Math 126: Calculus III

Geometry of 3D Space, Vector-Valued Functions, Partial Derivatives, and Taylor Series.

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Lecture 21: Section 15.4 - Applications of Integration

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I. Geometry of Space & Vectors

Lecture 1 Intro to 3D Systems
Lecture 2 Section 12.2: Vectors
Lecture 3 Section 12.3: Dot Product
Lecture 4 Section 12.4: Cross Product
Lecture 5 Section 12.5: Lines in 3D
Lecture 6 Section 12.5: Planes in 3D
Lecture 7 Section 12.6: Quadric Surfaces

II. Vector Functions & Motion

Lecture 8 Section 13.1: Vector Functions
Lecture 9 Section 13.2: Derivatives
Lecture 10 Section 13.3: Arc Length/Curvature
Lecture 11 Section 13.4: Velocity/Acceleration
Lecture 12 Section 10.3: Polar Coordinates

III. Derivatives of Multivariable Functions

Lecture 13 Section 14.1: Multi-var Functions
Lecture 14 Section 14.3: Partial Derivatives
Lecture 15 Section 14.4: Tangent Planes
Lecture 16 Section 14.7: Local Max/Min
Lecture 17 Section 14.7: Global Optimization

IV. Multiple Integrals

Lecture 18 Section 15.1: Double Integrals
Lecture 19 Section 15.2: General Regions
Lecture 20 Section 15.3: Integrals in Polar
Lecture 21 Section 15.4: Applications

V. Taylor Series & Summation