You do not need ten tabs open to study calculus. Pick a resource that explains the idea, then spend most of your session working through questions yourself. These are five places I return to when tutoring high school, college, and university students.
What are you studying?
Jump to a useful starting point for your course, then compare the resources below.
Course names vary between schools. Match the topics to your outline: Calculus 4 can include vector calculus, differential equations, or both.
Which resource should you use?
Start with the format that helps you most. All five recommendations are independent resources; our own Problem Bank is included separately so you can compare it too.
On a phone, swipe across the table to see every column.
| Resource | Coverage | What you can use | Access |
|---|---|---|---|
| Gilles Cazelais | Calculus and differential equations course pages | Notes, handouts, practice questions; solutions on selected pages | Free public materials |
| Paul's Online Math Notes | Calculus 1, 2, 3 and differential equations | Notes and worked examples; separate practice sets for calculus | Free |
| 1001 Practice Problems for Dummies | Single-variable calculus | Workbook questions and detailed answer explanations | Paid book |
| The Organic Chemistry Tutor | Calculus topics; choose videos by topic | Video explanations and worked examples | Linked YouTube lesson is free |
| Dr. Trefor Bazett | Calculus 1, 2, 3; vector calculus and ODEs | Course video playlists and linked learning materials | Free linked videos |
| Heywood Academies Problem Bank | Calculus 1, 2 and 3 | Practice questions, answer checking, solutions, and YouTube lessons for every topic | App account; current options on the homepage |
Calculus 1: start with the chain rule
If derivatives feel unpredictable, practise identifying the inside and outside functions before calculating. Here is a short route from explanation to practice.
- Read: Paul's chain rule notes and worked examples
- Practise: chain rule questions with solutions
- Study by topic: Calculus 1 lessons and questions in our Problem Bank
For a course organized by topic, our Problem Bank pairs Calculus 1 questions with YouTube lessons, so you can review the relevant idea before trying a problem.
Calculus 2: work through integration by parts
Start by deciding what to differentiate and what to integrate. Then solve a question independently before checking the solution.
- Read: integration by parts explained
- Practise: integration by parts questions with solutions
- Explore: Gilles' integration handouts and series resources
Our Problem Bank also brings Calculus 2 practice and topic-by-topic YouTube lessons together.
Calculus 3: get comfortable with partial derivatives
Start with what changes and what stays fixed when differentiating with respect to one variable. Use a visual explanation when the geometry is the sticking point.
- Read: partial derivatives with worked examples
- Practise: partial derivative questions with solutions
- Watch: Dr. Trefor Bazett's multivariable calculus playlist
Use our Problem Bank for Calculus 3 questions and YouTube lessons organized around each topic.
Differential Equations: recognize the method first
Start with separable equations, then compare methods as your course introduces them. Check a proposed solution by differentiating it and substituting back into the original equation.
- Read and work along: separable equations
- Explore: Gilles' differential equations notes and practice questions
- Watch: Dr. Trefor Bazett's vector calculus and ODE playlist
The video playlist combines vector calculus and ordinary differential equations, so select the parts that match your outline. Differential Equations is not currently available in our Problem Bank; use the external resources above for that course.
Want a closer look at each resource? Browse the five recommendations and our own Problem Bank below.
#1 Gilles Cazelais' website at Camosun College
Best for: course notes and extra practice organized around a course.
Gilles' course pages are a resource I have recommended to Camosun students for years. Look for the notes, practice questions, and test preparation that match the topics in your own course outline.
Course numbering differs between schools, so match the topic rather than assuming every Calculus 2 course covers the same material. Browse Gilles Cazelais' homepage.
#2 Paul's Online Math Notes
Best for: looking up a method and trying related questions.
Paul's Online Math Notes has Calculus I, II, and III notes, examples, and practice problems with solutions. There is also a separate differential equations course.
Use it when you know the topic you need to review. Read an explanation, try a problem without the solution beside you, and compare your working afterward. If algebra is slowing you down, the algebra and trigonometry review material is useful too.
For the transition from high school, see Is University Calculus Hard?
#3 Calculus: 1001 Practice Problems for Dummies
Best for: a paper workbook and detailed answer explanations.
I have used this book in tutoring sessions for years. It gives students plenty of opportunities to practise a method instead of moving on after one example.
Keep paper beside you, work through the question, and check the explanation after your attempt. Mark the questions you could not finish and return to them in a later study session.
#4 The Organic Chemistry Tutor's calculus videos
Best for: watching a method applied to worked examples.
Despite the name, The Organic Chemistry Tutor teaches plenty of calculus. His step-by-step walkthroughs are useful when a textbook explanation has not clicked.
Here is an introduction to limits. Pause before the next step and try it yourself.
Browse The Organic Chemistry Tutor's playlists.
#5 Dr. Trefor Bazett's calculus playlists
Best for: understanding what the symbols and calculations mean.
Dr. Trefor Bazett's course playlists combine clear explanations with visuals. His Calculus I playlist is a useful starting point for limits, derivatives, and integrals.
His UVic course page also links Calculus II, multivariable calculus, and vector calculus resources. Check coverage against your own outline, then follow the video with practice questions.
The Heywood Academies Problem Bank
These are our own practice problems, created by Heywood Academies to help you work through Calculus 1, 2, and 3. Each topic in Calculus 1, 2, and 3 includes a YouTube lesson alongside the practice questions. Choose what you are studying, review the explanation if you need it, then try a question and check your answer.
Explore our Problem Bank to see the current courses, topics, and access options.