First order ordinary differential equations: Direction fields, integrating factors, separable equations, homogeneous equations, exact equations, autonomous equations, modeling. Existence and uniqueness theorem. Higher order equations: Constant coefficient equations, reduction of order, Wronskian, method of undetermined coefficients, variation of parameters. Solutions by series and integrals. First order linear systems, fundamental matrices. Non-linear equations, phase plane, stability. Applications in life and physical sciences and economics.
- Prerequisite: (MAT135H1, MAT136H1)/MAT137Y1/MAT157Y1, MAT223H1/MAT240H1
- Corequisite: MAT235Y1/MAT237Y1/MAT257Y1
- Exclusion: MAT267H1, MAT212H5, MAT258Y5
- Distribution Requirements: Science
- Breadth Requirements: The Physical and Mathematical Universes (5)
In Canada it is available as electronic resource only; printed editions (hardcover or paperback) are not available (unless by premium price).
There are two different books ("with Boundary Value Problems" and without them; the second one is simply a shorter version but it costs the same; BVP for ODE are usually addressed in PDE (Partial Differential Equations) class).
Note: Chapter 5 will be covered (if at all) at the very end of the course, if the time permits.
Your Final Mark will be computed as follows: \begin{gather*} \mathsf{FM}= \min\bigl[ \mathsf{Q} + \mathsf{BM}+\mathsf{T}_1 + \mathsf{T}_2 + \mathsf{FEM},\, 100\bigr],\\[3pt] \mathsf{Q} = \mathsf{Q}_1 + \mathsf{Q}_2+\mathsf{Q}_3 + \mathsf{Q}_4 + \mathsf{Q}_5 + \mathsf{Q}_6 + \mathsf{Q}_7 \qquad \text{with 2 worst Quizzes dropped} \end{gather*} where $\mathsf{FM}$ and $\mathsf{FE}$ are your Final Mark, and the Final Exams Mark respectively,