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Library | Materyal Türü | Barkod | Yer Numarası | Durum |
|---|---|---|---|---|
Searching... Pamukkale Merkez Kütüphanesi | Kitap | 0017593 | QA303C83 1989 | Searching... Unknown |
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Özet
Özet
From the Preface: (...) The book is addressed to students on various levels, to mathematicians, scientists, engineers. It does not pretend to make the subject easy by glossing over difficulties, but rather tries to help the genuinely interested reader by throwing light on the interconnections and purposes of the whole. Instead of obstructing the access to the wealth of facts by lengthy discussions of a fundamental nature we have sometimes postponed such discussions to appendices in the various chapters. Numerous examples and problems are given at the end of various chapters. Some are challenging, some are even difficult; most of them supplement the material in the text. In an additional pamphlet more problems and exercises of a routine character will be collected, and moreover, answers or hints for the solutions will be given. This first volume of concerned primarily with functions of a single variable, whereas the second volume will discuss the more ramified theories of calculus (...).
Author Notes
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 (1948). He edited a mathematics series and contributed to journals and periodicals.
Courant received the Distinguished Service Award from the Mathematical Association of America in 1965. He earned the Navy Distinguished Public Service Award, the Knight-Commander's cross, and Germany's Star of the Order of Merit in 1958.
Courant died on January 27, 1972.
(Bowker Author Biography)
Table of Contents
| Relations Between Surface and Volume Integrals: Connection Between Line Integrals and Double Integrals in the Plane |
| Vector Form of the Divergence TheoremStokes's Theorem |
| Formula for Integration by Parts in Two Dimensions:Green's Theorem |
| 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 |