Course SummaryThis introductory calculus course covers differentiation and integration of functions of one variable, with applications. The basic objective of the course is to relate small-scale (differential) quantities to large-scale (integrated) quantities. This is accomplished by means of the Fundamental Theorem of Calculus. Students should demonstrate an understanding of the integral as a cumulative sum, of the derivative as a rate of change, and of the inverse relationship between integration and differentiation. (There is a full set of videos and lecture notes.)
(6 Oct 2009: Updated with a full set of video of lectures.)
Reading Material1. Textbook (MIT 18.01): Calculus with Analytic Geometry. 2nd ed.
Simmons, George F. Calculus with Analytic Geometry. 2nd ed. New York, NY: McGraw-Hill, October 1, 1996. ISBN: 9780070576421.
2. Supplementary notes 1
3. Supplementary notes 2
Continuity and discontinuity
4. Supplementary notes 3
Exponentials and logarithms
5. Supplementary notes 4
6. Supplementary notes 5
7. Supplementary notes 6
Properties of definite integrals
8. Supplementary notes 7
The second fundamental theorem of calculus
9. Supplementary notes 8
10. Supplementary notes 9
Heaviside's cover-up method
11. Supplementary notes 10
12. Exercises for sections 1-7
(File size: 2.3 MB)
13. Solutions to exercises for sections 1-7
(File size: 4.1 MB)
14. Review problems and solutions
Course Material1. Assignments (MIT 18.01)
Problem Set 1 (PDF)
Problem Set 3 (PDF)
Problem Set 4 (PDF)
Problem Set 5 (PDF)
Problem Set 6 (PDF)
Problem Set 7 (PDF)
2. Exams (MIT 18.01)
Review sheets, practice exam and exam questions with solutions.
Other Resources1. Calculus
Gilbert Strang, Calculus, Wellesley-Cambridge Press, 1991, ISBN 9780961408824.
This excellent book is written by Prof. Gilbert Strang of MIT and is a useful resource for both students and educators alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications. There is also an online Instructor's Manual and a student Study Guide availble. You can download the whole book in pdf format at this link (38.5 MB).