I bought the course when it went on sale. Now that I have gone thru it and seen what a fantastic course it is, I feel guilty for not paying the list price for it! The success of the course is due to the overwhelming enthusiasm of Professor Edwards which never lags throughout the difficult material. He has organized the material so well that learning from him is always a pleasure. At times his enthusiasm borders on corny, but he always comes across as sincere. As far as the material itself, it requires a lot of starting, stopping, rewinding, reviewing, but that's the way I learn a subject of this difficulty. Professor Edwards presents the material with enough depth to give a good feel for where the equations come from, but he doesn't disrupt the flow of the course by deriving and proving every concept. This makes the course flow without bogging down and holds my attention. To paraphrase Einstein, he makes the course as simple as possible but no simpler. In the end, I'd have to say this is just about the best course I have taken from TGC and it has given me a real sense of accomplishment.
Date published: 2015-01-09
Rated 5 out of 5 by from Very clear presentation This course manages to cover a great deal of material in a very digestible way. An understanding of basic calculus is needed, but other necessary topics such as vector algebra are covered within the material. Very good use is made of diagrams and other visualizations to make complex concepts clear and easy to digest. The workbook is concise but covers the key learning points and provides plenty of practice problems with answers, and as such will function as a very handy textbook. The emphasis is on concepts, developing good intuition, and practical applications rather than on mathematically rigorous proofs. Highly recommended, I needed a refresher on some of the advanced topics after a 40-year hiatus, and got more than I expected - a good understanding of concepts that I had either never learned or never properly understood. The superiority of good video lectures over "talk and chalk" shows through; the professor's presentation stye is nicely paced and easy to understand, and if he ever goes too fast, you can just hit the pause button and reflect on the material.
Date published: 2015-01-08
Rated 5 out of 5 by from One of the better mathematics courses. This is one of the better courses in the science/mathematics section. The professor presents the material very well with abundant examples and often steps back for quick reviews of points from previous lectures or more basic material. His method of "stepping things up a notch" is particularly effective wherein he starts with a simple example and then moves up to more complex 3D. I would like to see a sequel to this course, and several others in the mathematics/science section, 'stepped up a notch or two'. I believe there is a market for more advanced courses.
Date published: 2014-09-28
Rated 5 out of 5 by from Excellent, but Very Advanced Mathematics I have just finished viewing the course, and the overall quality is excellent. However, please be aware that of the many Great Courses I have purchased over several years (not all in mathematics), this one has been unquestionably the most "esoteric." Prof. Edwards is a very good presenter, and he has done a very good job here (I have purchased some of his other courses), but unless you (figuratively speaking) have a real need for a serious advanced mathematics course, I suggest that you decline. Of course, if you are an advanced mathematics student, you may find this course valuable, in which can I can recommend it.
Date published: 2014-07-29
Rated 5 out of 5 by from Perfect for the Non-Mathematician If you are looking for a mathematics course, this is not for you. If you are looking for a course on applying calculus to 3-dimensional space without going into the underlying mathematics, you will enjoy it as I did. I would have liked more in the way of derivations of the formulas presented instead of just applying the formulas to example problems. Dr. Edwards approaches his lectures in an organized and easy to follow manner. His enthusiasm for teaching and mathematics is evident. The use of animated text in the development of examples helped me to follow the steps to the solution. The course guidebook was helpful to me when I needed to ponder some of the more challenging topics. The "Extra Problems" sections contain well-chosen exercises that help clarify the topic at hand. I would recommend this course to folks interested in the application of Multivariable Calculus to disciplines outside of mathematics.
Date published: 2014-06-27
Rated 5 out of 5 by from This guy is AMAZING!!! These courses are a the absolute best purchases I have ever made in my life; without them I would have not gotten As in Calc 1 & 2. What I like best about Prof Edwards is how he makes math interesting. instead of simply doing a lot of practice problems like the youtube tutors, Prof Edwards gives us the full lecture content that he teaches in university. In Short It's amazing and I highly recommend purchasing.
Date published: 2014-06-10
Rated 5 out of 5 by from Another Home Run! I could not agree more with the previous reviewers, this is an excellent course! I have purchased all of Dr. Edward's courses, and they are all very well done and worthwhile. Also, the workbook problems are nicely selected and serve to both challenge and educate the learner. Now, a message to Dr. Edwards: please, please please do a Teaching Company course on Linear Algebra and/.or Differential Equations. You have a wonderful ability to make difficult concepts easy to understand.
