Classroom-tested and lucidly written, Multivariable Calculus gives a thorough and rigoroustreatment of differential and integral calculus of functions of several variables. Designed as ajunior-level textbook for an advanced calculus course, this book covers a variety of notions,including continuity , differentiation, multiple integrals, line and surface integrals, differentialforms, and infinite series. Numerous exercises and examples throughout the book facilitatethe student's understanding of important concepts.The level of rigor in this textbook is high; virtually every result is accompanied by a proof. Toaccommodate teachers' individual needs, the material is organized so that proofs can be deemphasizedor even omitted. Linear algebra for n-dimensional Euclidean space is developedwhen required for the calculus; for example, linear transformations are discussed for the treatmentof derivatives.Featuring a detailed discussion of differential forms and Stokes' theorem, Multivariable Calculusis an excellent textbook for junior-level advanced calculus courses and it is also usefulfor sophomores who have a strong background in single-variable calculus. A two-year calculussequence or a one-year honor calculus course is required for the most successful use of thistextbook. Students will benefit enormously from this book's systematic approach to mathematicalanalysis, which will ultimately prepare them for more advanced topics in the field.
Table of Contents
1. Some Preliminaries 2. Euclidean Spaces and Linear Transformations 3. Continuous Functions 4. The Derivative 5. The Geometry of Euclidean Spaces 6. Higher Order Derivatives and Taylor's Theorem 7. Compact and Connected Sets 8. Maxima and Minima 9. The Inverse and Implicit Function Theorems 10. Integration 11. Iterated Integrals and the Fubini Theorem 12. Line Integrals 13. Surface Integrals 14. Differential Forms 15. Integration of Differential Forms 16. Infinite Series 17. Infinite Series of Functions