This video lecture, part of the series 18.02 Multivariable Calculus by Prof. Denis Auroux, does not currently have a detailed description and video lecture title. If you have watched this lecture and know what it is about, particularly what Mathematics topics are discussed, please help us by commenting on this video with your suggested description and title. Many thanks from,

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1. Dot Product
2. Determinants and Cross Product
3. Matrices and Inverse Matrices
4. Square Systems and Equations of Planes
5. Parametric Equations for Lines and Curves
6. Velocity, Acceleration and Kepler's Second Law
7. Review
8. Level Curves, Partial Derivatives and Tangent Plane Approximation
9. Max-min Problems and Least Squares
10. Second Derivative Test, Boundaries and Infinity
11. Differentials and Chain Rule
12. Gradient, Directional Derivative and Tangent Plane
13. Lagrange Multipliers
14. Non-independent Variables
15. Partial Differential Equations (Review)
16. Double Integrals
17. Double Integrals in Polar Coordinates and Applications
18. Change of Variables
19. Vector Fields and Line Integrals in the Plane
20. Path Independence and Conservative Fields
21. Gradient fields and Potential Functions
22. Green Theorem
23. Flux and Normal Form of Green Theorem
24. Simply Connected Regions (Review)
25. Triple Integrals in Rectangular and Cylindrical Coordinates
26. Spherical Coordinates and Surface Area
27. Vector Fields in 3D and Surface Integrals and Flux
28. Divergence Theorem
29. Divergence Theorem (cont.) and Applications and Proof
30. Line Integrals in Space, Curl, Exactness and Potentials
31. Stokes' Theorem
32. Stokes' Theorem (cont.) and Review
33. Topological Considerations and Maxwell's Equations
34. Final Review
35. Final Review (cont.)

In this course, Prof. Denis Auroux 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.

MIT OpenCourseWare offers another version of 18.02, from the Spring 2006 term. Both versions cover the same material, although they are taught by different faculty and rely on different textbooks. Multivariable Calculus (18.02) is taught during the Fall and Spring terms at MIT, and is a required subject for all MIT undergraduates.

Tags: Math, Math Calculus

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