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Multivariable Calculus
Multivariable Calculus
44 lessons across 14 topics
1. Geometry and Vectors in Space
1
Coordinates In Three Dimensions
2
Distance, Spheres, Cylinders, Quadric Surfaces
3
Vectors, Dot Product, Cross Product
2. Lines, Planes, and Vector-Valued Functions
4
Equations Of Lines And Planes
5
Motion In Space
6
Velocity, Acceleration, Arc Length
3. Functions of Several Variables
7
Graphs, Level Curves, Level Surfaces
8
Introductory Examples
9
Limits And Continuity In Higher Dimensions
4. Partial Derivatives
10
Differentiability And Local Linearity
11
First-order Partials
12
Higher-order Partials
5. Tangent Planes and Chain Rule
13
Chain Rule In Multivariable Settings
14
Directional Derivatives And Gradients
15
Linear Approximation
16
Total Differential
6. Optimization
17
Constrained Optimization
18
Critical Points
19
Lagrange Multipliers
20
Second Derivative Test
7. Double Integrals
21
Area And Volume Applications
22
General Regions
23
Iterated Integrals
8. Midterm 1 and Change of Variables
24
Jacobians In Two Variables
25
Midterm 1
26
Polar Coordinates
9. Triple Integrals
27
Cylindrical And Spherical Coordinates
28
Triple Integration Over Boxes And General Regions
29
Volumes And Mass
10. Vector Fields and Line Integrals
30
Conservative Fields
31
Potential Functions
32
Work And Circulation
11. Parametric Surfaces and Surface Integrals
33
Flux Integrals
34
Orientation
35
Surface Area
12. Green’s Theorem
36
Applications To Area And Flow
37
Circulation Form
38
Flux Form
13. Stokes’ Theorem
39
Applications
40
Curl And Circulation
41
Surface-boundary Relationships
14. Divergence Theorem and Final Review
42
Divergence And Flux
43
Review And Synthesis
44
Triple Integral Formulation
