# Multivariable Calculus with Linear Algebra and Series

1st Edition - January 1, 1972

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• Authors: William F. Trench, Bernard Kolman
• eBook ISBN: 9781483259208

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## Description

Multivariable Calculus with Linear Algebra and Series presents a modern, but not extreme, treatment of linear algebra, the calculus of several variables, and series. Topics covered range from vectors and vector spaces to linear matrices and analytic geometry, as well as differential calculus of real-valued functions. Theorems and definitions are included, most of which are followed by worked-out illustrative examples. Comprised of seven chapters, this book begins with an introduction to linear equations and matrices, including determinants. The next chapter deals with vector spaces and linear transformations, along with eigenvalues and eigenvectors. The discussion then turns to vector analysis and analytic geometry in R3; curves and surfaces; the differential calculus of real-valued functions of n variables; and vector-valued functions as ordered m-tuples of real-valued functions. Integration (line, surface, and multiple integrals) is also considered, together with Green's and Stokes's theorems and the divergence theorem. The final chapter is devoted to infinite sequences, infinite series, and power series in one variable. This monograph is intended for students majoring in science, engineering, or mathematics.

• Preface

Acknowledgments

Chapter 1. Linear Equations and Matrices

1.1 Linear Systems and Matrices

1.2 Solution of Equations

1.3 The Inverse of a Matrix

1.4 Determinants

Chapter 2. Vector Spaces and Linear Transformations

2.1 Vector Spaces

2.2 Linear Independence and Bases

2.3 Linear Transformations

2.4 Rank of a Matrix

2.6 Eigenvalues and Eigenvectors

Chapter 3. Vectors and Analytic Geometry

3.1 Lines and Planes

3.2 Vectors in R3

3.3 Motion in R3

3.4 Parametrically Defined Curves

3.5 Coordinate Systems in R3

3.6 Surfaces in R3

Chapter 4. Differential Calculus of Real-Valued Functions

4.1 Functions, Limits, and Continuity

4.2 Directional and Partial Derivatives

4.3 Differentiable Functions

4.4 The Mean-Value Theorem

4.5 Graphs and Tangent Planes

4.6 Implicit Functions

4.8 Taylor's Theorem

4.9 Maxima and Minima

4.10 The Method of Lagrange Multipliers

Chapter 5. Differential Calculus of Vector-Valued Functions

5.1 Functions, Limits, and Continuity

5.2 Differentiable Functions

5.3 The Chain Rule

5.4 Vector and Scalar Fields

5.5 Implicit Functions

5.6 Inverse Functions and Coordinate Transformations

Chapter 6. Integration

6.1 Multiple Integrals

6.2 Iterated Integrals

6.3 Change of Variables

6.4 Physical Applications

6.5 Line Integrals

6.6 Surface Integrals of Scalar Fields

6.7 Surface Integrals of Vector Fields

6.8 The Divergence Theorem; Green's and Stokes's Theorems

Chapter 7. Series

7.1 Infinite Sequences

7.2 Infinite Series

7.3 Power Series

Index

## Product details

• No. of pages: 770
• Language: English
• Published: January 1, 1972
• eBook ISBN: 9781483259208

### Bernard Kolman

#### Affiliations and Expertise

Drexel University

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