Calculus of Several Variables / Edition 3by Serge Lang
Pub. Date: 02/01/1987
Publisher: Springer New York
This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its… See more details below
This new, revised edition covers all of the basic topics in calculus of several variables, including vectors, curves, functions of several variables, gradient, tangent plane, maxima and minima, potential functions, curve integrals, Green’s theorem, multiple integrals, surface integrals, Stokes’ theorem, and the inverse mapping theorem and its consequences. It includes many completely worked-out problems.
Table of ContentsI: Basic Material. 1: Vectors. 2: Differentiation of Vectors. 3: Functions of Several Variables. 4: The Chain Rule and the Gradient. II: Maxima, Minima, and Taylor's Formula. 5: Maximum and Minimum. 6: Higher Derivatives. III: Curve Integrals and Double Integrals. 7: Potential Functions. 8: Curve Integrals. 9: Double Integrals. 10: Green's Theorem. IV: Triple and Surface Integrals. 12: Triple Integrals. V: Mappings, Inverse Mappings, and Change of Variables Formula. 13: Matrices. 14: Linear Mappings. 15: Determinants. 16: Applications to Functions of Several Variables. 17: The Change of Variables Formula. Appendix: Fourier Series.
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This text provides a clear, if challenging, introduction to multi-variable calculus. Like his introductory text, A First Course in Calculus, this text teaches you how to solve challenging problems while effectively conveying the key concepts. Lang does an effective job of placing those concepts in context. Methods of solving problems are clearly explained in the examples. Working through the exercises enables you to build the skills you need in order to solve challenging problems. The text covers vector functions, maxima and minima, Taylor's Formula, line integrals, double and triple integrals, integration with respect to polar, cylindrical, and spherical coordinates, Green's Theorem, Stokes' Theorem, and applications of linear algebra to multi-variable calculus. While there is more material here than can comfortably be covered in a year course, working through the entire text will provide you with a solid foundation for subsequent courses in linear algebra, real analysis, or electricity and magnetism. Caveat: beware of errors.