# InfoCoBuild

## 18.02 Multivariable Calculus

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) 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 - Exam 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 Lecture 16 - Double Integrals Lecture 17 - Double Integrals in Polar Coordinates 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 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.) Lecture 33 - Topological Considerations - Maxwell's Equations Lecture 34 - Final Review Lecture 35 - Final Review (cont.)

 References 18.02 Multivariable Calculus Instructors: Prof. Denis Auroux. Lecture Notes. Exams and Solutions. Subtitles/Transcript. Assignments (no Solutions). This course covers vector and multi-variable calculus.