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Advanced calculus : a differential forms approach

Author: Harold M Edwards
Publisher: Boston : Birkhäuser, 1994.
Edition/Format:   Print book : English : [3rd ed.]View all editions and formats
Summary:

Offers an introduction to vector calculus based on differential forms. This book presents diverse applications, physical and mathematical, and provides a foundation for further studies.

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Genre/Form: Einführung
Problèmes et exercices
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Harold M Edwards
ISBN: 0817637079 9780817637071 3764337079 9783764337070
OCLC Number: 28255819
Notes: Originally published: Boston : Houghton Mifflin, ©1969.
Includes index.
Description: xv, 508 pages : illustrations ; 27 cm
Contents: ch. 1 Constant forms --
1.1 One-forms --
1.2 Two-forms --
1.3 The Evaluation of the two-forms, pullbacks --
1.4 Three-forms --
1.5 Summary --
ch. 2 Integrals 2.1 Non-constant forms --
2.2 Integration --
2.3 Definition of certain simple integrals, convergence and the cauchy criterion --
2.4 Integrals and pullbacks --
2.5 Independence --
2.6 Summary, Basic properties of integrals ch. 3 Integration and differentiation --
3.1 The Fundamental theorum of calculus --
3.2 The Fundamental theorum of two dimensions --
3.3 The Fundamental theorum of three dimensions --
3.4 Summary, Stokes theorum --
ch. 4 Linear algebra --
4.1 Introduction --
4.2 Constant k-form on n-space --
4.3 Matrix notation, Jacobians --
4.4 The Implicit function theorem for Affine maps --
4.5 Abstract vector spaces --
4.6 Summary, Affine manifolds --
ch. 5 Differential calculus --
5.1 The Implicit function theorem for differentiable maps --
5.2 k-forms on n-space. Differentiable maps --
5.3 Proofs --
5.4 Application: Lagrange multipliers --
5.5 Summary, Differentiable manifolds ch. 6 Integral calculus--
6.1 Summary --
6.2 k-dimensional volume --
6.3 Independence of parameter and the definiton of sine --
6.4 Manifolds-with-boundary and Stokes' theorem --
6.5 General properties of integrals --
6.6 Integrals as functions of S ch. 7 Practical methods of solution --
7.1 Successive approximation --
7.2 Solution of linear equations --
7.3 Newton's method --
7.4 Solution of ordinary differntial equations --
7.5 Three global problems --
ch. 8 Applications --
8.1 Vector calculus --
8.2 Elementary differential equations--
8.3 Harmonic functions and conformal coordinates --
8.4 Functions of a complex variable --
8.5 Integrability conditions --
8.6 Introduction to homology theory--
8.7 Flows--
8.8 Applications of mathematical physics --
ch. 9 Further study of limits --
9.1 The Real number system --
9.2 Real functions of real variables --
9.3 Uniform continuity and differentiability --
9.4 Compactness --
9.5 Other types of limits --
9.6 Interchange of limits --
9.7 Lebesgue integration --
9.8 Banach spaces.
Responsibility: Harold M. Edwards.
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"This book can serve as a delightful guide to advanced calculus, giving firm foundations to further studies." -Acta Sci. Math "An inviting, unusual, high-level introduction to vector calculus, based Read more...

 
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