TY  - BOOK
AU  - Marsden,Jerrold E
AU  - Hoffman,Michael J
TI  - Elementary classical analysis
SN  - 0716721058
AV  - QA300 .M2868 1993
PY  - 1993///]
CY  - New York
PB  - W.H. Freeman
KW  - Mathematical analysis
N1  - Includes bibliographical references and index; Contents; Preface; Preface to the First Edition; Introduction: Sets and Functions; 1	The Real Line and Euclidean Space; 1.1	Ordered Fields and the Number System; 1.2	Completeness and the Real Number System; 1.3	Least Upper Bounds; 1.4	Cauchy Sequences; 1.5	Cluster Points; lim inf and lim sup; 1.6	Euclidean Space; 1.7	Norms, Inner Products, and Metrics; 1.8	The Complex Numbers; 2	The Topology of Euclidean Space; 2.1	Open Sets; 2.2	Interior of a Set; 2.3	Closed Sets; 2.4	Accumulation Points; 2.5	Closure of a Set; 2.6	Boundary of a Set; 2.7	Sequences; 2.8	Completeness; 2.9	Series of Real Numbers and Vectors; 3	Compact and Connected Sets; 3.1	Compactness; 3.2	The Heine-Borel Theorem; 3.3	Nested Set Property; 3.4	Path-Connected Sets; 3.5	Connected Sets; 4	Continuous Mappings; 4.1	Continuity; 4.2	Images of Compact and Connected Sets; 4.3	Operations on Continuous Mappings; 4.4	The Boundedness of Continuous Functions on Compact Sets; 4.5	The Intermediate Value Theorem; 4.6	Uniform Continuity; 4.7	Differentiation of Functions of One Variable; 4.8	Integration of Functions of One Variable; 5	Uniform Convergence; 5.1	Pointwise and Uniform Convergence; 5.2	The Weierstrass M Test; 5.3	Integration and Differentiation of Series; 5.4	The Elementary Functions; 5.5	The Space of Continuous Functions; 5.6	The Arzela-Ascoli Theorem; 5.7	The Contraction Mapping Principle and Its Applications; 5.8	The Stone-Weierstrass Theorem; 5.9	The Dirichlet and Abel Tests; 5.10	Power Series and Cesaro and Abel Summability; 6	Differentiable Mappings; 6.1	Definition of the Derivative; 6.2	Matrix Representation; 6.3	Continuity of Differentiable Mappings; Differentiable Paths; 6.4	Conditions for Differentiability; 6.5	The Chain Rule; 6.6	Product Rule and Gradients; 6.7	The Mean Value Theorem; 6.8	Taylor's Theorem and Higher Derivatives; 6.9	Maxima and Minima; 7	The Inverse and Implicit Function Theorems and Related Topics; 7.1	Inverse Function Theorem; 7.2	Implicit Function Theorem; 7.3	The Domain-Straightening Theorem; 7.4	Further Consequences of the Implicit Function Theorem; 7.5	An Existence Theorem for Ordinary Differential Equations; 7.6	The Morse Lemma; 7.7	Constrained Extrema and Lagrange Multipliers; 8	Integration; 8.1	Integrable Functions; 8.2	Volume and Sets of Measure Zero; 8.3	Lebesgue's Theorem; 8.4	Properties of the Integral; 8.5	Improper Integrals; 8.6	Some Convergence Theorems; 8.7	Introduction to Distributions; 9	Fubini's Theorem and the Change of Variables Formula; 9.2	Fubini's Theorem; 9.3	Change of Variables Theorem; 9.4	Polar Coordinates; 9.5	Spherical and Cylindrical Coordinates; 9.6	A Note on the Lebesgue Integral; 9.7	Interchange of Limiting Operations; 10	Fourier Analysis; 10.1	Inner Product Spaces; 10.2	Orthogonal Families of Functions; 10.3	Completeness and Convergence Theorems; 10.4	Functions of Bounded Variation and Fejer Theory (Optional); 10.5	Computation of Fourier Series; 10.6	Further Convergence Theorems; 10.7	Applications; 10.8	Fourier Integrals; 10.9	Quantum Mechanical Formalism; Appendix A: Miscellaneous Exercises; Appendix B: References and Suggestions for Further Study; Appendix C: Answers and Suggestions for Selected Odd-Numbered Exercises; Index
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