Become a Calculus 3 Master

Getting started
1 Quick overview before we get underway
2 Download the Calc 3 formula sheet

Partial Derivatives – Three-dimensional coordinate systems
3 Introduction to three-dimensional coordinate systems
4 Plotting points in three dimensions
5 Plotting points in three dimensions
6 Distance between points in three dimensions
7 Distance between points in three dimensions
8 Center radius and equation of the sphere
9 Center radius and equation of the sphere
10 Describing a region in three-dimensional space
11 Using inequalities to describe the region

Partial Derivatives – Sketching graphs and level curves
12 Introduction to sketching graphs and level curves
13 Sketching level curves of multivariable functions

Partial Derivatives – Lines and planes
14 Introduction to lines and planes
15 Vector parametric and symmetric equations of a line
16 Vector and parametric equations of a line
17 Parametric and symmetric equations of a line
18 Symmetric equations of a line
19 Parallel intersecting skew and perpendicular lines
20 Parallel intersecting skew and perpendicular lines
21 Equation of a plane
22 Equation of a plane
23 Intersection of a line and a plane
24 Intersection of a line and a plane
25 Parallel perpendicular and angle between planes
26 Parallel perpendicular and angle between planes
27 Parametric equations for the line of intersection of two planes
28 Parametric equations for the line of intersection of two planes
29 Symmetric equations for the line of intersection of two planes
30 Symmetric equations for the line of intersection of two planes
31 Distance between a point and a line
32 Distance between a point and a plane
33 Distance between parallel planes

Partial Derivatives – Cylinders and quadric surfaces
34 Introduction to cylinders and quadric surfaces
35 Reference chart for cylinders and quadric surfaces
36 Reducing equations to standard form
37 Sketching the surface

Partial Derivatives – Limits and continuity
38 Introduction to limits and continuity
39 Domain of a multivariable function
40 Domain of a multivariable function example 2
41 Limit of a multivariable function
42 Precise definition of the limit for multivariable functions
43 Discontinuities of multivariable functions
44 Compositions of multivariable functions

Partial Derivatives – Partial derivatives
45 Introduction to partial derivatives
46 Partial derivatives in two variables
47 Partial derivatives in two variables
48 Partial derivatives in three or more variables
49 Partial derivatives in three or more variables
50 Higher order partial derivatives
51 Higher order partial derivatives

Partial Derivatives – Differentials
52 Introduction to differentials
53 Differential of a multivariable function
54 Differential of a multivariable function

Partial Derivatives – Chain rule
55 Introduction to chain rule
56 Chain rule for multivariable functions
57 Chain rule for multivariable functions
58 Chain rule for multivariable functions tree diagram

Partial Derivatives – Implicit differentiation
59 Introduction to implicit differentiation
60 Implicit differentiation for multivariable functions
61 Implicit differentiation for multivariable functions

Partial Derivatives – Directional derivatives
62 Introduction to directional derivatives
63 Directional derivatives in the direction of the vector
64 Directional derivatives in the direction of the vector
65 Directional derivatives in the direction of the angle

Partial Derivatives – Linear approximation and linearization
66 Introduction to linear approximation and linearization
67 Linear approximation in two variables
68 Linear approximation in two variables
69 Linearization of a multivariable function

Partial Derivatives – Gradient vectors
70 Introduction to gradient vectors
71 Gradient vectors
72 Gradient vectors
73 Gradient vectors and the tangent plane
74 Gradient vectors and the tangent plane
75 Maximum rate of change and its direction

Partial Derivatives – Tangent planes and normal lines
76 Introduction to tangent planes and normal lines
77 Equation of the tangent plane
78 Equation of the tangent plane
79 Normal line to the surface
80 Normal line to the surface

Partial Derivatives – Optimization
81 Introduction to optimization
82 Critical points
83 Second derivative test
84 Second derivative test
85 Local extrema and saddle points
86 Global extrema
87 Extreme value theorem
88 Extreme value theorem example 2

Partial Derivatives – Applied optimization
89 Introduction to applied optimization
90 Maximum product of three real numbers
91 Maximum volume of a rectangular box inscribed in a sphere
92 Minimum distance from the point to the plane
93 Points on the cone closest to the given point

Partial Derivatives – Lagrange multipliers
94 Introduction to lagrange multipliers
95 Lagrange multipliers
96 Two dimensions one constraint
97 Two dimensions one constraint example 2
98 Three dimensions one constraint
99 Three dimensions two constraints

Multiple Integrals – Approximating double integrals
100 Introduction to approximating double integrals
101 Approximating double integrals with rectangles
102 Midpoint rule for double integrals
103 Midpoint rule for double integrals
104 Riemann sums for double integrals

