18.02SC | Fall 2010 | Undergraduate

Multivariable Calculus

Lecture Videos

video
85 MB
Session 1 Clip: Vectors
video
85 MB
Session 2 Clip: Dot Products
video
85 MB
Session 3 Clip: Lengths and Angles
video
116 MB
Session 4 Clip: Vector Components
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116 MB
Session 5 Clip: Area and Determinants in 2D
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116 MB
Session 6 Clip: Volumes and Determinants in Space
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116 MB
Session 7 Clip 1: Cross Products
video
114 MB
Session 7 Clip 2: More on Cross Products
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114 MB
Session 8 Clip: Equations of Planes
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114 MB
Session 9 Clip: Matrix Multiplication
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114 MB
Session 10 Clip: Meaning of Matrix Multiplication
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114 MB
Session 11 Clip: Matrix Inverses
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108 MB
Session 12 Clip: Equations of Planes
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108 MB
Session 13 Clip: Linear Systems and Planes
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108 MB
Session 14 Clip: Solutions to Square Systems
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113 MB
Session 15 Clip: Equations of Lines
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113 MB
Session 16 Clip: Intersection of a Line and a Plane
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113 MB
Session 17 Clip: General Parametric Equations and the Cycloid
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113 MB
Session 18 Clip: Point (Cusp) of a Cycloid
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106 MB
Session 19 Clip: Velocity and Acceleration
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106 MB
Session 20 Clip: Velocity and Arc Length
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106 MB
Session 21 Clip: Kepler's Second Law
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110 MB
Session 22 Clip: Review of Topics
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110 MB
Session 23 Clip: Review of Problems
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103 MB
Session 24 Clip: Functions of Two Variables: Graphs
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103 MB
Session 25 Clip: Level Curves and Contour Plots
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103 MB
Session 26 Clip: Partial Derivatives
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111 MB
Session 27 Clip: Approximation Formula
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111 MB
Session 28 Clip: Optimization Problem
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111 MB
Session 29 Clip: Least Squares
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115 MB
Session 30 Clip 1: Quadratic Example
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115 MB
Session 30 Clip 2: Second Derivative Test
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115 MB
Session 31 Clip: Example
video
111 MB
Session 32 Clip: Total Differentials and Chain Rule
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111 MB
Session 33 Clip: Examples
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111 MB
Session 34 Clip: Chain Rule with More Variables
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110 MB
Session 35 Clip: Definition, Perpendicular to Level Curves
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110 MB
Session 36 Clip: Proof
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110 MB
Session 37 Clip: Example
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110 MB
Session 38 Clip: Directional Derivatives
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111 MB
Session 39 Clip: Lagrange Multipliers by Example
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111 MB
Session 40 Clip: Proof of Lagrange Multipliers
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111 MB
Session 41 Clip: Advanced Example
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109 MB
Session 42 Clip: Constrained Differentials
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109 MB
Session 43 Clip: Clearer Notation
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109 MB
Session 44 Clip: Example
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100 MB
Session 45 Clip: Review of Topics
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100 MB
Session 46 Clip: Review of Problems
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106 MB
Session 47 Clip: Definition of Double Integration
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106 MB
Session 48 Clip: Examples of Double Integration
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106 MB
Session 49 Clip: Exchanging the Order of Integration
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114 MB
Session 50 Clip: Double Integrals in Polar Coordinates
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114 MB
Session 51 Clip: Applications: Mass and Average Value
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114 MB
Session 52 Clip: Applications: Moment of Inertia
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110 MB
Session 53 Clip: Change of Variables
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110 MB
Session 54 Clip: Polar Coordinates
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110 MB
Session 55 Clip: Example
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112 MB
Session 56 Clip: Vector Fields
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112 MB
Session 57 Clip: Work and Line Integrals
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112 MB
Session 58 Clip: Geometric Approach
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111 MB
Session 59 Clip: Line Integrals
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111 MB
Session 60 Clip: An Important Non-Conservative Field
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111 MB
Session 60 Clip: Fundamental Theorem
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111 MB
Session 61 Clip: Conservative Fields, Path Independence, Exact
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110 MB
Session 62 Clip: Gradient Fields
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22 MB
Session 62: Non-Conservative Vector Fields
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110 MB
Session 63 Clip: Potential Functions
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110 MB
Session 64 Clip: Curl
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103 MB
Session 65 Clip: Green's Theorem
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103 MB
Session 66 Clip: Curl(F)=0 Implies Conservative
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103 MB
Session 67 Clip: Proof of Green's Theorem
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103 MB
Session 68 Clip: Planimeter: Green's Theorem and Area
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111 MB
Session 69 Clip: Calculating Flux
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111 MB
Session 69 Clip: Flux Across a Curve
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111 MB
Session 70 Clip: Introduction and Definition of Divergence
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108 MB
Session 71 Clip: Extended Green's Theorem
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108 MB
Session 72 Clip: Simply Connected Regions and Conservative Fields
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108 MB
Session 73 Clip: Exam Review
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107 MB
Session 74 Clip: Cylindrical Coordinates
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107 MB
Session 74 Clip: Triple Integrals
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107 MB
Session 75 Clip: Applications and Examples
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112 MB
Session 76 Clip: Spherical Coordinates
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112 MB
Session 77 Clip: Triple Integrals in Spherical Coordinates
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112 MB
Session 78 Clip: Gravitational Attraction
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111 MB
Session 79 Clip: Vector Fields in Space
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111 MB
Session 80 Clip: Flux Through a Surface
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111 MB
Session 81 Clip: Calculating Flux, Finding ndS
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108 MB
Session 82 Clip: ndS for a Surface z=f(x,y)
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108 MB
Session 83 Clip: Other Ways to Find ndS
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108 MB
Session 84 Clip: Divergence Theorem
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111 MB
Session 85 Clip: Physical Meaning of Flux, Del Notation
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111 MB
Session 86 Clip: Proof of the Divergence Theorem
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111 MB
Session 87 Clip: Diffusion Equation
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110 MB
Session 88 Clip: Line Integrals in Space
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110 MB
Session 89 Clip: Gradient Fields and Potential Functions
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110 MB
Session 90 Clip: Curl in 3D
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107 MB
Session 91 Clip: Stokes' Theorem
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107 MB
Session 92 Clip: Proof of Stokes' Theorem
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107 MB
Session 93 Clip: Example
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110 MB
Session 94 Clip: Simply Connected Regions, Topology
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110 MB
Session 95 Clip: Stokes' Theorem and Surface Independence
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110 MB
Session 96 Clip: Summary of Multiple Integration
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63 MB
Session 97 Clip: Curl and Physics
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63 MB
Session 98 Clip: Introduction
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97 MB
Session 99 Clip 1: Vectors, Equations of Lines/Curves/Planes
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97 MB
Session 99 Clip 2: Matrices, Determinants, Linear Systems
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97 MB
Session 100 Clip 1: Functions of 2 Variables, Partial Derivatives
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97 MB
Session 100 Clip 2: Max-Min Problems, Lagrange Multipliers
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108 MB
Session 101 Clip 1: Double Integrals, Jacobian, Triple Integrals
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108 MB
Session 101 Clip 2: Applications
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108 MB
Session 102 Clip 1: Work, Line Integrals, Curl
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108 MB
Session 102 Clip 2: Stokes, Green's, Divergence Theorems

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Fall 2010
Level
Undergraduate
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Exams with Solutions
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Lecture Notes
Problem Sets
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