Name: Multivariable Mathematics - Linear Algebra, Multivariable Calculus and Manifolds By T Shifrin
SKU: 9780471526384
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Multivariable Mathematics - Linear Algebra, Multivariable Calculus and Manifolds Summary

Multivariable Mathematics - Linear Algebra, Multivariable Calculus and Manifolds by T Shifrin

Multivariable Mathematics combines linear algebra and multivariable mathematics in a rigorous approach. The material is integrated to emphasize the recurring theme of implicit versus explicit that persists in linear algebra and analysis. In the text, the author includes all of the standard computational material found in the usual linear algebra and multivariable calculus courses, and more, interweaving the material as effectively as possible, and also includes complete proofs. Contains plenty of examples, clear proofs, and significant motivation for the crucial concepts. Numerous exercises of varying levels of difficulty, both computational and more proof-oriented. Exercises are arranged in order of increasing difficulty.

About T Shifrin

Theodore Shifrin is the author of Multivariable Mathematics: Linear Algebra, Multivariable Calculus, and Manifolds, published by Wiley.

Preface.Chapter 1. Vectors and Matrices.1.1 Vectors in Rn.1.2 Dot Product.1.3 Subspaces of Rn.1.4 Linear Transformations and Matrix Algebra.1.5 Introduction to Determinates and the Cross Product.Chapter 2. Functions, Limits, and Continuity.2.1. Scalar- and Vector-Valued Functions.2.2. A Bit of Topology in Rn.2.3. Limits and Continuity.Chapter 3. The Derivative.3.1. Partial Derivatives and Directional Derivatives.3.2. Differentiability.3.3. Differentiation Rules.3.4. The Gradient.3.5. Curves.3.6. Higher-Order Partial Derivatives.Chapter 4. Implicit and Explicit Solutions of Linear Systems.4.1. Gaussian Elimination and the Theory of Linear Systems.4.2. Elementary Matrices and Calculating Inverse Matrices.4.3. Linear Independence, Basis, and Dimension.4.4. The Four Fundamental Subspaces.4.5. The Nonlinear Case: Introduction to Manifolds.Chapter 5. Extremum Problems.5.1. Compactness and the Maximum Value Theorem.5.2. Maximum/Minimum Problems.5.3. Quadratic Forms and the Second Derivative Test.5.4. Lagrange Multipliers.5.5. Projections, Least Squares, and Inner Product Spaces. Chapter 6. Solving Nonlinear Problems.6.1. The Contraction Mapping Principle.6.2. The Inverse and Implicit Function Theorems.6.3. Manifolds Revisited.Chapter 7. Integration.7.1. Multiple Integrals.7.2. Iterated Integrals and Fubini's Theorem.7.3. Polar, Cylindrical, and Spherical Coordinates.7.4. Physical Applications.7.5. Determinants and n-Dimensional Volume.7.6. Change of Variables Theorem.Chapter 8. Differential Forms and Integration on Manifolds.8.1. Motivation.8.2. Differential Forms.8.3. Line Integrals and Green's Theorem.8.4. Surface Integrals and Flux.8.5. Stokes's Theorem.8.6. Applications to Physics.8.7. Applications to Topology.9. Eigenvalues, Eigenvectors, and Applications.9.1. Linear Transformations and Change of Basis.9.2. Eigenvalues, Eigenvectors, and Diagonalizability.9.3. Difference Equations and Ordinary Differential Equations.9.4. The Spectral Theorem.Glossary of Notations and Results from Single-Variable Calculus.For Further Reading.Answers to Selected Exercises.Index.

Additional information

Sku

CIN047152638XG

ISBN 13

9780471526384

ISBN 10

047152638X

Title

Multivariable Mathematics - Linear Algebra, Multivariable Calculus and Manifolds by T Shifrin

Author

T Shifrin

Condition

Used - Good

Binding type

Hardback

Publisher

John Wiley & Sons Inc

Year published

20040122

Number of pages

512

Prizes

N/A

Cover note

Book picture is for illustrative purposes only, actual binding, cover or edition may vary.

Note

This is a used book - there is no escaping the fact it has been read by someone else and it will show signs of wear and previous use. Overall we expect it to be in good condition, but if you are not entirely satisfied please get in touch with us

Multivariable Mathematics - Linear Algebra, Multivariable Calculus and Manifolds T Shifrin

Multivariable Mathematics - Linear Algebra, Multivariable Calculus and Manifolds by T Shifrin

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Multivariable Mathematics - Linear Algebra, Multivariable Calculus and Manifolds Summary

Multivariable Mathematics - Linear Algebra, Multivariable Calculus and Manifolds by T Shifrin

About T Shifrin

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