Multiple Integrals – Double integrals
105 Introduction to double integrals
106 Average value
107 Average value
108 Iterated and double integrals
109 Iterated integrals
110 Iterated integrals example 2
111 Double integrals
112 Type I and II regions
113 Type I and II regions
114 Finding surface area
115 Finding surface area
116 Finding volume
117 Finding volume
118 Changing the order of integration

Multiple Integrals – Double integrals in polar coordinates
119 Introduction to double integrals in polar coordinates
120 Changing iterated integrals to polar coordinates
121 Changing iterated and double integrals to polar coordinates
122 Changing double integrals to polar coordinates
123 Sketching area
124 Sketching area
125 Finding area
126 Finding area
127 Finding volume
128 Finding volume

Multiple Integrals – Applications of double integrals
129 Introduction to applications of double integrals
130 Double integrals to find mass and center of mass

Multiple Integrals – Approximating triple integrals
131 Introduction to approximating triple integrals
132 Midpoint rule for triple integrals
133 Midpoint rule for triple integrals

Multiple Integrals – Triple integrals
134 Introduction to triple integrals
135 Iterated and triple integrals
136 Iterated integrals
137 Triple integrals
138 Average value
139 Average value
140 Finding volume
141 Finding volume
142 Expressing the integral six ways
143 Expressing the integral six ways

Multiple Integrals – Triple integrals in cylindrical coordinates
144 Introduction to triple integrals in cylindrical coordinates
145 Cylindrical coordinates
146 Cylindrical coordinates
147 Changing triple integrals to cylindrical coordinates
148 Changing triple integrals to cylindrical coordinates
149 Finding volume
150 Finding volume

Multiple Integrals – Triple integrals in spherical coordinates
151 Introduction to triple integrals in spherical coordinates
152 Spherical coordinates
153 Spherical coordinates
154 Changing triple integrals to spherical coordinates
155 Changing triple integrals to spherical coordinates
156 Finding volume
157 Finding volume

Multiple Integrals – Change of variables
158 Introduction to change of variables
159 Jacobian for two variables
160 Jacobian for two variables
161 Jacobian for three variables
162 Jacobian for three variables

Multiple Integrals – Applications of triple integrals
163 Introduction to applications of triple integrals
164 Triple integrals to find mass and center of mass
165 Moments of inertia

Vectors – Introduction to vectors
166 Introduction to vectors
167 Vector from two points
168 Combinations of vectors
169 Combinations of vectors
170 Sum of two vectors
171 Sum of two vectors
172 Copying vectors and using them to find combinations
173 Unit vector in the direction of the given vector
174 Angle between a vector and the x-axis
175 Magnitude and angle of the resultant force
176 Magnitude and angle of the resultant force

Vectors – Dot products
177 Introduction to dot products
178 Dot product of two vectors
179 Dot product of two vectors
180 Angle between two vectors
181 Angle between two vectors
182 Orthogonal parallel or neither
183 Orthogonal parallel or neither
184 Acute angle between the lines
185 Acute angle between the lines
186 Acute angles between the curves
187 Acute angles between the curves
188 Direction cosines and direction angles
189 Direction cosines and direction angles
190 Scalar equation of a line
191 Scalar equation of a line
192 Scalar equation of a plane
193 Scalar equation of a plane
194 Scalar and vector projections
195 Scalar and vector projections

Vectors – Cross products
196 Introduction to cross products
197 Cross product of two vectors
198 Cross product of two vectors
199 Vector orthogonal to the plane
200 Vector orthogonal to the plane
201 Volume of the parallelepiped from vectors
202 Volume of the parallelepiped from vectors
203 Volume of the parallelepiped from adjacent edges
204 Volume of the parallelepiped from adjacent edges
205 Scalar triple product to prove vectors are coplanar
206 Scalar triple product to prove vectors are coplanar

Vectors – Vector functions and space curves
207 Introduction to vector functions and space curves
208 Domain of a vector function
209 Domain of a vector function
210 Limit of a vector function
211 Limit of a vector function
212 Sketching the vector equation
213 Projections of the curve
214 Projections of the curve
215 Vector and parametric equations of a line segment
216 Vector and parametric equations of a line segment
217 Vector function for the curve of intersection of two surfaces
218 Vector function for the curve of intersection of two surfaces

Vectors – Derivatives and integrals of vector functions
219 Introduction to derivatives and integrals of vector functions
220 Derivative of a vector function
221 Derivative of a vector function
222 Unit tangent vector
223 Unit tangent vector
224 Parametric equations of the tangent line
225 Parametric equations of the tangent line
226 Integral of a vector function
227 Integral of a vector function

Vectors – Arc length and curvature
228 Introduction to arc length and curvature
229 Arc length of a vector function
230 Arc length of a vector function
231 Reparametrizing the curve
232 Reparametrizing the curve
233 Unit tangent and unit normal vectors
234 Unit tangent and unit normal vectors
235 Curvature
236 Curvature
237 Maximum curvature
238 Maximum curvature
239 Normal and osculating planes
240 Normal and osculating planes

