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University of Alberta

UAlberta MATH 146 Calculus II: Syllabus, Topics and Practice

A study guide for University of Alberta MATH 146: integration techniques, improper integrals, differential equations and partial derivatives.

University of Alberta Updated 3 min read

At a glance

Course code
MATH 146
Units
3 (fi 6), 3 lecture hours per week, offered in either term
Prerequisites
One of MATH 100, 113, 114, 117, 134, 144 or 154
Credit restriction
Credit in at most one of MATH 101, 115, 118, 136, 146, 156 or SCI 100
Covers
Techniques and applications of integration, improper integrals, introduction to differential equations, partial differentiation
Next course
MATH 214 (Calculus III)
Practice here
Calculus 2

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For $\int x\,e^{x}\,dx$, which choice of $u$ makes things simpler?
\int x\,e^{x}\,dx
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On this page
  1. What UAlberta MATH 146 covers
  2. MATH 146 topic map
  3. Where MATH 146 sits
  4. Example problems at the MATH 146 level
  5. How to do well in MATH 146

MATH 146 is Calculus for the Mathematical and Physical Sciences II at the University of Alberta. It picks up where MATH 144 ends, at the Fundamental Theorem of Calculus, and builds out integration: the main techniques, their applications, improper integrals and a first course in differential equations. It also gives a short introduction to partial derivatives. This guide maps each MATH 146 topic to free practice.

What UAlberta MATH 146 covers

The UAlberta catalogue describes MATH 146 as: techniques and applications of integration; improper integrals; introduction to differential equations; partial differentiation; with applications in the context of the physical sciences. It is a 3-unit course with three lecture hours a week, and it needs one of MATH 100, 113, 114, 117, 134, 144 or 154.

Compared with a typical Calculus 2, MATH 146 has the integration and differential equations, but not sequences and series. Those appear in MATH 214. In their place, MATH 146 starts on several-variable calculus with partial differentiation.

MATH 146 topic map

MATH 146 topic Practice Read
Substitution review u-substitution refresher u-substitution rule
Integration by parts Integration by parts Integration by parts guide
Trig integrals Trig integrals Integral of sec x
Trig substitution Trig substitution Trig substitution guide
Partial fractions Partial fractions Partial fractions guide
Areas and volumes Volumes with disks Volumes of revolution
Arc length, work, centre of mass Work, centre of mass Arc length
Improper integrals Infinite limits of integration Improper integrals guide
Differential equations Separable equations Slope fields, Euler's method
Partial differentiation Partial derivatives Partial derivatives guide

Where MATH 146 sits

Course Title Main focus
MATH 144 Calculus for the Mathematical and Physical Sciences I Derivatives, definite integral, Taylor polynomials
MATH 146 Calculus for the Mathematical and Physical Sciences II Integration, differential equations, partial derivatives
MATH 214 Calculus III Series, curves, coordinates, multiple integrals

The catalogue allows credit in at most one of MATH 101, 115, 118, 136, 146, 156 or SCI 100.

Example problems at the MATH 146 level

1. Integration by parts.

\int x e^x\,dx = x e^x - \int e^x\,dx = e^x(x - 1) + C

2. An improper integral. \int_0^\infty e^{-2x}\,dx = \lim_{b\to\infty}\left[-\tfrac{1}{2}e^{-2x}\right]_0^b = \tfrac{1}{2}.

3. A separable equation. Solve \frac{dy}{dx} = xy. Then \int \frac{dy}{y} = \int x\,dx, so \ln|y| = \frac{x^2}{2} + C and y = Ae^{x^2/2}.

4. Partial derivatives. For f(x, y) = x^2 \sin y, f_x = 2x\sin y and f_y = x^2 \cos y.

How to do well in MATH 146

  • Practise choosing the method. Mixed sets such as choosing a strategy train you to spot which technique an integral needs.
  • Write limits for improper integrals. Replace the infinite bound with b and take a limit. Skipping this step costs marks.
  • Check differential equation answers. Substitute your solution back into the equation. It takes a few seconds and catches most errors.
  • Hold variables still. For a partial derivative, every other variable is a constant. Say it out loud the first few times.

Tip: for partial fractions, factor the denominator completely before you write the decomposition. A missed factor makes the whole setup wrong.

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Integration by parts

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Frequently asked questions

What is MATH 146 at the University of Alberta?
MATH 146 is Calculus for the Mathematical and Physical Sciences II. The catalogue lists techniques and applications of integration, improper integrals, an introduction to differential equations and partial differentiation, with applications in the physical sciences.

What do I need before MATH 146?
One of MATH 100, 113, 114, 117, 134, 144 or 154. Most science students come from MATH 144 or MATH 134.

Does MATH 146 cover series?
No. The catalogue description for MATH 146 does not list sequences or series. At UAlberta, sequences, series, convergence tests and Taylor series are in MATH 214, Calculus III.

MATH 146 vs MATH 136?
They have the same structure and you can only get credit for one. MATH 136 sets the applications in the life sciences and stresses mathematical modelling, while MATH 146 uses the physical sciences.

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Related university courses

UAlberta MATH 144 Calculus 1 Calculus for the Mathematical and Physical Sciences I A study guide for University of Alberta MATH 144: derivatives, the definite integral, the Fundamental Theorem and Taylor polynomials, with practice. UAlberta MATH 214 Calculus 2 and 3 Calculus III A study guide for University of Alberta MATH 214 (Calculus III): series, Taylor series, curves, polar and spherical coordinates and multiple integrals.