Multivariable Calculus (MIT 18.02) - Worked examples 2010
Christine Breiner and David Jordan and Joel Lewis

@article{,
title= {Multivariable Calculus (MIT 18.02) - Worked examples 2010},
journal= {},
author= {Christine Breiner and David Jordan and Joel Lewis},
year= {2010},
url= {http://ocw.mit.edu/18-02SCF10 },
abstract= {This course covers differential, integral and vector calculus for functions of more than one variable. These mathematical tools and methods are used extensively in the physical sciences, engineering, economics and computer graphics.

**Main course URL:** http://ocw.mit.edu/18-02SCF10 

---

**Prerequisites**:
* Single Variable Calculus (MIT 18.01) - [Video Lectures](https://academictorrents.com/details/c38ec459fd87f1672e917634addba301ad26b248) and [Worked Examples](https://academictorrents.com/details/6ed053c563f13e01a3526bd8b359810a9ea6a9ca)

**Related materials:**
* [Multivariable Calculus (MIT 18.02) - Video lectures 2007](https://academictorrents.com/details/81d27851df2879ed1307c8d60980d2b8af19264b)

---

**Table of contents:**

* Unit 1: Vectors and Matrices
  * Lecture 01: Dot product
    * Recitation 01: Coordinate Free Proofs: Centroid of a Triangle
    * Recitation 02: Dot Products and Angle
  * Lecture 02: Determinants; cross product
    * Recitation 03: Components of a Vector
    * Recitation 04: Area of a Parallelogram
    * Recitation 05: Determinants
    * Recitation 06: Volume of a Parallelepiped
  * Lecture 03: Matrices; inverse matrices
    * Recitation 07: Area Using Cross Product
    * Recitation 08: Matrix Multiplication Practice
    * Recitation 09: Solve a Linear System Using Matrices
  * Lecture 04: Square systems; equations of planes
    * Recitation 10: Equations of Planes
    * Recitation 11: Distance of a Point to a Plane
    * Recitation 12: Systems of Linear Equations
  * Lecture 05: Parametric equations for lines and curves
    * Recitation 13: Parametrized Lines and Intersections
    * Recitation 14: Parametric Line Intersecting a Plane
  * Lecture 06: Velocity, acceleration; Kepler's second law
    * Recitation 15: Differentiating a Vector Valued Function
    * Recitation 16: Parametric Curves: Velocity, Acceleration, Length
  * Lecture 07: Review


* Unit 2: Partial Derivatives
  * 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


* Unit 3: Double Integrals and Line Integrals in the Plane
  * 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


* Unit 4: Triple Integrals and Surface Integrals in 3-Space
  * 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.)

---

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