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Introduction to Calculus and Analysis I : Classics in Mathematics, - Richard Courant

Introduction to Calculus and Analysis I

Classics in Mathematics,

Paperback Published: 3rd December 1998
ISBN: 9783540650584
Number Of Pages: 661

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From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)" The Mathematical Gazette (75.1991.471)

From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. [...]It is the best text known to the reviewer for anyone trying to make an analysis course less abstract." --The Mathematical Gazette

Relations Between Surface and Volume Integrals: Connection Between Line Integrals and Double Integrals in the Plane
Vector Form of the Divergence Theorem
Formula for Integration by Parts in Two Dimensions:
The Divergence Theorem Applied to the Transformation of Double Integrals
Area Differentiation
Interpretation of the Formulae of Gauss and Stokes by Two-Dimensional Flows
Orientation of Surfaces
Integrals of Differential Forms and of Scalars over Surfaces
Gauss's and Green's Theorems in Space
Appendix: General Theory of Surfaces and of Surface Integrals.- Differential Equations: The Differential Equations for the Motion of a Particle in Three Dimensions
The General Linear Differential Equation of the First Order
Linear Differential Equations of Higher Order
General Differential Equations of the First Order
Systems of Differential Equations and Differential Equations of Higher Order
Integration by the Method of Undermined Coefficients
The Potential of Attracting Charges and Laplace's Equation
Further Examples of Partial Differential Equations from Mathematical Physics
Calculus of Variations: Functions and Their Extreme Values of a Functional
Generalizations
Problems Involving Subsidiary Conditions. Lagrange Multipliers
Functions of a Complex Variable: Complex Functions Represented by Power Series
Foundations of the General Theory of Functions of a Complex Variable
The Integration of Analytic Functions
Cauchy's Formula and Its Applications
Applications to Complex Integration (Contour Integration)
Many-Valued Functions and Analytic Extension.
List of Biographical Dates
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540650584
ISBN-10: 354065058X
Series: Classics in Mathematics, : Book 1
Audience: General
Format: Paperback
Language: English
Number Of Pages: 661
Published: 3rd December 1998
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.98  x 3.99
Weight (kg): 1.04