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High School Calculus 3

39 lessons across 6 topics

1. Vectors and Geometry

1Cross Product 2Cylinders And Quadrics 3Dot Product 4Lines And Planes 5Vector Basics

2. Vector-Valued Functions

6Arc Length 7Curvature And The Tnb Frame 8Derivatives Of Vector Functions 9Integrals Of Vector Functions 10Vector Functions

3. Partial Derivatives

11Chain Rule And Implicit Differentiation 12Directional Derivatives And Gradient 13Functions Of Several Variables 14Lagrange Multipliers 15Limits And Continuity 16Maxima, Minima, And Saddle Points 17Partial Derivatives 18Tangent Planes And Linearization

4. Multiple Integrals

19Applications Of Multiple Integrals 20Change Of Variables And Jacobians 21Double Integrals 22Double Integrals In Polar Coordinates 23Triple Integrals 24Triple Integrals In Cylindrical Coordinates 25Triple Integrals In Spherical Coordinates

5. Vector Calculus

26Conservative Vector Fields And Potential Functions 27Divergence And Curl 28Divergence Theorem 29Fundamental Theorem For Line Integrals 30Green’s Theorem 31Line Integrals 32Stokes’ Theorem 33Surface Integrals 34Surface Parameterization And Normal Vectors 35Vector Fields

6. Applications and Extensions

36Advanced Optimization 37Applications In Engineering 38Applications In Physics 39Differential Forms (honors Extension)