18.02SC | Fall 2010 | Undergraduate

Multivariable Calculus

Problem Sets with Solutions

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140 kB
Section 1 Part A: Problem Set 1 Solutions
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336 kB
Section 1 Part A: Supplemental Problem Set 1 Solutions
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181 kB
Section 1 Part B: Problem Set 2 Solutions
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167 kB
Section 1 Part C: Problem Set 3 Solutions
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89 kB
Session 1 Example: Force is a Vector
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113 kB
Session 1 Example: Proofs Using Vectors
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95 kB
Session 1 Example: Vector Lengths
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131 kB
Session 1 Solutions: Vectors
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203 kB
Section 2 Part A: Problem Set 4 Solutions
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127 kB
Section 2 Part B: Problem Set 5 Solutions
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125 kB
Section 2 Part C: Problem Set 6 Solutions
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426 kB
Session 2 Part A: Supplemental Problem Solutions
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96 kB
Session 2 Solutions: Dot Products
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453 kB
Section 3 Part A: Problem Set 7 Solutions
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162 kB
Section 3 Part B: Problem Set 8 Solutions
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202 kB
Section 3 Part B: Supplemental Problem Set 8 Solutions
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155 kB
Section 3 Part C: Problem Set 9 Solutions
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119 kB
Session 3 Example: Lengths and Angles
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139 kB
Session 3 Solutions: Lengths and Angles
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295 kB
Section 4 Part A: Problem Set 4 Solutions
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167 kB
Section 4 Part A: Supplemental Problem Set 10 Solutions
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211 kB
Section 4 Part B: Problem Set 11 Solutions
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196 kB
Section 4 Part B: Supplemental Problem Set 11
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246 kB
Section 4 Part B: Supplemental Problem Set 11 Solutions
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167 kB
Section 4 Part C: Problem Set 12 Solutions
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145 kB
Session 4 Example: Vector Components
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112 kB
Session 4 Solutions: Vector Components
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120 kB
Session 5 Example: Area and Determinants in 2D
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92 kB
Session 5 Solutions: Area and Determinants in 2D
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98 kB
Session 6 Example: Volumes and Determinants in Space
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91 kB
Session 6 Solutions: 3x3 Determinants
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92 kB
Session 6 Solutions: Volumes and Determinants in Space
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129 kB
Problem Set 7: Supplemental Problems
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204 kB
Problem Set 7: Supplemental Problems and Solutions
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138 kB
Session 7 Example: Cross Products
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90 kB
Session 7 Solutions: Cross Products
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146 kB
Session 8 Example: Equations of Planes
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105 kB
Session 8 Solutions: Equations of Planes
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88 kB
Session 9 Solutions: Matrix Multiplication
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137 kB
Session 10 Solutions: Meaning of Matrix Multiplication
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110 kB
Session 11 Solutions: Matrix Inverses
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119 kB
Session 12 Solutions: Equations of Planes II
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92 kB
Session 12 Solutions: Equations of Planes II
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74 kB
Session 13 Solutions: Linear Systems and Planes
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110 kB
Session 14 Example: Solutions to Square Systems
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120 kB
Session 14 Solutions: Solutions to Square Systems
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129 kB
Session 15 Solutions: Equations of Lines
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98 kB
Session 16 Solutions: Intersection of a Line and a Plane
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98 kB
Session 17 Solutions: General Parametric Equations; the Cycloid
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164 kB
18.02SC Solutions: Directional Derivatives
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104 kB
Session 19 Solutions: Velocity and Acceleration
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127 kB
Session 20 Example : Velocity and Arc Length
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115 kB
Session 20 Solutions: Velocity and Arc Length
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91 kB
Session 21 Solutions: Kepler's Second Law
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111 kB
Session 24 Solutions: Functions of Two Variables: Graphs
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79 kB
Session 25 Solutions: Level Curves and Contour Plots
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104 kB
Session 26 Solutions: Partial Derivatives
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105 kB
Session 27 Solutions: Approximation Formula
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84 kB
Session 28 Solutions: Optimization Problems
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102 kB
Session 29 Example: Least Squares
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114 kB
Session 29 Solutions: Least Squares
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97 kB
Session 30 Solutions: Second Derivative Test
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129 kB
Session 32 Example: Total Differentials and the Chain Rule
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98 kB
Session 32 Solutions: Total Differentials and the Chain Rule
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143 kB
Session 33 Solutions: Examples
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123 kB
Session 34 Solutions: Chain Rule Practice
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139 kB
Session 35 Solutions: Elliptic Paraboloid
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98 kB
