UAlberta MATH 144 Calculus I: Syllabus, Topics and Practice
A study guide for University of Alberta MATH 144: derivatives, the definite integral, the Fundamental Theorem and Taylor polynomials, with practice.
University of Alberta Updated 3 min read
At a glance
- Course code
- MATH 144
- Units
- 3 (fi 6), 3 lecture hours per week, offered in either term
- Prerequisites
- Mathematics 30-1
- Credit restriction
- Credit in at most one of MATH 100, 113, 114, 117, 134, 144, 154 or SCI 100
- Covers
- The derivative as a rate of change, differentiation of elementary, trig, exponential and log functions, the definite integral, the Fundamental Theorem of Calculus, Taylor polynomials
- Next course
- MATH 146 (Calculus for the Mathematical and Physical Sciences II)
- Practice here
- Calculus 1
Try it yourself
On this page
MATH 144 is Calculus for the Mathematical and Physical Sciences I at the University of Alberta. It is the first calculus course for many science students, and it covers both halves of single-variable calculus: derivatives and the definite integral, finishing with Taylor polynomials. This guide maps each MATH 144 topic to free practice so you can learn every idea by solving problems.
What UAlberta MATH 144 covers
The University of Alberta catalogue describes MATH 144 as covering the derivative as a rate of change; differentiation of elementary, trigonometric, exponential and logarithmic functions; the definite integral as a summation; integration; the Fundamental Theorem of Calculus; and Taylor polynomials, with applications in the context of the physical sciences. It is a 3-unit course with three lecture hours a week, and the only listed prerequisite is Mathematics 30-1.
That matches a standard Calculus 1 course, plus Taylor polynomials, which many schools leave for Calculus 2. The catalogue does not list a separate limits unit, but you will meet limits when the derivative is defined as a rate of change.
MATH 144 topic map
| MATH 144 topic | Practice | Read |
|---|---|---|
| Limits behind the derivative | What is a limit? | What is a limit |
| The derivative as a rate of change | Instantaneous rate of change | Limit definition of the derivative |
| Elementary functions | Power rule | Power rule, product rule |
| Trigonometric functions | Trig derivatives | Derivatives of trig functions |
| Exponential and log functions | Exponential and log derivatives | Derivative of ln x, derivative of e^x |
| Chain rule | Chain rule in general | Chain rule |
| Applications of derivatives | Optimization | Related rates, optimization |
| The definite integral as a summation | Riemann sums | Riemann sums guide |
| Integration | Reverse power rule | Antiderivatives |
| The Fundamental Theorem | FTC part 2 | FTC guide |
| Taylor polynomials | Taylor polynomials | Taylor's theorem, Taylor series |
MATH 144 and the other first-year options
| Course | Title | Notes from the catalogue |
|---|---|---|
| MATH 134 | Calculus for the Life Sciences I | Same core, life science applications |
| MATH 144 | Calculus for the Mathematical and Physical Sciences I | Adds Taylor polynomials |
| MATH 100 | Calculus for Engineering I | Engineering only, needs Math 30-1 and Math 31 |
The catalogue says you can earn credit in at most one of MATH 100, 113, 114, 117, 134, 144, 154 or SCI 100. After MATH 144, continue to MATH 146 and then MATH 214.
Example problems at the MATH 144 level
1. A rate of change. A ball's height is h(t) = 20t - 4.9t^2 metres. Its velocity is h'(t) = 20 - 9.8t, so at t = 1 it is rising at 10.2 m/s.
2. The Fundamental Theorem.
3. A Taylor polynomial. The degree 2 Taylor polynomial of e^x at 0 is 1 + x + \frac{x^2}{2}, so e^{0.1} \approx 1.105.
How to do well in MATH 144
- Strengthen your Math 30-1 skills. Since Math 31 is not required, brush up on functions, logarithms and trig identities in the first weeks.
- Make derivative rules automatic. Short sets in practice every day on the power rule and chain rule pay off later in integration.
- Connect the two halves. The Fundamental Theorem links derivatives and integrals. Check every antiderivative by differentiating it.
- Think physically. Applications are set in the physical sciences, so read velocity, acceleration and work problems slowly and label units.
Tip: a Taylor polynomial is only accurate near its centre. Pick the centre close to the value you want to approximate.
Practice it now
Instantaneous rate of change
Solve real problems on this topic with instant feedback, hints and a step-by-step walkthrough for every answer. Free, no sign-up needed to start.
Practice this lesson