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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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