Calculus with Differential Equations
by Dale Varberg, Edwin Purcell, Steve Rigdon
This ninth edition textbook by Dale Varberg, Edwin J. Purcell, and Steve E. Rigdon offers a complete course in calculus, from limits and derivatives to multivariable analysis and differential equations. It emphasizes theoretical rigor alongside practical problem-solving, with chapters on integrals, series, vectors, and advanced applications for in-depth mathematical learning.
About This Book
Calculus with Differential Equations provides a thorough introduction to the principles of calculus, starting with preliminaries on real numbers, inequalities, and functions. It builds a strong foundation for understanding limits, derivatives, and their applications in optimization and graphing.
The book explores integrals, transcendental functions, and techniques of integration, including methods for handling indeterminate forms and improper integrals. It also delves into infinite series, conic sections, and polar coordinates to expand geometric and analytical skills.
Advanced sections cover multivariable calculus, including partial derivatives, multiple integrals, and vector calculus theorems like Green's, Gauss's, and Stokes's. The text concludes with differential equations, offering solutions to linear and nonhomogeneous types with practical applications.
An appendix on mathematical induction and proofs supports the rigorous approach, making this edition suitable for university-level study.
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