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Introduction to Calculus and Analysis 2/2, Kapitel 5 - 8

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ISBN-10: 354065058X

ISBN-13: 9783540650584

Edition: 1999 (Reprint)

Authors: Richard Courant, Fritz John

List price: $59.99
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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 There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry.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…    
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Book details

List price: $59.99
Copyright year: 1999
Publisher: Springer Berlin / Heidelberg
Publication date: 12/3/1998
Binding: Paperback
Pages: 661
Size: 6.10" wide x 9.25" long x 0.54" tall
Weight: 2.530
Language: English

Richard Courant was born in Lublintz, Germany, on January 8, 1888, later becoming an American citizen. He was a mathematician, researcher and teacher, specializing in variational calculus and its applications to physics, computer science, and related fields. He received his Ph.D. from the University of Gottingen, Germany, lectured at Cambridge University and headed the mathematics department at New York University. Courant's writings include Introduction to Calculus and Analysis (1965), written with John Fritz, Differential and Integral Calculus (1965), Methods of Mathematical Physics: Dirichlet's Principle, Conformal Mapping and Minimal Surfaces (1950), and Supersonic Flow and Shock Waves…    

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