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). Meanwhile 10th Edition is out of print.
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).
In comparison with 10th Edition, 11th has an additional author. Usually the main difference between edition is that the problems are shuffled; so their numeration differ. Home assignments will use numbers from the textbook. This makes older editions unusable for home assignments.
Note: Chapter 5 will be covered (if at all) at the very end of the course.
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,