| Description |
1 online resource (xv, 508 pages) : illustrations |
| 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 |
| Notes |
Originally published: Boston : Houghton Mifflin, ©1969 |
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Includes index |
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Print version record |
| Subject |
Calculus.
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Differential forms.
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Calculus -- Problems, exercises, etc
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calculus.
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Differential forms
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Calculus
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Infinitesimalrechnung
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Calculo (matematica) -- avancado.
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calcul différentiel.
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| Genre/Form |
Problems and exercises
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| Form |
Electronic book
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| ISBN |
9781461202714 |
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146120271X |
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