This is a large collection of practice problems, solutions and references on Differential Calculus. The material here was created by instructors at various universities and colleges for their introductory calculus courses. It takes the form of worksheets, homework, and quizzes, with solutions provided in all cases. We’ve also included good open source video and text references.
We also have a page on Integral Calculus. If you’re self studying calculus, we recommend beginning by watching a series of lecture videos listed under the “Good Viewing” tab below. Once you’ve watched a particular video, try some relevant problems, and then look through the solutions. We think this is an effective way to master the subject. Please write to us at info@tutorterrace.com with any questions, suggestions or comments!
(For pre-calculus problems and references see this page.)
This is an accessible series of lecture videos on Differential Calculus by Prof Enciso of UC Irvine.
This is a complete series of lecture videos from a great introductory Calculus course by Prof David Jerison of MIT.
This excellent video by Prof Strang of MIT explains the ideas of Limits and Continuity.
This video by Prof Strang explains the idea of Derivatives.
This excellent series of 18 videos by Prof Strang explains the “basic ideas” behind calculus (the previous two videos are part of this series).
This highly recommended series of 12 videos by 3Blue1Brown discusses the “essence of calculus”.
This concise yet clear introduction to Calculus from OpenStax is edited by Professors Gilbert Strang and Edwin Herman. It covers mainly Differential Calculus and is suitable for both high school and college students learning calculus.
This classic textbook by Professor Gilbert Strang of MIT is a thorough introduction to Calculus and its applications. There is also an accompanying Study Guide which has model problems and solutions.
Limits and Continuity
[Limits] Worksheet, Solutions (Prof Buehler, UC Berkeley) || Worksheet 1 and Solutions; Worksheet 2 and Solutions; Worksheet 3 and Solutions, Worksheet 4 and Solutions (Prof Kouba, UC Davis) || Homework 1 (see Pages 3, 4), Solutions (Prof O. Knill, Harvard) || Quiz, Solutions (Prof Boas, Texas A&M University) || Worksheet, Solutions (R Fernando, UC Berkeley)
[Continuity] Worksheet and Solutions (Prof Kouba, UC Davis) || Worksheet (See Page 4), Solutions (Prof Jiang, University of Michigan) || Homework 2 (Pages 3, 4) , Solutions (Prof O. Knill, Harvard) || Worksheet, Solutions (R Fernando, UC Berkeley) || Worksheet (See Page 4), Solutions (See Page 7) (Prof Jerison, MIT)
The Derivative - Definition and Properties/Rules (sum, product, etc.)
[Basic Definition via Limit] Worksheet 1, Solutions (see Page 2) (R Fernando, UC Berkeley) || Homework (see Page 4), Solutions (Prof Knill, Harvard) || Worksheet, Solutions (Prof Buehler, UC Berkeley) || Worksheet and Solutions (Prof Kouba, UC Davis) || Worksheet (Page 4), Solutions (Prof Jiang, University of Michigan)
[Sum, Scaling, Product Properties] Worksheet 1, Solutions; Worksheet 2, Solutions; Worksheet 3, Solutions; (R. Fernando, UC Berkeley) || Worksheet, Solutions (Prof Buehler, UC Berkeley) || Homework 1 (See Page 4), Solutions; Homework 2 (Page 4) , Solutions (Prof Knill, Harvard) || Worksheet, Solutions (Dr. Leingang, Harvard) || Worksheet 1 (See Page 3), Solutions (Prof Jiang, University of Michigan)
Chain rule (with applications) and Implicit Differentiation
Worksheet 1, Solutions; Worksheet 2, Solutions ; Worksheet 3, Solutions (R Zhao, UC Berkeley) || Worksheet 1 and Solutions, Worksheet 2 and Solutions (Dr. Kouba, UC Davis) || Worksheet 1, Solutions; Worksheet 2, Solutions; Worksheet 3, Solutions (R Fernando, UC Berkeley) || Homework (see Page 4), Solutions (Prof Knill, Harvard) || Worksheet (see Page 5), Solutions (Prof Jiang, University of Michigan) || Worksheet (see Page 6), Solutions (Page 11) (Prof Jerison, MIT) || Worksheet, Solutions (Prof Leingang, MIT)
Maxima and Minima, Critical Points
Worksheet 1, Solutions; Worksheet 2, Solutions (Dr. Leingang, Harvard) || Worksheet and Solutions (Prof Kouba, UC Davis) || Worksheet 1, Solutions; Worksheet 2, Solutions; Worksheet 3, Solutions (R Fernando, UC Berkeley) || Homework1 (see Page 4) , Solutions; Homework 2 (Page 3) ,Solutions (Prof Knill, Harvard) || Worksheet 1 (Page 4), Solutions; Worksheet 2 (Page 4), Solutions (Prof Jiang, University of Michigan) || Worksheet (see Page 5), Solutions (Page 10) (Prof Leingang, MIT) || Worksheet (see Page 2), Solutions (Page 4) (R Zhao, UC Berkeley)
L'Hospital's Rule
Worksheet and Solutions (Prof Kouba, UC Davis) || Homework, Solutions (Prof Reinholz, UC Berkeley) || Worksheet, Solutions (Dr. Leingang, Harvard) || Homework (see Page 4), Solutions (Prof Knill, Harvard)
Approximation, Taylor Expansion
[Linear approximation/ “Differentials”] Worksheet and Solutions (Prof Kouba, UC Davis) || Worksheet, Solutions (Prof Jerison, MIT) || Worksheet, Solutions (Y Pan, UC Berkeley) [Taylor Expansion/Series] Worksheet, Solutions (R Zhao, UC Berkeley) || Practice Test, Solutions (Prof Jiang, University of Michigan) [Newton’s Method] Worksheet and Solutions (Prof Kouba, UC Berkeley) || Homework, Solutions (Prof Reinholz, UC Berkeley) || Homework (see Page 4), Solutions (Prof Knill, Harvard) || Worksheet, Solutions (R Zhao, UC Berkeley) || Worksheet, Solutions (R Fernando, UC Berkeley)
