Classroom-tested and lucidly written

Multivariable Calculus gives a thorough and rigorous treatment of differential and integral calculus of functions of several variables. Designed as a junior-level textbook for an advanced calculus course, this book covers a variety of notions, including continuity, differentiation, multiple integrals, line and surface integrals, differential forms, and infinite series. Numerous exercises and examples throughout the book facilitate the student’s understanding of important concepts.

The level of rigor in this textbook is high; virtually every result is accompanied by a proof. To accommodate teachers' individual needs, the material is organized so that proofs can be deemphasized or even omitted. Linear algebra for n-dimensional Euclidean space is developed when required for the calculus; for example, linear transformations are discussed for the treatment of derivatives.

Featuring a detailed discussion of differential forms and Stokes' theorem, Multivariable Calculus is an excellent textbook for junior-level advanced calculus courses and it is also useful for sophomores who have a strong background in single-variable calculus. A two-year calculus sequence or a one-year honor calculus course is required for the most successful use of this textbook. Students will benefit enormously from this book’s systematic approach to mathematical analysis, which will ultimately prepare them for more advanced topics in the field.