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麻省理工開放課程:多變量微積分 Multivariable Calculus 英文版 DVD 只於電腦播放



Denis Auroux received the Ma?trice in mathematics from the école Normale Supérieure, Paris VII in 1994, the Licence in physics from Paris VI in 1995, the Diploma in mathematics from the Université de Paris Sud, 1995, and the Ph.D. from école Polytechnique in 1999. Jean-Pierre Bourguignon and Misha Gromov were his doctoral advisors. He completed the habilitation at the University of Paris Sud in 2003. He came to MIT as a CLE Moore instructor in 1999 and joined the MIT mathematics faculty in 2002. He was promoted to associate professor in 2004 and tenured in 2006. Professor Auroux's research interests are in the fields of symplectic topology and mirror symmetry. His distinctions include the Prix de Thèse, école Polytechnique, 1999; the Prix Peccot & Cours Peccot, Collège de France, January 2002, and the Alfred P. Sloan Research Fellowship, 2005. He received the MIT School of Science Prize for Excellence in Undergraduate Teaching in 2006.

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 47:59 Denis Auroux
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.)