Differential and Integral Calculus, Volume 1

The classic introduction to the fundamentals of calculus Richard Courant's classic text Differential and Integral Calculus is an essential text for those preparing for a career in physics or applied math. Volume 1 introduces the foundational concepts of "function" and "limit", and offers detailed explanations that illustrate the "why" as well as the "how". Comprehensive coverage of the basics of integrals and differentials includes their applications as well as clearly-defined techniques and essential theorems. Multiple appendices provide supplementary explanation and author notes, as well as solutions and hints for all in-text problems.

Partial table of contents: The Continuum of Numbers, The Concept of Function, The Concept ofthe Limit of a Sequence, The Concept of Continuity. The Fundamental Ideas of the Integral and Differential Calculus:The Definite Integral, The Derivative, The Estimation of Integralsand the Mean Value Theorem of the Integral Calculus. Differentiation and Integration of the Elementary Functions: Maximaand Minima, The Logarithm and the Exponential Function, TheHyperbolic Functions. Further Development of the Integral Calculus: The Method ofSubstitution, Integration by Parts, Integration of RationalFunctions, Improper Integrals. Applications. Taylor's Theorem and the Approximate Expression of Functions byPolynomials. Numerical Methods. Infinite Series and Other Limiting Processes. Fourier Series. A Sketch of the Theory of Functions of Several Variables. The Differential Equations for the Simplest Types ofVibration. Answers and Hints. Index.