# 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.

Source: https://practicecalculus.com/courses/university-of-alberta-math-146
Updated: 2026-11-08

## 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](/learn/calculus-2)

## Key takeaways

- MATH 146 is the 3-unit second calculus course at the University of Alberta for the mathematical and physical sciences.
- It covers techniques and applications of integration, improper integrals and an introduction to differential equations.
- It also introduces partial differentiation, a first step into calculus of several variables.
- Series are not in MATH 146 at UAlberta; they come in MATH 214.

**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](/learn/calculus-2/integration-techniques/u-substitution-refresher) | [u-substitution rule](/rules/u-substitution-rule) |
| Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts guide](/blog/integration-by-parts) |
| Trig integrals | [Trig integrals](/learn/calculus-2/integration-techniques/trig-integrals) | [Integral of sec x](/integrals/sec-x) |
| Trig substitution | [Trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution guide](/blog/trig-substitution) |
| Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions guide](/blog/partial-fractions) |
| Areas and volumes | [Volumes with disks](/learn/calculus-1/applications-of-integrals/volumes-disks) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Arc length, work, centre of mass | [Work](/learn/calculus-2/improper-integrals-and-applications/work), [centre of mass](/learn/calculus-2/improper-integrals-and-applications/center-of-mass) | [Arc length](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) |
| Improper integrals | [Infinite limits of integration](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration) | [Improper integrals guide](/blog/improper-integrals) |
| Differential equations | [Separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Slope fields](/learn/calculus-2/improper-integrals-and-applications/slope-fields), [Euler's method](/learn/calculus-2/improper-integrals-and-applications/eulers-method) |
| Partial differentiation | [Partial derivatives](/learn/calculus-3/partial-derivatives/partial-derivatives) | [Partial derivatives guide](/blog/partial-derivatives) |

## Where MATH 146 sits

| Course | Title | Main focus |
| --- | --- | --- |
| [MATH 144](/courses/university-of-alberta-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](/courses/university-of-alberta-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](/learn/calculus-2/integration-techniques/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.

## 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.