Differential and Integral Calculus, Volume 1, Second Edition

✍ Scribed by R. Courant, E. J. McShane(auth.)

• Year: 1988
• Tongue: English
• Leaves: 627
• Category: Library

✦ Synopsis

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.Content:
Chapter 1 Introduction (pages 5–75):
Chapter 2 The Fundamental Ideas of the Integral and Differential Calculus (pages 76–135):
Chapter 3 Differentiation and Integration of the Elementary Functions (pages 136–203):
Chapter 4 Further Development of the Integral Calculus (pages 204–257):
Chapter 5 Applications (pages 258–314):
Chapter 6 Taylor's Theorem and the Approximate Expression of Functions by Polynomials (pages 315–341):
Chapter 7 Numerical Methods (pages 342–364):
Chapter 8 Infinite Series and Other Limiting Processes (pages 365–424):
Chapter 9 Fourier Series (pages 425–456):
Chapter 10 A Sketch of the Theory of Functions of Several Variables (pages 457–500):
Chapter 11 The Differential Equations for the Simplest Types of Vibration (pages 501–527):