Rigorous multivariable calculus book

Suggestions for a rigorous multivariate calculus book. Rigorous text in multivariable calculus and linear algebra. You should try the 2 calculus books by tom apostol calculus, vol. Linear algebra, multivariable calculus and manifolds, and. An introductory level single variable calculus book, covering standard topics in differential and integral calculus, and infinite series. Alternatively, you could learn basic calculus from any less rigorous book and then begin to study real analysis to really understand the theory behind calculus. Teds book on multivariable calculus is absolutely the best ive seen. Multivariable analysis mathematical association of america. Stewart was the author of a bestselling calculus textbook series published by cengage, including calculus, calculus. Suggestions for a rigorous multivariate calculus book physics. References for multivariable calculus mathematics stack exchange. Great calculus reference texts for students who want to. This is a textbook for a rigorous multivariable analysis course.

Albert schueller, barry balof, and mike wills have contributed additional material. I really want a rigorous book dealing with multivariable calculus and linear algebra. A modern approach to classical theorems of advanced calculus 1965 by michael spivak is a brief, rigorous, and modern textbook of multivariable calculus, differential forms. This textbook presents a rigorous approach to multivariable calculus in the.

This rigorous twopart treatment advances from functions of one variable to those of several. With multivariable calculus, seventh edition, stewart conveys not only the utility of calculus to help you develop technical competence, but also gives you an appreciation for the intrinsic beauty of the subject. Another classic, known among mathematicians for its thoroughness, rigor, and mathematical elegance. I really like hubbard and hubbards vector calculus, linear algebra, and differential forms. There are many great books that cover multivariable calculusanalysis, but im not.

This short but rigorous book approaches the main ideas of linear algebra through carefully selected examples and relevant applications. This treatment is far from standard but is quite rigorous and the author works. Implicit function theorem and the inverse function theorem based on total derivatives is explained along with the results and the connection to solving systems of equations. Intermediate versions can be proved, but in view of the preceding. Granted, id skip some parts he gets kinda crazy with the implicit function theorem and bounds in chapter 2, but overall its a fantastic book that actually gives you some high level stuff without losing you details. There is an extensive treatment of extrema, including constrained extrema and lagrange multipliers, covering both first. The books aim is to use multivariable calculus to teach mathematics as a blend. Derivatives and integrals of multivariable functions is a rigorous introduction to multivariable calculus that will help students build a foundation for further explorations in analysis and differential geometry. Derivatives and integrals of multivariable functions. Ive read spivaks book,and greatly enjoyed its problems but i felt unstatisfied by the explanations and the illustration were very poor,and the only chapter on. Concepts and contexts, as well as a series of precalculus texts. The purpose of this text is to provide a rigorous treatment of vector calculus, for interested second year undergraduates.

This book goes nicely with his lecture series on youtube, which is again brilliant. Students with an interest in rigor benefit from placing the study of. I have a solid background in calculus and am currently working through baby rudin. The books covers a lot from basics of mvc to manifold theory and differential forms. Late transcendentals and multivariable versions are also available. Fractional and multivariable calculus model building and. The exercises are good, and motivated mainly from physics. His patient examples and builtin learning aids will help you build your mathematical confidence and achieve your goals in the course. What book is good for learning multivariable calculus with a. It is difficult to name a calculus reference text having the clarity and precision as that of apostols book.