Multivariable Calculus with Linear Algebra and Series

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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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.

Table of Contents

  • Preface


    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

    2.5 More About Rn

    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

    4.7 The Gradient

    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

    Answers to Selected Problems


Product details

  • No. of pages: 770
  • Language: English
  • Copyright: © Academic Press 1972
  • Published: January 1, 1972
  • Imprint: Academic Press
  • eBook ISBN: 9781483259208

About the Authors

William F. Trench

Bernard Kolman

Affiliations and Expertise

Drexel University

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