Differential Equations and Linear Algebra
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,...
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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 Equations2. Matrices and Systems of Linear Equations3. Determinants4. Vector Spaces5. Linear Transformation6. Linear Differential Equations of Order n7. Systems of Differential Equations8. The Laplace Transform and Some Elementary Applications9. Series Solutions to Linear Differential EquationsAppendicesA. Review of Complex NumbersB. Review of Partial FractionsC. Review of Integration TechniquesD. Linearly Independent Solutions to x2yn + xp(x)y1 + q(x)y = 0E. Answers to Odd-Numbered Exercises