Vectors – Velocity and acceleration
241 Introduction to velocity and acceleration
242 Velocity and acceleration vectors
243 Velocity and acceleration vectors
244 Velocity acceleration and speed given position
245 Velocity acceleration and speed given position
246 Velocity and position given acceleration and initial conditions
247 Tangential and normal components of acceleration
248 Tangential and normal components of acceleration

Vectors – Line integrals
249 Introduction to line integrals
250 Line integrals
251 Line integral of a curve
252 Line integral of a vector function
253 Conservative vector fields
254 Potential function of a conservative vector field
255 Potential function of a conservative vector field to evaluate a line integral
256 Independence of path
257 Independence of path
258 Work done by the force field
259 Open connected and simply-connected

Vectors – Greens theorem
260 Introduction to greens theorem
261 Greens theorem for one region
262 Greens theorem for one region
263 Greens theorem for two regions
264 Greens theorem for two regions

Vectors – Curl and divergence
265 Introduction to curl and divergence
266 Curl and divergence of a vector field
267 Potential function of a conservative vector field three dimensions

Vectors – Parametric surfaces and areas
268 Introduction to parametric surfaces and areas
269 Points on the surface
270 Surface of the vector equation
271 Parametric representation of the surface
272 Tangent plane to the parametric surface
273 Area of a surface

Vectors – Surface integrals
274 Introduction to surface integrals
275 Surface integrals
276 Surface integrals example 2

Vectors – Stokes and divergence theorem
277 Introduction to stokes and divergence theorem
278 Stokes theorem
279 Divergence theorem

Differential Equations – Introduction
280 Introduction to differential equations
281 Overview of differential equations
282 Sketching direction fields
283 Sketching direction fields

Differential Equations – Eulers method
284 Introduction to eulers method
285 Eulers method
286 Eulers method

Differential Equations – Separable differential equations
287 Introduction to separable differential equations
288 Separable differential equations
289 Separable differential equations
290 Change of variable for separable differential equations
291 Change of variable for separable differential equations
292 Separable differential equations initial value problems
293 Separable differential equations initial value problems
294 Mixing problems
295 Mixing problems
296 Orthogonal trajectories
297 Orthogonal trajectories

Differential Equations – Logistic models
298 Introduction to logistic models
299 Population growth
300 Population growth
301 Logistic growth model for a population
302 Predator-prey systems
303 Predator-prey systems
304 Equilibrium solutions and stability

Differential Equations – Exact differential equations
305 Introduction to exact differential equations
306 Exact differential equation
307 Exact differential equations
308 Exact differential equations initial value problems

Differential Equations – Linear differential equations
309 Introduction to linear differential equations
310 Linear differential equations
311 Linear differential equations
312 Linear differential equations for circuits
313 Linear differential equations initial value problems
314 Linear differential equations initial value problems

Differential Equations – Second-order homogeneous
315 Introduction to second-order homogeneous
316 Homogeneous distinct real roots
317 Homogeneous distinct real roots
318 Homogeneous distinct real roots example 2
319 Homogeneous equal real roots
320 Homogeneous equal real roots
321 Homogeneous complex conjugate roots
322 Homogeneous complex conjugate roots
323 Homogeneous initial value problems
324 Homogeneous initial value problems
325 Homogeneous initial value problems example 2
326 Homogeneous initial value problems example 3
327 Homogeneous initial value problems example 4
328 Boundary value problems
329 Boundary value problems with distinct real roots
330 Boundary value problems with complex conjugate roots
331 Homogeneous working backwards
332 Linear dependence and independence

Differential Equations – Second-order nonhomogeneous
333 Introduction to second-order nonhomogeneous
334 Undetermined coefficients
335 Undetermined coefficients
336 Undetermined coefficients example 2
337 Undetermined coefficients example 3
338 Undetermined coefficients example 4
339 Variation of parameters system of equations
340 Variation of parameters system of equations
341 Variation of parameters Cramers rule
342 Nonhomogeneous initial value problems
343 Nonhomogeneous initial value problems

Differential Equations – Laplace transforms
344 Introduction to laplace transforms
345 Laplace transforms using the table
346 Laplace transforms using the table
347 Laplace transforms using the definition
348 Laplace transforms using the definition

Differential Equations – Methods of Laplace transforms
349 Introduction to methods of laplace transforms
350 Laplace transforms and initial value problems
351 Laplace transforms and initial value problems
352 Laplace transforms and integration by parts
353 Inverse Laplace transforms
354 Inverse Laplace transforms

Differential Equations – Advanced Laplace transforms
355 Introduction to advanced laplace transforms
356 Convolution integrals and initial value problems
357 Convolution integrals and initial value problems

Conclusion
358 Wrap-up