18.02 Multivariable Calculus

Course Description


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

Copyright Information

Denis Auroux, 18.02 Multivariable Calculus, Fall 2007. (MIT OpenCourseWare: Massachusetts Institute of Technology), http://ocw.mit.edu/OcwWeb/Mathematics/18-02Fall-2007/CourseH... (Accessed November 06, 2008). License: Creative commons BY-NC-SA
18.02 Multivariable Calculus

Lagrange multipliers with two variables Mathlet from the d'Arbeloff Interactive Math Project. (Image courtesy of Jean-Michel Claus.)
5 ratings

Video Lectures & Study Materials

# Lecture Play Lecture
I. Vectors and Matrices
1 Dot Product (39:00) Play Video
2 Determinants and Cross Product (53:00) Play Video
3 Matrices and Inverse Matrices (51:00) Play Video
4 Square Systems and Equations of Planes (49:00) Play Video
5 Parametric Equations for Lines and Curves (51:00) Play Video
6 Velocity, Acceleration and Kepler's Second Law (48:00) Play Video
7 Review (49:50) Play Video
II. Partial Derivatives
8 Level Curves, Partial Derivatives and Tangent Plane Approximation (46:00) Play Video
9 Max-min Problems and Least Squares (49:44) Play Video
10 Second Derivative Test, Boundaries and Infinity (52:18) Play Video
11 Differentials and Chain Rule (50:00) Play Video
12 Gradient, Directional Derivative and Tangent Plane (50:00) Play Video
13 Lagrange Multipliers (50:00) Play Video
14 Non-independent Variables (49:00) Play Video
15 Partial Differential Equations (Review) (45:00) Play Video
III. Double Integrals and Line Integrals in the Plane
16 Double Integrals (48:00) Play Video
17 Double Integrals in Polar Coordinates and Applications (51:00) Play Video
18 Change of Variables (50:00) Play Video
19 Vector Fields and Line Integrals in the Plane (51:00) Play Video
20 Path Independence and Conservative Fields (50:00) Play Video
21 Gradient fields and Potential Functions (50:00) Play Video
22 Green Theorem (47:00) Play Video
23 Flux and Normal Form of Green Theorem (50:00) Play Video
24 Simply Connected Regions (Review) (49:00) Play Video
IV. Triple Integrals and Surface Integrals in 3-space
25 Triple Integrals in Rectangular and Cylindrical Coordinates (49:00) Play Video
26 Spherical Coordinates and Surface Area (51:00) Play Video
27 Vector Fields in 3D and Surface Integrals and Flux (51:00) Play Video
28 Divergence Theorem (49:00) Play Video
29 Divergence Theorem (cont.) and Applications and Proof (50:00) Play Video
30 Line Integrals in Space, Curl, Exactness and Potentials (50:00) Play Video
31 Stokes' Theorem (48:00) Play Video
32 Stokes' Theorem (cont.) and Review (50:00) Play Video
33 Topological Considerations and Maxwell's Equations (29:00) Play Video
34 Final Review (44:00) Play Video
35 Final Review (cont.) (49:00) Play Video

Comments

Displaying 3 comments:

Amelia wrote 13 years ago.
Amazing! So easy to understand, thank you.

R.D wrote 15 years ago.
Excellent lectures. Very lucid, clear and easy to
understand. Grateful to MIT for putting them up.


Syed Waqar wrote 15 years ago.
This is really a great work for students and should have
more topics and courses.
We should be thankful to Prof. Denis Auroux.

Kind regards.

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