MIT 18.02 Multivariable Calculus - Fall 2007

MIT 18.02 Multivariable Calculus - Fall 2007

35 Lectures ยท Sep 3, 2007

About

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.

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.

Course Homepage: 18.02 Multivariable Calculus Fall 2007

Course features at MIT OpenCourseWare page: *Syllabus *Calendar *Readings *Lecture Notes *Assignments *Download Tools *Download this Course

Complete MIT OCW video collection at MIT OpenCourseWare - VideoLectures.NET

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Lecture 1: Dot product

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Lecture 2: Determinants; cross product

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Lecture 3: Matrices; inverse matrices

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Lecture 4: Square systems; equations of planes

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Lecture 5: Parametric equations for lines and curves

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Lecture 6: Velocity, acceleration - Kepler's second law

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Lecture 7: Review

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Lecture 8: Level curves; partial derivatives; tangent plane approximation

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Lecture 9: Max-min problems; least squares

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Lecture 10: Second derivative test; boundaries and infinity

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Lecture 11: Differentials; chain rule

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Lecture 12: Gradient; directional derivative; tangent plane

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Lecture 13: Lagrange multipliers

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Lecture 14: Non-independent variables

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Lecture 15: Partial differential equations; review

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Lecture 16: Double integrals

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Lecture 17: Double integrals in polar coordinates; applications

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Lecture 18: Change of variables

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Lecture 19: Vector fields and line integrals in the plane

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Lecture 20: Path independence and conservative fields

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Lecture 21: Gradient fields and potential functions

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Lecture 22: Green's theorem

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Lecture 23: Flux; normal form of Green's theorem

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Lecture 24: Simply connected regions; review

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Lecture 25: Triple integrals in rectangular and cylindrical coordinates

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Lecture 26: Spherical coordinates; surface area

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Lecture 27: Vector fields in 3D; surface integrals and flux

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Lecture 28: Divergence theorem

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Lecture 29: Divergence theorem (cont.): applications and proof

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Lecture 30: Line integrals in space, curl, exactness and potentials

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Lecture 31: Stokes' theorem

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Lecture 32: Stokes' theorem (cont.); review

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Lecture 33: Topological considerations - Maxwell's equations

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Lecture 34: Final review

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Lecture 35: Final review (cont.)

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