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Full Description
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.
Contents
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
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