For students who are already fluent with single-variable derivatives and integrals, this workbook offers practice with essential skills from multivariable calculus (including vector calculus). Each chapter begins with a review of the essential ideas and includes fully solved examples to help serve as a guide. The full solution to every exercise can be found at the back of the book. Authored by experienced teacher, Chris McMullen, Ph.D., this self-study math workbook covers:
- partial derivatives
- extreme values with multiple variables (including saddle points)
- vectors, vector analysis (such as the dot and cross products), and vector calculus
- the gradient, divergence, and curl
- the main coordinate systems: Cartesian, 2D polar, spherical, and cylindrical
- path integrals, surface integrals, and volume integrals
- flux integrals, center of mass, and moment of inertia
- tangent and normal vectors
- and more
The author, Chris McMullen, Ph.D., has over twenty years of experience teaching math skills to physics students. He prepared this workbook of the Improve Your Math Fluency series to share his strategies for solving calculus problems with multiple variables or vectors.
Smith –
Good Book
John Carpenter –
This is a really fabulous book. It gives tests on the basics of degree level Maths. I think it bridges the gap nicely between A level and degree level. My favourite aspect is gradient, divergence and curl. There are some nice basic questions on those topics. It is a great confidence booster since some degree level maths books are too complicated for me.
. –
This is a very practical book to review and practice multivariable calculus. Thank you to the author for writing this book. I am hoping the author will also write a Differential Equations book similar to this one. I will definitely buy.
MCG –
It is a great workbook. It will help prep one for advanced courses requiring multiple variable calculations.
Dennis B –
While not to be used as a stand alone calculus book but certainly invaluable for a course supplement. Worked examples, and lots of problems (including space to write your solutions out in the book) for each chapter AND all problem sets are fully worked out in the back – not just answers alone but worked out! Can’t find a better book and the price is a steal.
Mathematical Kunde –
Calculus=Rechnen ist nicht zu verwechseln mit Analysis. Es werden hier nur die Rechenregeln für differenzieren, integrieren etc. trainiert, die sich aus der Analysis ergeben. Dafür ist es gut strukturiert und didaktisch sinnvoll aufgebaut. Mit den Seiten wird großzügig umgegangen, man kann seine Rechnungen direkt ins Buch schreiben. Das bläht das Buch etwas auf, bei Schaum sind im Vergleich mehr übungen. Keine Aufgaben für Beweise etc. wie in der Analysis!
Stephen Maharaj –
I take this book and a pencil wherever I go. And I find myself enjoying long queues at government offices. Big fonts, but fairly small and light and very cheap. The book lures you in with some easy exercises at first and gradually gets you wading through some longer and harder problems. Includes solutions to all questions.
Dr. Bryan Nolan –
Compact and well worth the price
All the books by this author are fantastic and well organized and well explained with very low price despite the high quality of the book.
Fabio –
Alle Bücher dieser Serie ind wirklich hilfreich um das “Handwerk” zu üben. Die Theorie ist sehr knapp gehalten, dafür sind die Lösungen zu den Uebungen sehr gut dokumentiert.
Mathematical Customer –
Es muy buen libro, para mantenerlo de consulta y ejercitar. Muy divertido.
Dale A. Smolinski –
Back binding of book started to come apart when opened wide. Good refresher book for people who do not use calculus very much.
Michel G Paiement –
Like all books in Chris McMullen’s collection, this book is a great tool for reviewing the basics of calculus from a physics perspective.
Simone M –
I am taking differential geometry more than 25 years after taking vector calculus. This book provided clear explanations of tangent, normal and binormal vectors that were holding me back from understanding the Frenet Formulas. The examples were adequate for me to complete the practice problems independently. I truly appreciate the author’s direct, no-nonsense approach.
Jeff, Intelligent Adult –
Someone said about the cover of the book, “If the integral with respect to y is inside the integral with respect to x in an iterated integral, then dy should appear to the left of dx.” That’s correct, but the integrals on the cover show an inside integral with respect to x, not y. Thus you treat y as a constant and integrate with respect to x, then evaluate y from 4 to 9 (in the cover’s example). Finally evaluate the outer integral with respect to y. It’s analogous to reversing the operation of partial diff of f with respect to x. The cover is correct.
Someone else said (in German) that this book is all about calculations, methods, and procedures, not proofs. That is true, it’s not an analysis book.
Errol –
The worked examples are clear and easy to understand.
Omah –
I’m relearning calc after 40 years.
Ron Toolsie –
This is not a textbook nor does it pretend to be one, although the explanations-when present- are quite well written. Learn multivariable calculus elsewhere, and then uses these excercises to reinforce that.
This is very much like all the authors other workbooks, inexpensive and a tremendous way to consolidate knowledge aquired elsewhere.
Very high value for money….after all, what is the point of LEARNING about multivariable calculus, if you cannot actually DO it.
Darren Hennig –
Got this to remind myself of some of the MVC (multi-variable) Calculus stuff I used to use in University. Good layout and examples are excellent to illustrate principles. Came well packed and on time – recommended!
Robert –
These calculus workbooks by Chris McMullen Ph.D. are excellent.
This one in particular covers a great range of topics, from the multi variable chain rule, to surface and volume integrals. Most importantly, every step in every calculation is shown, as well as alternative forms of the solutions.
Examples of exactly the types of questions asked all have steps, reasons for whats being done, and solutions. If definitely recommend this if you’re looking to learn and improve your calculus skills.
One important note is that the focus is on learning the content, so there are not a massive amount of problems per chapter. Usually about 8 to 12.
Malek Mun –
Arrived in mint condition; serves it’s purpose.
David Martinez –
Como Ingeniero, lo recomiendo, las matemáticas, así como cualquier cosa en la vida, para aprender algo, se tiene que practicar. Así que lo recomiendo.
Elia –
it’s a good book with exercises and explanations, vary easy to follow, would raccomend
Dra Teresa Silva –
Liked all of it.
そこら –
問題数も難易度も適切で解説が丁寧
Jane –
Good book!
Jerry Semler –
Great review of multivariable calculus. At this price buy now, learn calculus, and read later.
roberto –
Lo recomiendo
Rodrigo Ribeiro –
It’s simple and to the point. I think that it’s wonderful for practicing, however you would definitely need a more comprehensive Calculus book to better understand its concepts.