Multivariable Calculus 18.02 MIT
Online Free Online Course by
World Mentoring Academy
Online
/ Free Online Course
Details
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.
Resources: OpenCourseware from MIT, UC Berkeley, Stanford along with many of the World's finest University's.
Language: English
Professors: Joshua Coleman, Michael Williams
Units: 35
Lesson content
- Lecture 01: Dot product.
- Lecture 02: Determinants; cross product.
- Lecture 03: Matrices; inverse matrices.
- Lecture 04: Square systems; equations of planes.
- Lecture 05: Parametric equations for lines and curves.
- Lecture 06: Velocity, acceleration; Kepler's second law.
- Lecture 07: Review.
- Lecture 08: Level curves; partial derivatives; tangent plane approximation.
- Lecture 09: Max-min problems; least squares.
- Lecture 10: Second derivative test; boundaries and infinity.
- Lecture 11: Differentials; chain rule.
- Lecture 12: Gradient; directional derivative; tangent plane.
- Lecture 13: Lagrange multipliers.
- Lecture 14: Non-independent variables.
- Lecture 15: Partial differential equations; review.
- Lecture 16: Double integrals.
- Lecture 17: Double integrals in polar coordinates; applications.
- Lecture 18: Change of variables.
- Lecture 19: Vector fields and line integrals in the plane.
- Lecture 20: Path independence and conservative fields.
- Lecture 21: Gradient fields and potential functions.
- Lecture 22: Green's theorem.
- Lecture 23: Flux; normal form of Green's theorem.
- Lecture 24: Simply connected regions; review
- Lecture 25: Triple integrals in rectangular and cylindrical coordinates.
- Lecture 26: Spherical coordinates; surface area.
- Lecture 27: Vector fields in 3D; surface integrals and flux.
- Lecture 28: Divergence theorem.
- Lecture 29: Divergence theorem (cont.): applications and proof.
- Lecture 30: Line integrals in space, curl, exactness and potentials.
- Lecture 31: Stokes' theorem.
- Lecture 32: Stokes' theorem (cont.); review.
- Lecture 33: Topological considerations; Maxwell's equations.
- Lecture 34: Final review.
- Lecture 35: Final review (cont.).
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