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 Angles
  * 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
    * Recitation 17: Graphing Surfaces
    * Recitation 18: Level Curves
    * Recitation 19: Level Curves and Critical Points
    * Recitation 20: Partial Derivatives
  * Lecture 09: Max-min problems; least squares
    * Recitation 21: Tangent Plane Approximation
    * Recitation 22: Least Squares
  * Lecture 10: Second derivative test; boundaries and infinity
   * Recitation 23: Second Derivative Test
   * Recitation 24: Max/Min
  * Lecture 11: Differentials; chain rule
    * Recitation 25: Total Differentials and the Chain Rule
  * Lecture 12: Gradient; directional derivative; tangent plane
    * Recitation 26: Tangent Planes
    * Recitation 27: Gradient and Directional Derivative
  * Lecture 13: Lagrange multipliers
    * Recitation 28: Lagrange Multipliers
    * Recitation 29: Lagrange Multipliers (3 Variables)
  * Lecture 14: Non-independent variables
    * Recitation 30: The Chain Rule with Constraints
    * Recitation 31: Gradients - Composition
  * Lecture 15: Partial differential equations; review


* Unit 3: Double Integrals and Line Integrals in the Plane
  * Lecture 16: Double integrals
    * Recitation 32: Regions of Integration
    * Recitation 33: Changing the Order of Integration
  * Lecture 17: Double integrals in polar coordinates; applications
    * Recitation 34: Integration in Polar Coordinates
    * Recitation 35: Integrals with Density
  * Lecture 18: Change of variables
    * Recitation 36: Change of Variables
    * Recitation 37: Integral of exp(-x²)
    * Recitation 38: Change of Variables
  * Lecture 19: Vector fields and line integrals in the plane
    * Recitation 39: Line Integrals: Path dependence
    * Recitation 40: Line Integrals: Parametrization Independence
    * Recitation 41: Line Integrals by Geometric Reasoning
  * Lecture 20: Path independence and conservative fields
    * Recitation 42: Fundamental Theorem of Line Integrals
  * Lecture 21: Gradient fields and potential functions
    * Recitation 43: Non-Conservative Vector Fields
    * Recitation 44: Potentials of Gradient Fields
  * Lecture 22: Green's theorem
    * Recitation 45: Green's Theorem: An Off Center Circle
    * Recitation 45a: Green's Theorem: Area Under an Arch
    * Recitation 46: Application of Green's Theorem
  * Lecture 23: Flux; normal form of Green's theorem
    * Recitation 47: Flux Across a Curve
    * Recitation 48: Green's Theorem in Normal Form
  * Lecture 24: Simply connected regions; review
    * Recitation 49: Extended Green's Theorem
    * Recitation 50: Domains of Vector Fields


* Unit 4: Triple Integrals and Surface Integrals in 3-Space
  * Lecture 25: Triple integrals in rectangular and cylindrical coordinates
    * Recitation 51: Volume in Cylindrical Coordinates
    * Recitation 52: Average Height
    * Recitation 53: Moment of Inertia of a Cylinder
  * Lecture 26: Spherical coordinates; surface area
    * Recitation 54: Average Distance on a Sphere
    * Recitation 55: Gravity and a Half-Sphere
  * Lecture 27: Vector fields in 3D; surface integrals and flux
    * Recitation 56: Flux Through Easy Surfaces
    * Recitation 57: Flux Through a Square
    * Recitation 58: Flux Through Surfaces
  * Lecture 28: Divergence theorem
    * Recitation 59: Flux
    * Recitation 60: Flux and the Divergence Theorem
    * Recitation 61: Extended Gauss' Theorem
  * Lecture 29: Divergence theorem (cont.): applications and proof
    * Recitation 62: Del and the Product Rule
  * Lecture 30: Line integrals in space, curl, exactness and potentials
    * Recitation 63: Line Integral on a Helix
    * Recitation 64: Conservative Fields and Exact Differentials
  * Lecture 31: Stokes' theorem
    * Recitation 65: Stokes' Theorem
    * Recitation 66: Extended Stokes' Theorem
  * Lecture 32: Stokes' theorem (cont.)
    * Recitation 67: Simply Connected Regions
    * Recitation 68: More Stokes' Theorem
    * Recitation 69: Consequences of Stokes' Theorem
  * Lecture 33: Topological considerations; Maxwell's equations
  * Lecture 34: Final review
  * Lecture 35: Final review (cont.)


---

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