A Modern Introduction to Differential Equations, Third Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical and numerical aspects of first-order equations, including slope fields and phase lines. The comprehensive resource then covers methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients, systems of linear differential equations, the Laplace transform and its applications to the solution of differential equations and systems of differential equations, and systems of nonlinear equations.
Throughout the text, valuable pedagogical features support learning and teaching. Each chapter concludes with a summary of important concepts, and figures and tables are provided to help students visualize or summarize concepts. The book also includes examples and updated exercises drawn from biology, chemistry, and economics, as well as from traditional pure mathematics, physics, and engineering.
1. Chapter 1: Introduction to differential equations - p. 1 2. Chapter 2: First-order differential equations - p. 27 3. Chapter 3: The numerical approximation of solutions - p. 111 4. Chapter 4: Second- and higher-order equations - p. 143 5. Chapter 5: The Laplace transform - p. 185 6. Chapter 6: Systems of linear differential equations - p. 231 7. Chapter 7: Systems of nonlinear differential equations - p. 361 8. Appendix A: Some calculus concepts and results - p. 421 9. Appendix B: Vectors and matrices - p. 433 10. Appendix C: Complex numbers - p. 445 11. Appendix D: Series solutions of differential equations - p. 449 12. Answers and hints to odd-numbered exercises - p. 461 13. Index - p. 525
A Modern Introduction to Differential Equations, Third Edition, provides an introduction to the basic concepts of differential equations. The book begins by introducing the basic concepts of differential equations, focusing on the analytical, graphical and numerical aspects of first-order equations, including slope fields and phase lines. The comprehensive resource then covers methods of solving second-order homogeneous and nonhomogeneous linear equations with constant coefficients, systems of linear differential equations, the Laplace transform and its applications to the solution of differential equations and systems of differential equations, and systems of nonlinear equations.
Throughout the text, valuable pedagogical features support learning and teaching. Each chapter concludes with a summary of important concepts, and figures and tables are provided to help students visualize or summarize concepts. The book also includes examples and updated exercises drawn from biology, chemistry, and economics, as well as from traditional pure mathematics, physics, and engineering.
1. Chapter 1: Introduction to differential equations - p. 1 2. Chapter 2: First-order differential equations - p. 27 3. Chapter 3: The numerical approximation of solutions - p. 111 4. Chapter 4: Second- and higher-order equations - p. 143 5. Chapter 5: The Laplace transform - p. 185 6. Chapter 6: Systems of linear differential equations - p. 231 7. Chapter 7: Systems of nonlinear differential equations - p. 361 8. Appendix A: Some calculus concepts and results - p. 421 9. Appendix B: Vectors and matrices - p. 433 10. Appendix C: Complex numbers - p. 445 11. Appendix D: Series solutions of differential equations - p. 449 12. Answers and hints to odd-numbered exercises - p. 461 13. Index - p. 525
