Review limits, derivatives and optimization in differential calculus, or integrals and accumulation in integral calculus. Choose your college and exact course code to find the relevant guide, try a worked example or ask for one-to-one help.
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Start with the topic you need help with. For a specific course, use your college and exact course code in the next section.
Limits, derivatives, curve analysis and optimization.
Start with eight questions on limits and derivatives, with hints and explained answers. Use the optional optimization and L’Hôpital questions only when they match your outline.
Antiderivatives, definite integrals, integration methods and applications.
Choose your exact course code: calculus requirements vary by program. Science course guides follow below.
Go directly to examples and revision for your course. Each institution guide explains the other courses and their differences; follow your section’s outline and announced chapters.
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Browse courses in this subjectFind course guides and practice for your college.
Try practice for your course:
Your tutor can help you read the question and use a graph to decide whether it concerns a rate of change or accumulated change. Together, you can choose a derivative or integral, work through the algebra and explain the result in its units. If you have already started, you can review your setup together.
This table matches current and former codes by Science program subject. Your institution must confirm any transfer-credit equivalence. The prefix matters: 201-SN1 is probability and statistics, while 203-SN1 is mechanics. Course codes and topics can vary by institution. Check your current course outline.
| Subject | Current code | Former code |
|---|---|---|
| Differential calculus | 201-SN2-RE | 201-NYA-05 |
| Integral calculus | 201-SN3-RE | 201-NYB-05 |
Check current names and content in the official Dawson mathematics list and Dawson physics list.
Let be time in seconds. If position is metres, its derivative m/s describes instantaneous velocity. Integrating from 1 to 3 seconds gives 8 metres, the displacement . Differentiation and integration answer related but different questions.
Why is displacement not always total distance? Negative velocity contributes negatively to displacement; total distance accumulates the speed .
An object moves along a straight line. Let time be measured in seconds and let give velocity in metres per second, for . Find both displacement and total distance.
Factor . Velocity is negative between 0 and 2 seconds, then positive between 2 and 3 seconds. An antiderivative is , with , and .
The displacement is The total distance is
The object returns to its starting position after travelling 8 metres. Taking the absolute value of the final displacement would give the wrong distance.
For differential calculus, begin with algebra and the limits-and-derivatives practice. For integral calculus, begin with method choice. Use your own course outline to select questions; the two routes cover different topics.
Try the self-checks on fractions, powers and functions; review only the operations that interrupt your calculus work.
Attempt the questions that match your assessment, compare the explained solutions, then redo a missed step without notes.
Read the structure of the integrand before choosing substitution, integration by parts or partial fractions; check by differentiating.
Choose the questions on your topic list. State the bounds and what a slice represents before doing the calculation.
At each step: read the example, attempt a question before opening its solution, then redo a missed step without notes. Finish by applying the method to permitted practice from your own course.
Separate variables, keep equilibrium solutions and use the initial value to choose a branch and interval. Worked examples include exponential growth and an optional logistic model.
Five core questions and an optional logistic extension, with hints, worked solutions and changed retries. Check separation, equilibria, initial values and solution intervals.
Compare substitution, integration by parts, partial fractions and trigonometric substitution, with sign-aware radical choices, worked examples and progressive checks.
Ten essential algebra skills with worked examples, common mistakes and self-checks: a practical starting point before university or CEGEP calculus.
Build a three-branch rational-function graph from its domain, one-sided limits and derivative signs. Compare local and global extrema, diagnose false inflection points and try two explained checks.
For differential calculus, mix rule selection with complete optimization setups. For integral calculus, practise choosing bounds, checking antiderivatives and interpreting signed area. Use the current outline to decide whether sequences, series or particular integration techniques are assessed.
For differential-calculus revision: Choose a derivative rule: three-question check
Use the questions that match your current course outline.
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