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Lectures (Video)

Calculus II

Course Summary

This course is based on 18.02 Multivariable Calculus, Fall 2007 made available by Massachusetts Institute of Technology: MIT OpenCourseWare under the Creative Commons BY-NC-SA license.
This course covers vector and multi-variable calculus. It is the second semester in the freshman calculus sequence. Topics include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. The lectures were conducted by Prof. Denis Auroux at MIT.

Reading Material

1. Textbook (MIT 18.02): Multivariable Calculus. 6th ed.
Edwards, Henry C., and David E. Penney. Multivariable Calculus. 6th ed. Lebanon, IN: Prentice Hall, 2002. ISBN: 9780130339676.
2. Supplementary Notes I
3. Supplementary Notes II
Matrices and linear algebra
4. Supplementary Notes III
Kepler's second law
5. Supplementary Notes IV
The tangent approximation
6. Supplementary Notes V
Second derivative test
7. Supplementary Notes VI
Least squares interpolation
8. Supplementary Notes VII
Non-independent variables
9. Supplementary Notes VIII
Partial differential equations
10. Supplementary Notes IX
Limits in iterated integrals
11. Supplementary Notes X
Changing variables in multiple integrals
12. Supplementary Notes XI
Gravitational attraction
13. Supplementary Notes XII
Plane vector fields
14. Supplementary Notes XIII
Gradient fields and exact differentials
15. Supplementary Notes XIV
Two-dimensional flux
16. Supplementary Notes XV
Green's theorem in normal form
17. Supplementary Notes XVI
Simply-connected regions
18. Supplementary Notes XVII
Multiply-connected regions; topology
19. Supplementary Notes XVIII
Laplace's equation and harmonic functions
20. Supplementary Notes XIX
Vector fields in space
21. Supplementary Notes XX
Surface integrals
22. Supplementary Notes XXI
The divergence theorem
23. Supplementary Notes XXII
Line integrals in space
24. Supplementary Notes XXIII
Gradient fields in space
25. Supplementary Notes XXIV
Stokes' theorem
26. Supplementary Notes XXV
Some topological questions
27. Supplementary Notes XXVI
Relation to physics

Course Material

1. Assignments (MIT 18.02)
Problem Set 1 (PDF)
Problem Set 2 (PDF)
Problem Set 3 (PDF)
Problem Set 4 (PDF)
Problem Set 5 (PDF)
Problem Set 6 (PDF)
Problem Set 7 (PDF)
Problem Set 8 (PDF)
Problem Set 9 (PDF)
Problem Set 10 (PDF)
Problem Set 11 (PDF)
Problem Set 12 (PDF)

2. Exams (MIT 18.02)
Practice exam 1A (PDF) (PDF)
Practice exam 1B (PDF) (PDF)
Practice exam 2A (PDF) (PDF)
Practice exam 2B (PDF) (PDF)
Practice exam 3A (PDF) (PDF)
Practice exam 3B (PDF) (PDF)
Practice exam 4A (PDF) (PDF)
Practice exam 4B (PDF) (PDF)

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).


1. Interactive math applets
A series of specially written interactive math applets ("mathlets"), which let you visualize and experiment with various concepts in the course.



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