Date published: 2014-05-07
Rated 5 out of 5 by from Best Math Presentation Ever Dr. Edwards is, without question, the absolute best mathematics teacher I've ever experienced. I am reviewing all the math taken over the past 40 years, which I took in getting my undergraduate and graduate degrees in math and physics. I am amazed at his ability to make the topics I found so difficult years ago appear easy! His presentation style, verbal articulation, content organization, examples, and explanations are superb; and his enthusiasm reflects his love for teaching, which is infectious for the student's learning. In short, I found this set (Calculus I, II, and III) the best courses, especially for review, possible. I only wish the Great Courses would have him also teach a new course titled "Advanced Math For Scientists and Engineers", covering the material covered in similarly titled textbooks and university courses. I would give Dr. Edwards a hundred stars, but I'm unfortunately limited to only 5.
Date published: 2014-05-02
Rated 5 out of 5 by from Better Than Being in a Classroom On another review (Thermodynamics) I recommended it for all educations. Not so for this course. I agree with the previous reviewer. This course is centered on skills and everyone is different in that department. When I say, “skills” I mean putting pen to paper. So become familiar with the Algebra (I / II) and Calculus (I / II) courses before taking this one. These courses are well liked according to the reviews. So if you like them, you will like Multivariable Calculus. This course is like being in a university class. I know this because I took this course about ten years ago in university. The questions on this course are challenging! (Otherwise I would not buy it). Clearly, this course matches the 2nd year university mathematics curriculum. I can’t say that for all TTC science courses. As a matter of fact, I would recommend this course as a supplement if you are already enrolled in Multivariable Calculus. Why is it better? I like Professor Edward’s teaching style. He often solves questions in multiple ways so that you get a better understanding of the principles taught. With the animations you can bounce back and forth between equations and the 3D view (often laid out side-by-side). He highlights particular parts of equations and their counterpart in the 3D object. He spends most of his time setting up the equation and then skipping most of the algebra (referring to his workbook). This is appropriate as we don’t want to waste time doing algebra. It is cumbersome and below the level of this course. The setup is the crux and essence of this course. I am excited about the science courses that are coming out. According TTC User Forum (yuku) there are future courses in Vector Calculus, Civil Engineering and Linear Algebra. I was going to pester TTC about producing some physics courses modelled after Professor Edward’s courses in Calculus. I stopped myself and thought….maybe it is in the future now that we have these courses in place. I took a Classical Mechanics course from the Physics department. Let’s just say, I struggled. I would love to re-visit these advance physics subjects. This Multivariable Calculus course, along with some recent and future courses, had just opened some doors for me. I am glad to call myself a student of Professor Edwards. Thank you.
Date published: 2014-04-14
Rated 5 out of 5 by from THREE EQUALS TWO PLUS ONE Let me begin by stating I’m a retired high school mathematics instructor who had a very rewarding career of 39 years including a highly successful Advanced Placement Calculus class for the last eighteen. I actually used the Calculus and PreCalculus textbooks, which I thought were the best available, written by Dr. Edwards and his coauthors. Professor Edwards’ presentation in his third Calculus Great Course takes up where the previous two left off. Whereas his first Calculus course was equivalent to a first-semester college-level course or to a high school-level Advanced Placement Calculus AB class and the second was equivalent to a second-semester college class or to a high school Advanced Placement BC class, Understanding Multivariable Calculus is equivalent to a second-year college course that takes Calculus into the real world of three-dimensional problems and their solutions . Dr. Edwards’ third Calculus course is every bit as good as and the equal of the previous two. It encompasses the key topics necessary for solving actual problems in the third dimension and he presents the topics in a manner that is logical and clear. His enthusiasm, techniques and pleasing personality easily hold your interest and the carefully chosen examples are especially insightful and illuminating. This is not a superficial survey course but instead uses an in-depth approach, like his PreCalculus/Trigonometry and previous Calculus courses, that will leave you feeling knowledgeable, satisfied, and confident upon its completion. Let's hope TTC will soon add in-depth courses in the areas of Linear Algebra, Non-Euclidean Geometry, and Statistics to extend its now excellent offerings in mathematics. I would like to conclude with a warning: Mathematics is not a spectator subject; you cannot just listen to an instructor, no matter how good he might be, but must actually work out many examples yourself in order to find and correct mistakes that may be unique to you. It takes practice, practice, practice along with an excellent instructor to guarantee success; therefore, I highly recommend you work out all of the problems given in the accompanying workbook in order to get the most out of this course and increase your chances of success.
Date published: 2014-04-05
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