Differential Equations and Linear Algebra, Global Edition (4^th Ed.)

For courses in Differential Equations and Linear Algebra.
The right balance between concepts, visualisation, applications, and skills
Differential Equations and Linear Algebra provides the conceptual development and geometric visualisation of a modern differential equations and linear algebra course that is essential to science and engineering students. It balances traditional manual methods with the new, computer-based methods that illuminate qualitative phenomena - a comprehensive approach that makes accessible a wider range of more realistic applications.
The book combines core topics in elementary differential equations with concepts and methods of elementary linear algebra. It starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout.

• Chapter 1: First-Order Differential Equations
• Chapter 2: Mathematical Models and Numerical Methods
• Chapter 3: Linear Systems and Matrices
• Chapter 4: Vector Spaces
• Chapter 5: Higher-Order Linear Differential Equations
• Chapter 6: Eigenvalues and Eigenvectors
• Chapter 7: Linear Systems of Differential Equations
• Chapter 8: Matrix Exponential Methods
• Chapter 9: Nonlinear Systems and Phenomena
• Chapter 10: Laplace Transform Methods
• Chapter 11: Power Series Methods
• Appendix A: Existence and Uniqueness of Solutions
• Appendix B: Theory of Determinants
• Answers to Selected Problems
• Index

Download the detailed table of contents

About the Book

Build on conceptual ideas and the use of applications and projects to involve students in active problem-solving experiences

• 600 computer-generated figures show students vivid pictures of direction fields, solution curves, and phase plane portraits that bring symbolic solutions of differential equations to life.
  • NEW! Nearly 80 new figures illustrating interactive computer applications
• Application modules follow key sections throughout. Most outline "technology neutral" investigations illustrating the use of technical computing systems and seek to actively engage students in the application of new technology.
• A fresh numerical emphasis is afforded by the early introduction of numerical solution techniques in Chapter 2 (on mathematical models and numerical methods). Includes numerical algorithms presented in parallel fashion for systems ranging from graphing calculators to MATLAB.
• A conceptual perspective shaped by the availability of computational aids permits a leaner and more streamlined coverage of certain traditional symbolic methods (like exact equations and variation of parameters).

Widely used technical computing environments used by practicing engineers and scientists are heavily integrated with content

• NEW! Now includes Python, an increasingly popular computer platform that is freely available on the internet and an all-purpose scientific computing environment.
• NEW! The online Expanded Applications companion website enhances the text's applications material through technology, and provides detailed coverage of Maple, Mathematica, and M