Green's Theorem-Boundaries and Regions
Course Content
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Limits, Continuity, and Partial Derivatives
A Visual Introduction to 3-D Calculus
Partial Derivatives-One Variable at a Time
Total Differentials and Chain Rules
Extrema of Functions of Two Variables
Applications to Optimization Problems
Linear Models and Least Squares Regression
Vectors and the Dot Product in Space
The Cross Product of Two Vectors in Space
Lines and Planes in Space
Curved Surfaces in Space
Vector-Valued Functions in Space
Kepler's Laws-The Calculus of Orbits
Directional Derivatives and Gradients
Tangent Planes and Normal Vectors to a Surface
Lagrange Multipliers-Constrained Optimization
Applications of Lagrange Multipliers
Iterated integrals and Area in the Plane
Double Integrals and Volume
Double Integrals in Polar Coordinates
Centers of Mass for Variable Density
Surface Area of a Solid
Triple Integrals and Applications
Triple Integrals in Cylindrical Coordinates
Triple Integrals in Spherical Coordinates
Vector Fields-Velocity, Gravity, Electricity
Curl, Divergence, Line Integrals
More Line Integrals and Work by a Force Field
Fundamental Theorem of Line Integrals
Green's Theorem-Boundaries and Regions
Applications of Green's Theorem
Surface Integrals and Flux Integrals
Parametric Surfaces in Space
Divergence Theorem-Boundaries and Solids
NA NA
Stokes's Theorem and Maxwell's Equations