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Book Cover
E-book
Author Corwin, Lawrence

Title Calculus in Vector Spaces, Second Edition, Revised Expanded
Edition 2nd ed
Published New York : CRC Press, 1994

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Description 1 online resource (604 pages)
Series Chapman and Hall/CRC Pure and Applied Mathematics ; v. 189
Chapman and Hall/CRC Pure and Applied Mathematics
Contents Cover; Half Title; Title Page; Copyright Page; Preface to the Second Edition; Preface to the First Edition; Table of Contents; Chapter 1: Some Preliminaries; 1. The Rudiments of Set Theory; 2. Some Logic; 3. Mathematical Induction; 4. Inequalities and Absolute Value; 5. Equivalence Relations; Chapter 2: Vector Spaces; 1. The Cartesian Plane; 2. The Definition of a Vector Space; 3. Some Elementary Properties of Vector Spaces; 4. Subspaces; 5. Linear Transformations; 6. Linear Transformations on Euclidean Spaces; Chapter 3: The Derivative; 1. Normed Vector Spaces; 2. Open and Closed Sets
3. Continuous Functions Between Normed Vector Spaces4. Elementary Properties of Continuous Functions; 5. The Derivative; 6. Elementary Properties of the Derivative; 7. Partial Derivatives and the Jacobian Matrix; Chapter 4: The Structure of Vector Spaces; 1. Spans and Linear Independence; 2. Bases; 3. Bases and Linear Transformations; 4. The Dimension of a Vector Space; 5. Inner Product Spaces; 6. The Norm on an Inner Product Space; 7. Orthonormal Bases; 8. The Cross Product in R3; Chapter 5: Compact and Connected Sets; 1. Convergent Sequences; 2. Compact Sets; 3. Upper and Lower Bounds
4. Continuous Functions on Compact Sets5. A Characterization of Compact Sets; 6. Uniform Continuity; 7. Connected Sets; Chapter 6: The Chain Rule, Higher Derivatives, and Taylorâ#x80;#x99;s Theorem; 1. The Chain Rule; 2. Proof of the Chain Rule; 3. Higher Derivatives; 4. Taylorâ#x80;#x99;s Theorem for Functions of One Variable; 5. Taylorâ#x80;#x99;s Theorem for Functions of Two Variables; 6. Taylorâ#x80;#x99;s Theorem for Functions of n Variables; 7. A Sufficient Condition for Differentiability; 8. The Equality of Mixed Partial Derivatives; Chapter 7: Linear Transformations and Matrices
1. The Matrix of a Linear Transformation2. Isomorphisms and Invertible Matrices; 3. Change of Basis; 4. The Rank of a Matrix; 5. The Trace and Adjoint of a Linear Transformation; 6. Row and Column Operations; 7. Gaussian Elimination; Chapter 8: Maxima and Minima; 1. Maxima and Minima at Interior Points; 2. Quadratic Forms; 3. Criteria for Local Maxima and Minima; 4. Constrained Maxima and Minima: I; 5. The Method of Lagrange Multipliers; 6. Constrained Maxima and Minima: II; 7. The Proof of Proposition 2.3; Chapter 9: The Inverse and Implicit Function Theorems; 1. The Inverse Function Theorem
2. The Proof of Theorem 1.33. The Proof of the General Inverse Function Theorem; 4. The Implicit Function Theorem: I; 5. The Implicit Function Theorem: II; Chapter 10: The Spectral Theorem; 1. Complex Numbers; 2. Complex Vector Spaces; 3. Eigenvectors and Eigenvalues; 4. The Spectral Theorem; 5. Determinants; 6. Properties of the Determinant; 7. More on Determinants; 8. Quadratic Forms; Chapter 11: Integration; 1. Integration of Functions of One Variable; 2. Properties of the Integral; 3. The Integral of a Function of Two Variables; 4. The Integral of a Function of n Variables
Notes 5. Properties of the Integral
Print version record
Form Electronic book
Author Szczarba, Robert H
ISBN 9781351462822
1351462822