Linear Algebra - Richard C. Penney

. .

Auteur(s) : Richard C. Penney

Editeur : Wiley

Langue : Anglais

Parution : 30/11/2020

Format : Moyen, de 350g à 1kg

Nombre de pages : 514

Expédition : 889

Dimensions : 23.5 x 15.7 x 3.2

ISBN : 1119656923

Résumé :

Praise for the Third Edition

This volume is ground-breaking in terms of mathematical texts in that it does not teach from a detached perspective, but instead, looks to show students that competent mathematicians bring an intuitive understanding to the subject rather than just a master of applications.
-Electric Review

Learn foundational and advanced topics in linear algebra with this concise and approachable resource

A comprehensive introduction, Linear Algebra: Ideas and Applications, Fifth Edition provides a discussion of the theory and applications of linear algebra that blends abstract and computational concepts. With a focus on the development of mathematical intuition, the book emphasizes the need to understand both the applications of a particular technique and the mathematical ideas underlying the technique.

The book introduces each new concept in the context of explicit numerical examples, which allows the abstract concepts to grow organically out of the necessity to solve specific problems. The intuitive discussions are consistently followed by rigorous statements of results and proofs. Linear Algebra: Ideas and Applications, Fifth Edition also features:

• A new application section on section on Google's Page Rank Algorithm.
• A new application section on pricing long term health insurance at a Continuing Care Retirement Community (CCRC).
• Many other illuminating applications of linear algebra with self-study questions for additional study.
• End-of-chapter summaries and sections with true-false questions to aid readers with further comprehension of the presented material
• Numerous computer exercises throughout using MATLAB code

Linear Algebra: Ideas and Applications, Fifth Edition is an excellent undergraduate-level textbook for one or two semester undergraduate courses in mathematics, science, computer science, and engineering. With an emphasis on intuition development, the book is also an ideal self-study reference.

...

Biographie:

RICHARD C. PENNEY, PHD is Emeritus Professor in the Department of Mathematics and former Director of the Mathematics/Statistics Actuarial Science Program at Purdue University. He has authored numerous journal articles, received several major teaching awards, and is an active researcher. He received his graduate education at MIT.

Sommaire:

Preface xi

Features of the Text xiii

Acknowledgments xvii

About the Companion Website xviii

1 Systems of Linear Equations 1

1.1 The Vector Space of m ? n Matrices 1

The Space ?n 4

Linear Combinations and Linear Dependence 7

What Is a Vector Space? 11

Why Prove Anything? 15

Exercises 16

1.1.1 Computer Projects/Exercises/Exercises 22

Exercises 24

1.1.2 Applications to Graph Theory I 25

Exercises 27

1.2 Systems 27

Rank: The Maximum Number of Linearly Independent Equations 34

Exercises 37

1.2.1 Computer Projects/Exercises 39

Exercises 39

1.2.2 Applications to Circuit Theory 40

Exercises 44

1.3 Gaussian Elimination 46

Spanning in Polynomial Spaces 56

Computational Issues: Pivoting 59

Exercises 60

1.3.1 Using tolerances in MATLAB's rref and rank 66

Using Tolerances in rref and Rank 66

Exercises 67

1.3.2 Applications to Traffic Flow 68

Exercises 70

1.4 Column Space and Nullspace 71

Subspaces 74

Exercises 82

1.4.1 Computer Projects/Exercises 89

Exercises 90

Chapter Summary 91

2 Linear Independence and Dimension 93

2.1 The Test for Linear Independence 93

Bases for the Column Space 100

Testing Functions for Independence 102

Exercises 104

2.1.1 Computer Projects/Exercises 108

Exercises 108

2.2 Dimension 109

Exercises 118

2.2.1 Computer Projects/Exercises 123

Exercises 123

2.2.2 Applications to Differential Equations 125

Exercises 128

2.3 Row Space and the Rank-Nullity Theorem 128

Bases for the Row Space 130

Computational Issues: Computing Rank 138

Exercises 140

2.3.1 Computer Projects/Exercises 143

Exercises 143

Chapter Summary 144

3 Linear Transformations 147

3.1 The Linearity Properties 147

Exercises 155

3.1.1 Computer Projects/Exercises 160

Exercises 161

3.2 Matrix Multiplication (Composition) 162

Partitioned Matrices 169

Computational Issues: Parallel Computing 171

Exercises 171

3.2.1 Computer Projects/Exercises 177

3-D Computer Graphics 177

Exercises 177

3.2.2 Applications to Graph Theory II 178

Exercises 180

3.2.3 Computer Projects/Exercises 180

Google's Page Rank Algorithm 180

Exercises 183

3.3 Inverses 184

Computational Issues: Reduction versus Inverses 190

Exercises 192

3.3.1 Computer Projects/Exercises 197

Ill-Conditioned Systems 197

Exercises 197

3.3.2 Applications to Economics: The Leontief Open Model 199

Exercises 204

3.4 The LU Factorization 205

Exercises 213

3.4.1 Computer Projects/Exercises 216

Exercises 216

3.5 The Matrix of a Linear Transformation 217

Coordinates 217

Application to Differential Equations 225

Isomorphism 228

Invertible Linear Transformations 229

Exercises 231

3.5.1 Computer Projects/Exercises 236

Graphing in Skewed-Coordinates 236

Exercises 236

3.5.2 Computer Projects/Exercises 237

Pricing Long Term Health Care Insurance 237

Exercises 242

Chapter Summary 242

4 Determinants 245

4.1 Definition of the Determinant 245

4.1.1 The Rest of the Proofs 252

Exercises 256

4.1.2 Computer Projects/Exercises 258

4.2 Reduction and Determinants 259

Exercises 266

4.2.1 Volume 268

Exercises 271

4.3 A Formula for Inverses 271

Exercises 275

Ch...