Linear Algebra with Applications

About our authors

Mimi Bres, Ph.D, tenured Professor, Prince George's Community College, Largo, Marylan Dr. Bres has over 20 years experience with the development of curriculum materials designed to stimulate interest in science and to improve critical thinking skills. Of particular note is her recent work developing an interactive web and video-based curriculum, including a virtual field component, to teach environmental concepts without the need for student travel.

Dr. Bres has also worked as a consultant to corporations and government agencies. She served as team leader and developer for the Environmental Protection Agency's Environmental Education Library, a series of video curriculum modules for college and high school classes which highlight hazardous chemical response and remediation projects carried out under the SuperFund Program. Dr. Bres has also served as a consultant to the Prince George's County School District in an initiative to improve the delivery of high school science courses.

As a result of her expertise, Dr. Bres has been an invited speaker at a number of national meetings and seminars. Her work on the use of cooperative learning techniques has improved both student performance and interest in science. Dr. Bres' excellence in science education has been recognized by her selection for the National Award for Innovative Excellence in Teaching, Learning, and Technology by the Center for the Advancement of Teaching and Learning, the Teaching Recognition Award by the University of Maryland University College, and Outstanding Faculty Mentor of the Year by the science division students of Prince George's Community College.

Recent books include: Thinking About Biology, 4th edition (a laboratory manual for general biology), Hands-On Biology: Laboratories for Distance Learning (a laboratory manual for online general biology courses), Human Biology: Condensed, 7th edition (a simplified lecture study guide that incorporates problem solving activities into the curriculum), and Cooperative Learning: Making Connections in General Biology (a collection of cooperative activities).

Arnold Weisshaar, Professor Emeritus, Prince George's Community College, Largo, Maryland

Professor Weisshaar has had a distinguished 36 year career in higher education. During his career, he has been the spearhead of several initiatives to improve science education and expand the College's program offerings. In the classroom, Professor Weisshaar has worked extensively with underprepared students of diverse social and ethnic backgrounds.

In an attempt to improve instructional delivery, he has co-authored a variety of support materials for students. Recent publications include laboratory manuals for general biology, including: Thinking About Biology, 4th edition and Hands-On Biology: Laboratories for Distance Learning and a simplified lecture study guide that incorporates problem solving activities into the curriculum (Human Biology: Condensed, 7th edition).

1. Linear Equations

1.1 Introduction to Linear Systems

1.2 Matrices, Vectors, and Gauss-Jordan Elimination

1.3 On the Solutions of Linear Systems; Matrix Algebra

2. Linear Transformations

2.1 Introduction to Linear Transformations and Their Inverses

2.2 Linear Transformations in Geometry

2.3 Matrix Products

2.4 The Inverse of a Linear Transformation

3. Subspaces of Rⁿ and Their Dimensions

3.1 Image and Kernel of a Linear Transformation

3.2 Subspace of Rⁿ; Bases and Linear Independence

3.3 The Dimension of a Subspace of Rⁿ

3.4 Coordinates

4. Linear Spaces

4.1 Introduction to Linear Spaces

4.2 Linear Transformations and Isomorphisms

4.3 The Matrix of a Linear Transformation

5. Orthogonality and Least Squares

5.1 Orthogonal Projections and Orthonormal Bases

5.2 Gram-Schmidt Process and QR Factorization

5.3 Orthogonal Transformations and Orthogonal Matrices

5.4 Least Squares and Data Fitting

5.5 Inner Product Spaces

6. Determinants

6.1 Introduction to Determinants

6.2 Properties of the Determinant

6.3 Geometrical Interpretations of the Determinant; Cramer's Rule

7. Eigenvalues and Eigenvectors

7.1 Diagonalization

7.2 Finding the Eigenvalues of a Matrix

7.3 Finding the Eigenvectors of a Matrix

7.4 More on Dynamical Systems

7.5 Complex Eigenvalues

7.6 Stability

8. Symmetric Matrices and Quadratic Forms

8.1 Symmetric Matrices

8.2 Quadratic Forms

8.3 Singular Values

9. Linear Differential Equations

9.1 An Introduction to Continuous Dynamical Systems

9.2 The Complex Case: Euler's Formula

9.3 Linear Differential Operators and Linear Differential Equations

Appendix A. Vectors

Appendix B: Techniques of Proof

Answers to Odd-numbered Exercises

Subject Index

Name Index

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.