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Uedu Open / Multivariable Calculus
18.02

Multivariable Calculus

Prof. David Jerison, Prof. Arthur Mattuck | Spring 2006
Science & Math Mathematics Calculus Differential Equations Linear Algebra
前往原始課程
CC BY-NC-SA 4.0
課程簡介
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.
Course Information
SourceMIT 開放式課程
科系Mathematics
LanguageEnglish
影片數35
課程影片 (35)
1
Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 1: Dot product | MIT 18.02 Multivariable Calculus, Fall 2007
2
Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 2: Determinants; cross product | MIT 18.02 Multivariable Calculus, Fall 2007
3
Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 3: Matrices; inverse matrices | MIT 18.02 Multivariable Calculus, Fall 2007
4
Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 4: Square systems; equations of planes | MIT 18.02 Multivariable Calculus, Fall 2007
5
Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 5: Parametric equations for lines and curves | MIT 18.02 Multivariable Calculus, Fall 2007
6
Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 6: Velocity, acceleration; Kepler's second law | MIT 18.02 Multivariable Calculus, Fall 2007
7
Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 7: Review | MIT 18.02 Multivariable Calculus, Fall 2007
8
Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07
Lec 8: Level curves; partial derivatives; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07
9
Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 9: Max-min problems; least squares | MIT 18.02 Multivariable Calculus, Fall 2007
10
Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 10: Second derivative test; boundaries & infinity | MIT 18.02 Multivariable Calculus, Fall 2007
11
Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 11: Differentials; chain rule | MIT 18.02 Multivariable Calculus, Fall 2007
12
Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07
Lec 12: Gradient; directional derivative; tangent plane | MIT 18.02 Multivariable Calculus, Fall 07
13
Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 13: Lagrange multipliers | MIT 18.02 Multivariable Calculus, Fall 2007
14
Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 14: Non-independent variables | MIT 18.02 Multivariable Calculus, Fall 2007
15
Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 15: Partial differential equations; review | MIT 18.02 Multivariable Calculus, Fall 2007
16
Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 16: Double integrals | MIT 18.02 Multivariable Calculus, Fall 2007
17
Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 17: Double integrals in polar coords; applications | MIT 18.02 Multivariable Calculus, Fall 2007
18
Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 18: Change of variables | MIT 18.02 Multivariable Calculus, Fall 2007
19
Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 19: Vector fields and line integrals in the plane | MIT 18.02 Multivariable Calculus, Fall 2007
20
Lec 20: Path independence and conservative fields | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 20: Path independence and conservative fields | MIT 18.02 Multivariable Calculus, Fall 2007
21
Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 21: Gradient fields and potential functions | MIT 18.02 Multivariable Calculus, Fall 2007
22
Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 22: Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007
23
Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 23: Flux; normal form of Green's theorem | MIT 18.02 Multivariable Calculus, Fall 2007
24
Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 24: Simply connected regions; review | MIT 18.02 Multivariable Calculus, Fall 2007
25
Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 25: Triple integrals in rectangular & cylindrical | MIT 18.02 Multivariable Calculus, Fall 2007
26
Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 26: Spherical coordinates; surface area | MIT 18.02 Multivariable Calculus, Fall 2007
27
Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 27: Vector fields in 3D; surface integrals & flux | MIT 18.02 Multivariable Calculus, Fall 2007
28
Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 28: Divergence theorem | MIT 18.02 Multivariable Calculus, Fall 2007
29
Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07
Lec 29: Divergence theorem (cont.): applications & proof | MIT 18.02 Multivariable Calculus, Fall 07
30
Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 30: Line integrals in space, curl, exactness... | MIT 18.02 Multivariable Calculus, Fall 2007
31
Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 31: Stokes' theorem | MIT 18.02 Multivariable Calculus, Fall 2007
32
Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 32: Stokes' theorem (cont.); review | MIT 18.02 Multivariable Calculus, Fall 2007
33
Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07
Lec 33: Topological considerations; Maxwell's equations | MIT 18.02 Multivariable Calculus, Fall 07
34
Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 34: Final review | MIT 18.02 Multivariable Calculus, Fall 2007
35
Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007
Lec 35: Final review (cont.) | MIT 18.02 Multivariable Calculus, Fall 2007