Trench / Kolman Multivariable Calculus with Linear Algebra and Series

1. Auflage 2014
ISBN: 978-1-4832-5920-8
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 770 Seiten, Web PDF

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.

Autoren/Hrsg.

Trench, William F.

Kolman, Bernard

Inhaltsverzeichnis

1;Front Cover;1
2;Multivariable Calculus with Linear Algebra and Series;4
3;Copyright Page;5
4;Table of Contents;8
5;Dedication
;6
6;Preface;10
7;Acknowledgments;12
8;Chapter 1. Linear Equations and Matrices;14
8.1;1.1 Linear Systems and Matrices;14
8.2;1.2 Solution of Equations;39
8.3;1.3 The Inverse of a Matrix;59
8.4;1.4 Determinants;78
9;Chapter 2. Vector Spaces and Linear Transformations;107
9.1;2.1 Vector Spaces;107
9.2;2.2 Linear Independence and Bases;118
9.3;2.3 Linear Transformations;137
9.4;2.4 Rank of a Matrix;164
9.5;2.5 More about Rn;180
9.6;2.6 Eigenvalues and Eigenvectors;200
10;Chapter 3. Vectors and Analytic Geometry;228
10.1;3.1 Lines and Planes;228
10.2;3.2 Vectors in R3;246
10.3;3.3 Motion in R3;271
10.4;3.4 Parametrically Defined Curves;286
10.5;3.5 Coordinate Systems in R3;300
10.6;3.6 Surfaces in R3;311
11;Chapter 4. Differential Calculus of Real-Valued Functions;321
11.1;4.1 Functions, Limits, and Continuity;321
11.2;4.2 Directional and Partial Derivatives;340
11.3;4.3 Differentiable Functions;352
11.4;4.4 The Mean-Value Theorem;365
11.5;4.5 Graphs and Tangent Planes;371
11.6;4.6 Implicit Functions;379
11.7;4.7 The Gradient;388
11.8;4.8 Taylor's Theorem;399
11.9;4.9 Maxima and Minima;413
11.10;4.10 The Method of Lagrange Multipliers;425
12;Chapter 5. Differential Calculus of Vector- Valued Functions;439
12.1;5.1 Functions, Limits, and Continuity;439
12.2;5.2 Differentiable Functions;455
12.3;5.3 The Chain Rule;465
12.4;5.4 Vector and Scalar Fields;479
12.5;5.5 Implicit Functions;494
12.6;5.6 Inverse Functions and Coordinate Transformations;505
13;Chapter 6. Integration;517
13.1;6.1 Multiple Integrals;517
13.2;6.2 Iterated Integrals;533
13.3;6.3 Change of Variables;548
13.4;6.4 Physical Applications;569
13.5;6.5 Line Integrals;592
13.6;6.6 Surface Integrals of Scalar Fields;627
13.7;6.7 Surface Integrals of Vector Fields;645
13.8;6.8 The Divergence Theorem; Green's and Stokes's Theorems;661
14;Chapter 7. Series;676
14.1;7.1 Infinite Sequences;676
14.2;7.2 Infinite Series;689
14.3;7.3 Power Series;708
15;Answers to Selected Problems;726
16;Subject Index;764