Session 36 Solutions: Proof
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116 kB
Session 37 Solutions: Equation of a Tangent Plane
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141 kB
Session 39 Solutions: Lagrange Multipliers
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98 kB
Session 41 Solutions: Advanced Example for Lagrange's Multipliers
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118 kB
Session 42 Example: Constrained Differentials
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119 kB
Session 42 Solutions: Non-independent Variables
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125 kB
Session 43 Solutions: The Chain Rule with Constraints
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99 kB
Session 44 Solutions: Example
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120 kB
Session 47 Solutions: Definition of Double Integration
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156 kB
Session 48 Solutions: Regions of Integration
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136 kB
Session 49 Solutions: Exchanging the Order of Integration
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125 kB
Session 50 Solutions: Double Integrals in Polar Coordinates
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137 kB
Session 51 Solutions: Mass and Average Value
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116 kB
Session 52 Solutions: Applications: Moment of Inertia
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141 kB
Session 53 Solutions: Change of Variables
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142 kB
Session 54 Solutions: Polar Coordinates and the Jacobian
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159 kB
Session 55 Solutions: Change of Variables Example
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121 kB
Session 55: Example
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581 kB
Session 56 Solutions: Vector Fields
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130 kB
Session 57 Solutions: Work and Line Integrals
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125 kB
Session 58 Solutions: Geometric Approach to Line Integrals
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129 kB
Session 59 Solutions: Line Integrals for Work
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145 kB
Session 60 Solutions: Fundamental Theorem for Line Integrals
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136 kB
Session 60 Solutions: Line Integrals of Vector Fields
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119 kB
Session 62 Solutions: Identifying Gradient Fields and Exact Differentials
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601 kB
Session 63 Solutions: Identifying Potential Functions
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114 kB
Session 64 Solutions: Two Dimensional Curl
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124 kB
Session 65 Example: Green's Theorem
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127 kB
Session 65 Solutions: Using Green's Theorem
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147 kB
Session 66 Solutions: Identifying Gradient Fields and Exact Differentials
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123 kB
Session 68 Solutions: Green's Theorem and Area
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117 kB
Session 69 Solutions: Flux Across Curves
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129 kB
Session 70 Example: Verify Green's Theorem in Normal Form
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116 kB
Session 70 Solutions: Normal Form of Green's Theorem
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165 kB
Session 71 Example: Extended Green's Theorem
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605 kB
Session 71 Solutions: Extended Green's Theorem
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134 kB
Session 72 Solutions: Simply Connected Regions
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601 kB
Session 74 Example: Triple Integrals: Rectangular and Cylindrical Coordinates
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156 kB
Session 74 Solutions: Triple Integrals
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147 kB
Session 75 Solutions: Practice with Triple Integrals
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180 kB
Session 76 Solutions: Limits in Spherical Coordinates
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163 kB
Session 77 Example: Integrals in Spherical Coordinates
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110 kB
Session 77 Solutions: Jacobian for Spherical Coordinates
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161 kB
Session 77 Solutions: Spherical Coordinates
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151 kB
Session 78 Solutions: Applications of Spherical Coordinates
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150 kB
Session 79 Solutions: Vector Fields in Space
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135 kB
Session 80 Solutions: Calculating Flux
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139 kB
Session 81 Solutions: Flux Through Surfaces
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160 kB
Session 82 Solutions: Flux Through General Surfaces
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146 kB
Session 83 Example: General Formula for ndS
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155 kB
Session 83 Solutions: Flux Through a Paraboloid
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155 kB
Session 84 Solutions: Divergence Theorem
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616 kB
Session 85 Solutions: Problems: Del Notation; Flux
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184 kB
Session 87 Solutions: Harmonic Functions and Averages
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152 kB
Session 88 Solutions: Work Along a Space Curve
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149 kB
Session 89 Solutions: Gradient Fields and Potential Functions
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157 kB
Session 90 Example: Testing for a Conservative Field
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140 kB
Session 90 Solutions: Curl in 3D
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165 kB
Session 91 Solutions: Stokes' Theorem
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137 kB
Session 93 Examples: Extended Stokes' Theorem
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620 kB
Session 93 Solutions: Extended Stokes' Theorem
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141 kB
Session 94: Simply Connected Regions; Topology
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149 kB
Session 95 Solutions: Surface Independence

Course Info

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As Taught In
Fall 2010
Level
Undergraduate
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Simulations
Exams with Solutions
Problem Sets with Solutions
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