Differential and Integral Calculus, Volume 1 2e

Partial table of contents: The Continuum of Numbers, The Concept of Function, The Concept of the 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 Integrals and the Mean Value Theorem of the Integral Calculus. Differentiation and Integration of the Elementary Functions: Maxima and Minima, The Logarithm and the Exponential Function, The Hyperbolic Functions. Further Development of the Integral Calculus: The Method of Substitution, Integration by Parts, Integration of Rational Functions, Improper Integrals. 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. Answers and Hints. Index.