We will cover the following topics:
- Introduction, examples, models and classification [B&D, Sections 1.1, 1.2].
- First order differential equations. Linear equations, separable equations, solution by substitution and other tricks, exact equations and integrating factors. Direction field, orthogonal curves. [B&D, Sections 2.1, 2.2, 2.3, 2.5, 2.6]
- The existence an uniqueness theorem [B&D, 2.8].
- Second order and higher order linear equations. Fundamental solutions of homogeneous equations, linear independence, the Wronskian, Abel’s formula, reduction of order. Homogeneous equations with constant coefficients. Euler equations.
- Inhomogeneous linear equations. The method of undetermined coefficients, variation of parameters. [B&D, Chapters 3 and 4, Euler equation in Chapter 5]
- Systems of linear equations. Homogeneous systems with constant coefficients. Nonhomogeneous systems and variation of parameters. Linear systems in the phase plane [B&D, 7.4 – 7.9, 9.1]
- Series solutions. Solution of differential equations near an ordinary point
- Section numbers are taken from editions 7 – 9. In older editions some numbers are different.
2 hours of lecture per week
1 hours of TA per week
Elementary Differential Equations by Boyce and DiPrima, 9th edition
Course Expectations & Grading