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Last updated:

September 21, 2023

Duration:

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FREE

This course includes:

Unlimited Duration

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Description

18.02 Multivariable Calculus (Fall 2007, MIT OCW). This consists of 35 video lectures given by Professor Denis Auroux, covering vector and multi-variable calculus.

Topics covered in this course include vectors and matrices, partial derivatives, double and triple integrals, and vector calculus in 2 and 3-space. (from ocw.mit.edu)

Course Curriculum

  • Lecture 01 – Dot Product Unlimited
  • Lecture 02 – Determinants; Cross Product Unlimited
  • Lecture 03 – Matrices; Inverse Matrices Unlimited
  • Lecture 04 – Square Systems; Equations of Planes Unlimited
  • Lecture 05 – Parametric Equations for Lines and Curves Unlimited
  • Lecture 06 – Velocity, Acceleration; Kepler’s Second Law Unlimited
  • Lecture 07 – Exam Review Unlimited
  • Lecture 08 – Level Curves; Partial Derivatives; Tangent Plane Approximation Unlimited
  • Lecture 09 – Max-Min Problems; Least Squares Unlimited
  • Lecture 10 – Second Derivative Test; Boundaries and Infinity Unlimited
  • Lecture 11 – Differentials; Chain Rule Unlimited
  • Lecture 12 – Gradient; Directional Derivative; Tangent Plane Unlimited
  • Lecture 13 – Lagrange Multipliers Unlimited
  • Lecture 14 – Non-Independent Variables Unlimited
  • Lecture 15 – Partial Differential Equations Unlimited
  • Lecture 16 – Double Integrals Unlimited
  • Lecture 17 – Double Integrals in Polar Coordinates Unlimited
  • Lecture 18 – Change of Variables Unlimited
  • Lecture 19 – Vector Fields and Line Integrals in the Plane Unlimited
  • Lecture 20 – Path Independence and Conservative Fields Unlimited
  • Lecture 21 – Gradient Fields and Potential Functions Unlimited
  • Lecture 22 – Green’s Theorem Unlimited
  • Lecture 23 – Flux; Normal Form of Green’s Theorem Unlimited
  • Lecture 24 – Simply Connected Regions Unlimited
  • Lecture 25 – Triple Integrals in Rectangular and Cylindrical Coordinates Unlimited
  • Lecture 26 – Spherical Coordinates; Surface Area Unlimited
  • Lecture 27 – Vector Fields in 3D; Surface Integrals and Flux Unlimited
  • Lecture 28 – Divergence Theorem Unlimited
  • Lecture 29 – Divergence Theorem (cont.): Applications and Proof Unlimited
  • Lecture 30 – Line Integrals in Space, Curl, Exactness and Potentials Unlimited
  • Lecture 31 – Stokes’ Theorem Unlimited
  • Lecture 32 – Stokes’ Theorem (cont.) Unlimited
  • Lecture 33 – Topological Considerations – Maxwell’s Equations Unlimited
  • Lecture 34 – Final Review Unlimited
  • Lecture 35 – Final Review (cont.) Unlimited

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