Lectures (Video)

- 1. Derivatives
- 2. Trigonometric limits
- 3. Derivatives of products, quotients, sine, cosine
- 4. Chain rule
- 5. Implicit differentiation
- 6. Exponential and log
- 7. Hyperbolic functions
- 9. Linear and quadratic approximations
- 10. Curve sketching
- 11. Max-min problems
- 12. Related Rates
- 13. Newton's method
- 14. Mean value theorem
- 15. Differentials, antiderivatives
- 16. Differential equations, separation of variables
- 18. Definite integrals
- 19. First fundamental theorem of calculus
- 20. Second fundamental theorem
- 21. Applications to logarithms and geometry
- 22. Volumes by disks and shells
- 23. Work, average value, probability
- 24. Numerical integration
- 25. Review
- 26. Trigonometric integrals and substitution
- 28. Integration by inverse substitution
- 29. Partial fractions
- 30. Integration by parts, reduction formulae
- 31. Parametric equations
- 32. Polar coordinates
- 33. Review II
- 34. Indeterminate forms
- 35. Improper integrals
- 36. Infinite series and convergence tests
- 37. Taylor's series
- 38. Final review

## Calculus I

### Course Summary

This course is based on

This 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.)
*18.01 Single Variable Calculus, Fall 2006*made available by*Massachusetts Institute of Technology: MIT OpenCourseWare*under the*Creative Commons BY-NC-SA*license.(6 Oct 2009: Updated with a full set of video of lectures.)

*(source - MIT OpenCourseWare)*

### Reading Material

1.**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**

Graphing functions

3.

**Supplementary notes 2**

Continuity and discontinuity

4.

**Supplementary notes 3**

Exponentials and logarithms

5.

**Supplementary notes 4**

Approximation

6.

**Supplementary notes 5**

Mean-value theorem

7.

**Supplementary notes 6**

Properties of definite integrals

8.

**Supplementary notes 7**

The second fundamental theorem of calculus

9.

**Supplementary notes 8**

Average value

10.

**Supplementary notes 9**

Heaviside's cover-up method

11.

**Supplementary notes 10**

Improper integrals

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 Material

1.**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 Resources

1.**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).