Differential Equations and Linear Algebra, 4th Edition

Differential Equations and Linear Algebra is designed for use in combined differential equations and linear algebra courses. It is best suited for students who have successfully completed three semesters of calculus.

Differential Equations and Linear Algebra presents a carefully balanced and sound integration of both differential equations and linear algebra. It promotes in-depth understanding rather than rote memorization, enabling readers to fully comprehend abstract concepts and leave the course with a solid foundation in key areas. Flexible in format, it explains concepts clearly and logically with an abundance of examples and illustrations, without sacrificing level or rigor. The Fourth Edition includes many updated problems to support the material, with varying difficulty levels from which students/instructors can choose.

Table of Contents

Chapter 1 First-Order Differential Equations
Chapter 2 Matrices And Systems Of Linear Equations
Chapter 3 Determinants
Chapter 4 Vector Spaces
Chapter 5 Inner Product Spaces
Chapter 6 Linear Transformations
Chapter 7 Eigenvalues And Eigenvectors
Chapter 8 Linear Differential Equations Of Order N
Chapter 9 Systems Of Differential Equations
Chapter 10 The Laplace Transform And Some Elementary Applications
Chapter 11 Series Solutions To Linear Differential Equations
Appendix A Review Of Complex Numbers
Appendix B Review Of Partial Fractions
Appendix C Review Of Integration Techniques
Appendix D Linearly Independent Solutions To X2Y″ + Xp(X)Y′ + Q(X)Y = 0