Introduction to Linear Algebra for Science and Engineering, 3rd edition

  • Dan Wolczuk
  • Daniel Norman

Introduction to Linear Algebra for Science and Engineering

ISBN-13:  9780134682631


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Norman/Wolczuk’s An Introduction to Linear Algebra for Science and Engineering has been widely respected for its unique approach, which helps students understand and apply theory and concepts by combining theory with computations and slowly bringing students to the difficult abstract concepts. This approach includes an early treatment of vector spaces and complex topics in a simpler, geometric context. An Introduction to Linear Algebra for Science and Engineering promotes advanced thinking and understanding by encouraging students to make connections between previously learned and new concepts and demonstrates the importance of each topic through applications.


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Table of contents

CHAPTER 1 Euclidean Vector Spaces

1.1 Vectors in R2 and R3

1.2 Spanning and Linear Independence in R2 and R3

1.3 Length and Angles in R2 and R3

1.4 Vectors in Rn

1.5 Dot Products and Projections in Rn


CHAPTER 2 Systems of Linear Equations

2.1 Systems of Linear Equations and Elimination

2.2 Reduced Row Echelon Form, Rank, and Homogeneous Systems

2.3 Application to Spanning and Linear Independence

2.4 Applications of Systems of Linear Equations


CHAPTER 3 Matrices, Linear Mappings, and Inverses

3.1 Operations on Matrices

3.2 Matrix Mappings and Linear Mappings

3.3 Geometrical Transformations

3.4 Special Subspaces

3.5 Inverse Matrices and Inverse Mappings

3.6 Elementary Matrices

3.7 LU-Decomposition


CHAPTER 4 Vector Spaces

4.1 Spaces of Polynomials

4.2 Vector Spaces

4.3 Bases and Dimensions

4.4 Coordinates

4.5 General Linear Mappings

4.6 Matrix of a Linear Mapping

4.7 Isomorphisms of Vector Spaces


CHAPTER 5 Determinants

5.1 Determinants in Terms of Cofactors

5.2 Properties of the Determinant

5.3 Inverse by Cofactors, Cramer’s Rule

5.4 Area, Volume, and the Determinant


CHAPTER 6 Eigenvectors and Diagonalization

6.1 Eigenvalues and Eigenvectors

6.2 Diagonalization

6.3 Applications of Diagonalization


CHAPTER 7 Inner Products and Projections

7.1 Orthogonal Bases in Rn

7.2 Projections and the Gram-Schmidt Procedure

7.3 Method of Least Squares

7.4 Inner Product Spaces

7.5 Fourier Series


CHAPTER 8 Symmetric Matrices and Quadratic Forms

8.1 Diagonalization of Symmetric Matrices

8.2 Quadratic Forms

8.3 Graphs of Quadratic Forms

8.4 Applications of Quadratic Forms

8.5 Singular Value Decomposition


CHAPTER 9 Complex Vector Spaces

9.1 Complex Numbers

9.2 Systems with Complex Numbers

9.3 Complex Vector Spaces

9.4 Complex Diagonalization

9.5 Unitary Diagonalization


APPENDIX A Answers toMid-Section Exercises

APPENDIX B Answers to Practice Problems and Chapter Quizzes

Published by Pearson Canada (January 18th 2019) - Copyright © 2020