Vector Fields and Line Integrals
Conservative Vector Fields and the Fundamental Theorem
Calc III Notes
Coordinates in 3D space
3d Coordinate System
Distance in 3d
Equations in 3 (or more) variables
Vectors
Vectors
Dot Product
Dot Product continued
Cross Product
Equations of Lines and Planes
Lines in 3d
Equations of Planes
Lines and Planes
Vector Functions
Vector functions
Derivatives of vector functions
Velocity and Acceleration
Arc length
TNB Frame, Osculating Planes and Circles
Functions of Several Variables
Functions of Several Variables
Visualizing Functions of Several Variables
Limits of Functions of Several Variables
Derivatives of Functions of Several Variables
Derivatives of Functions of Several Variables
Gradient vector, higher derivatives, …
Optimization in Multiple Variables
Absolute Maxima and Minima
Local extrema and the second derivative test.
Lagrange Multipliers
Multiple Integrals
Integrals of Functions of Two Variables
Changing the Order of Integration
Triple Integrals
Substitution for Multiple Integrals
Vector Fields and Line Integrals
“Line” Integrals of Functions
“Line” Integrals of Vector Fields
Conservative Vector Fields and the Fundamental Theorem
Green’s Theorem
Operators
Operator Notation, Divergence and Curl
Curl of a Vector Field
Divergence of a Vector Field
Surfaces and Surface Integrals
Parametric Surfaces
Flux Integrals over Surfaces
Divergence Theorem
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Conservative Vector Fields
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Fundamental Theorem of Calculus for Line Integrals
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Vector Fields and Line Integrals
Conservative Vector Fields and the Fundamental Theorem
Conservative Vector Fields and the Fundamental Theorem
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Conservative Vector Fields
Try it yourself
Fundamental Theorem of Calculus for Line Integrals
Try it yourself
“Line” Integrals of Vector Fields
Green’s Theorem