Differential Equations

For combined differential equations and linear algebra courses teaching students who have successfully completed three semesters of calculus. This complete introduction to both differential equations and linear algebra presents a carefully balanced and sound integration of the two topics. It promotes in-depth understanding rather than rote memorization, enabling students to fully comprehend abstract concepts and leave the course with a solid foundation in linear algebra. Flexible in format, it explains concepts clearly and logically with an abundance of examples and illustrations, without sacrificing level or rigor. A vast array of problems supports the material, with varying levels from which students/instructors can choose.1. First-Order Differential Equations 2. Matrices and Systems of Linear Equations 3. Determinants 4. Vector Spaces 5. Linear Transformation 6. Linear Differential Equations of Order n 7. Systems of Differential Equations 8. Series Solutions to Linear Differential Equations 9. The Laplace Transform and Some Elementary Applications Appendices A. Review of Complex Numbers B. Review of Partial Fractions C. Review of Integration Techniques D. Linearly Independent Solutions to x2yn + xp(x)y1 + q(x)y = 0 E. Answers to Odd-Numbered Exercises