Differential Equations and Linear Algebra 4th Edition Goode Solutions Manual
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Differential Equations and Linear Algebra 4th Edition Goode Solutions Manual.
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Product details:
- ISBN-10 : 013449718X
- ISBN-13 : 978-0134497181
- Author:
In a contemporary introduction to differential equations and linear algebra, acclaimed authors Edwards and Penney combine core topics in elementary differential equations with concepts and methods of elementary linear algebra. Renowned for its real-world applications and blend of algebraic and geometric approaches, Differential Equations and Linear Algebra introduces you to mathematical modeling of real-world phenomena and offers the best problems sets in any differential equations and linear algebra textbook. The 4th Edition includes fresh new computational and qualitative flavor evident throughout in figures, examples, problems, and applications. Additionally, an Expanded Applications website containing expanded applications and programming tools is now available.
Table of contents:
Preface ix 1 First-Order Differential Equations 1
1.1 Differential Equations Everywhere 1
1.2 Basic Ideas and Terminology 13
1.3 The Geometry of First-Order Differential Equations 23
1.4 Separable Differential Equations 34
1.5 Some Simple Population Models 45
1.6 First-Order Linear Differential Equations 53
1.7 Modeling Problems Using First-Order Linear Differential Equations 61
1.8 Change of Variables 71
1.9 Exact Differential Equations 82
1.10 Numerical Solution to First-Order Differential Equations 93
1.11 Some Higher-Order Differential Equations 101
1.12 Chapter Review 106 2 Matrices and Systems of Linear Equations 114
2.1 Matrices: Definitions and Notation 115
2.2 Matrix Algebra 122
2.3 Terminology for Systems of Linear Equations 138
2.4 Row-Echelon Matrices and Elementary Row Operations 146
2.5 Gaussian Elimination 156
2.6 The Inverse of a Square Matrix 168
2.7 Elementary Matrices and the LU Factorization 179
2.8 The Invertible Matrix Theorem I 188
2.9 Chapter Review 190
3 Determinants 196
3.1 The Definition of the Determinant 196
3.2 Properties of Determinants 209
3.3 Cofactor Expansions 222
3.4 Summary of Determinants 235
3.5 Chapter Review 242
4 Vector Spaces 246
4.1 Vectors in Rn 248
4.2 Definition of a Vector Space 252
4.3 Subspaces 263
4.4 Spanning Sets 274
4.5 Linear Dependence and Linear Independence 284
4.6 Bases and Dimension 298
4.7 Change of Basis 311
4.8 Row Space and Column Space 319
4.9 The Rank-Nullity Theorem 325
