uOttawa MAT 1322 Calculus II: Syllabus, Topics and Practice
A study guide for University of Ottawa MAT 1322 (Calculus II): improper integrals, differential equations, series, Taylor series and partial derivatives.
University of Ottawa Updated 3 min read
At a glance
- Course code
- MAT 1322
- Units
- 3 (lecture and discussion group)
- Prerequisites
- MAT 1320 or MAT 1321
- Credit restriction
- MAT 1322, MAT 1303, MAT 1332 and MAT 1325 cannot be combined for units
- Covers
- Improper integrals, applications of the integral, separable differential equations, Euler's method, sequences, series, Taylor's formula and series, functions of two and three variables, partial derivatives, chain rule, directional derivatives, tangent planes and normal lines
- Next course
- MAT 2322 (Calculus III for Engineers)
- Practice here
- Calculus 2
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On this page
MAT 1322 is Calculus II at the University of Ottawa, the English-language course that follows MAT 1320 or MAT 1321. Since uOttawa already teaches integration techniques in Calculus I, MAT 1322 can spend its time on what you do with integrals, on differential equations and series, and on a first look at functions of several variables. This guide maps every MAT 1322 topic to free practice.
What uOttawa MAT 1322 covers
The uOttawa catalogue lists: improper integrals; applications of the integral; separable differential equations; Euler's method for differential equations; sequences and series; Taylor's formula and series; functions of two and three variables; and partial derivatives, the chain rule, directional derivatives, tangent planes and normal lines. The course has lectures and discussion groups, and the prerequisite is MAT 1320 or MAT 1321.
That combines most of a standard Calculus 2 with the first part of Calculus 3. Parametric and polar curves are not in the catalogue description.
MAT 1322 topic map
| MAT 1322 topic | Practice | Read |
|---|---|---|
| Improper integrals | Infinite limits of integration, infinite discontinuities | Improper integrals guide |
| Applications of the integral | Volumes with washers, arc length, work | Volumes of revolution |
| Separable differential equations | Separable equations | Growth and decay |
| Euler's method | Euler's method | Slope fields |
| Sequences | Sequences | Squeeze theorem |
| Series and convergence | Series and partial sums, choosing a test | Convergence tests |
| Taylor's formula | Taylor polynomials, estimating with Taylor | Taylor's theorem |
| Taylor series | Maclaurin series | Taylor series guide |
| Functions of two and three variables | Functions of several variables | |
| Partial derivatives and the chain rule | Partial derivatives, multivariable chain rule | Partial derivatives guide |
| Directional derivatives | Gradient and directional derivatives | Gradient guide |
| Tangent planes and normal lines | Tangent planes |
MAT 1322 in the uOttawa sequence
| Course | Title | Main focus |
|---|---|---|
| MAT 1320 | Calculus I | Derivatives, integration techniques, numerical integration |
| MAT 1322 | Calculus II | Improper integrals, ODEs, series, partial derivatives |
| MAT 2322 | Calculus III for Engineers | Multiple integrals and vector calculus |
MAT 1322 cannot be combined for units with MAT 1303, MAT 1332 or MAT 1325.
Example problems at the MAT 1322 level
1. An improper integral with a discontinuity.
2. Euler's method. For y' = y, y(0) = 1 and step h = 0.5: y_1 = 1 + 0.5(1) = 1.5 and y_2 = 1.5 + 0.5(1.5) = 2.25, an estimate of e \approx 2.718.
3. Taylor's formula. The degree 3 Taylor polynomial of \ln(1 + x) at 0 is x - \frac{x^2}{2} + \frac{x^3}{3}.
4. A normal line. For the surface x^2 + y^2 + z^2 = 14 at (1, 2, 3), the gradient \langle 2, 4, 6 \rangle gives the normal line \langle 1 + 2t,\; 2 + 4t,\; 3 + 6t \rangle.
How to do well in MAT 1322
- Keep MAT 1320 techniques ready. Improper integrals and applications assume fluent substitution, parts and partial fractions.
- Write limits explicitly. Every improper integral is a limit. Show it in your working.
- Practise series reasoning. Name the test, check its conditions, and state convergence or divergence clearly.
- Change gears for several variables. The last unit is new territory. Slow down and practise partial derivatives until holding variables constant feels natural.
Tip: the gradient of F(x, y, z) is normal to the level surface F = c. That gives both tangent planes and normal lines in one step.
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