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Created by:
Last updated:
September 21, 2023
Duration:
Unlimited Duration
FREE
This course includes:
Unlimited Duration
Badge on Completion
Certificate of completion
Unlimited Duration
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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