Calculus III
160 videos • 5,071 views • by Bob Davis
These videos were created for use in MAT 273 at Alamance Community College. Occasionally I reference a textbook, it is Thomas' Calculus in its 14th edition.
1
Working in Space
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2
Sets of Points
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3
Distance and Midpoints
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4
Spheres
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5
Intro to Vectors
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6
Standard Position and Component Form
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7
Magnitude
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8
Vector operations
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9
Unit Vectors
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10
Angles and Dots
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11
Orthogonal Vectors
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12
Projections
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13
Work
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14
Intro to cross products
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15
Intro to matrix algebra
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16
transformations
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17
Three by Three determinants
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18
The cross product as a determinant
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19
Lines in Space
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20
Distance from point to a line
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21
Planes in Space
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22
plane through three points
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23
Distance from a point to a plane
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24
finding the distance between a point and a plane
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25
Exploring the hyperbolic paraboloid
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26
Parametric Equations and Vector functions
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27
Limits of Vector Functions
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28
Continuity of Vector Functions
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29
Using Geogebra to graph a vector function
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30
Derivatives
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31
Application of the derivative
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32
Vector functions of constant length
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33
The indefinite integral
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34
The definite integral
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35
An initial value problem
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36
The arc length formula
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37
Arc length of a helix
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38
The arc length parameter
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39
Problems from Week 3
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40
The Chain Rule
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41
Curvature
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42
The Principal Unit Normal Vector
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43
An example and a Helix
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44
The Binormal Vector
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45
The Frenet Frame
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46
Acceleration, the Osculating Plane, and a Helix
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47
problems from week 4, curvature and acceleration
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48
Intro to functions on several variables
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49
Finding domains and ranges for functions on two variables
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50
Sets in the plane terminology
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51
Surfaces level curves and contour curves
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52
Functions on 3 variables and level surfaces
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53
Sketching a level surface that passes through a given point
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54
intro to limits of functions on 2 variables
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55
examples of limits of functions on two variables
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56
Limits that do not exist
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57
Continuity at a point
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58
Using polar coordinates to evaluate a limit
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59
An intro to partial derivatives
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60
The definitions of partial derivatives and an example
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61
Partials of a function on three variables
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62
Higher order partials
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63
The mixed partials theorem
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64
A Laplace equation
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65
A higher order mixed partial
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66
Intro to the chain rule
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67
Using the chain rule
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68
A chain rule for a function on 3 variables
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69
A chain rule for two independent variables
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70
Implicit differentiation and the chain rule
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71
Intro to Directional Derivatives
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72
Directional Derivatives calculation formula
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73
Using the definition to calculate a directional derivative
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74
The gradient vector
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75
Properties of the gradient vector
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76
Gradients and level curves
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77
Tangents to level curves
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78
Chain rule for paths
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79
Tangent Planes to Level Surfaces
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80
Finding tangent planes to surfaces
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81
Finding a tangent plane and a normal line
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82
Linearizations and Linear approximations
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83
Differentials and linear approximations
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84
Differentiability
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85
Intro to extreme values and saddle points
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86
The second derivative test for local extreme values
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87
Using the second derivative test for local extreme values
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88
Absolute extreme values
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89
Iterated integration
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90
What does iterated integration calculate
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91
The double integral
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92
Fubini's Theorem
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93
Using Fubini's Theorem to evaluate a double integral
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94
Double integrals over general regions
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95
Finding limits of integration
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96
An example where one order of integration is better
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97
Properties of double integrals
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98
Setting up 2 iterated integrals
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99
Using double integration to describe areas
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100
Finding an area from a double integral
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101
Sketching a region and finding an area
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102
The average value of a function on two variables
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103
Double integrals in polar coordinates
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104
Finding an area using a double integral in polar coordinates
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105
Setting up a double integral in polar coordinates
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106
Converting from rectangular to polar coordinates
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107
Finding a volume
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108
Triple integration
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109
Finding bounds for a triple integral
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110
Triple integrals as volumes
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111
Setting up a triple integral to find a volume
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112
Finding a volume
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113
The average value of a function on 3 variables
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114
Evaluating a triple integral
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115
Introduction to cylindrical coordinates
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116
Understanding dV in cylindrical coordinates
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117
Integrating in cylindrical coordinates
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118
Finding bounds in cylindrical coordinates
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119
Introduction to spherical coordinates
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120
Relationships between the coordinate systems
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121
A spherical region
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122
Understanding dV in spherical coordinates
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123
Integrating in spherical coordinates
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124
Setting up three triple integrals
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125
Substitution in multiple integrals
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126
A Jacobian
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127
Integrating using a substitution
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128
Substitution in Triple integrals
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129
Finding the volume of an ellipsoid
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130
Problems from Week 13 15 8
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131
Line integrals in the plane
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132
A line integral over a circle
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133
A line integral over a path
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134
Line integrals in space
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135
A line integral over a helix
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136
Additivity of line integrals
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137
Vector Fields
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138
Gradient Fields
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139
Line integral of a vector field
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140
Evaluating a line integral of a vector field
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141
Writing a line integral of a vector field in terms of dx, dy, and dz
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142
Work done by a force field
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143
Calculating work
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144
Flow over a velocity field
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145
Flux over a velocity field
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146
Calculating Circulation Flow and Flux
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147
Path Independence, Conservative fields, and Potential functions
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148
The Fundamental Theorem of Line Integrals
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149
Conservative Fields are Vector Fields
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150
The Component Test
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151
Evaluating a Path Integral over a Conservative Field
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152
Green's Theorem
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153
Using Green's Theorem
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154
Circulation and Flux
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155
Areas and Green's Theorem
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156
Finding an Area
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157
Problems From Week 16 (16.3 & 16.4)
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158
Surface Integrals
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159
Surface Integrals of Vector Fields
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160
Stokes' Theorem
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