Differential and integral calculus/
R. Courant
- New York: Wiley-Interscience, 2014.
- 2 v. (x, 682 p.) ; 23 cm.
v. 1. Differential and integral calculus -- Introduction -- The fundamental ideas of the integral and differential calculus -- Differentiation and integration of the elementary functions -- Further development of the integral calculus -- Applications -- Taylor's theorem and the approximate expression of functions by polynomials -- 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 of vibration -- Summary of important theorems and formulae -- Miscellaneous examples -- Answers and hints -- v. 2. Preliminary remarks on analytical geometry and vector analysis -- Functions of several variables and their derivatives -- Developments and applications of the differential calculus -- Multiple integrals -- Integration over regions in several dimensions -- Differential equations -- Calculus of variations -- Functions of a complex variable -- Supplement: real numbers and the concept of limit -- Miscellaneous examples -- Summary of important theorems and formulae -- Answers and hints.