Science:Math Exam Resources/Courses/MATH215/Syllabus

Official course syllabus here.

First order equations

Integrals as solutions 1.1

Slope fields and unique existence 1.2

Separable equations 1.3

Linear equations and the integrating factor 1.4

Exact equations (notes)

Autonomous equations 1.6

Numerical methods: Euler’s method 1.7

Second order linear equations

Second order linear ODEs (method of reduction of order) 2.1

Constant coefficient second order linear ODEs (2.2 and notes)

Mechanical vibrations 2.4

Nonhomogeneous equations (undetermined coefficients and variation of parameters) 2.5

Forced oscillations and resonance 2.6

Laplace transforms

Definition and examples 6.1

Transforms of derivatives and ODEs 6.2

Convolution 6.3

Dirac delta and impulse response 6.4

4. Linear systems

Introduction to systems of ODEs 3.1–3.3

Eigenvalue method 3.4

Two dimensional systems and their vector fields 3.5

Second order systems and applications 3.6

Multiple eigenvalues 3.7

Matrix exponentials 3.8

Nonhomogeneous systems 3.9

Nonlinear autonomous planar systems

Critical points and linearization 8.1

Stability and classification of isolated critical points 8.2

Applications 8.3