Calculus 3

Overview

Calculus of Vectors, Vector Functions, Surfaces, and Vector Fields. Topics include an Introduction and study of vectors in 2-D and 3-D, a study of 3-D functions and surfaces, vector functions and calculus of vector functions, partial derivatives and multiple integrals using several coordinate systems, and a study of vector fields with interpretations of Green's Theorem, Divergence Theorem, and Stokes' Theorem.

Syllabus

Calculus 3 Lecture 11.1: An Introduction to Vectors.
Calculus 3 Lecture 11.2: Vectors in 3-D Coordinate System.
Calculus 3 Lecture 11.3: Using the Dot Product.
Calculus 3 Lecture 11.4: The Cross Product.
Calculus 3 Lecture 11.5: Lines and Planes in 3-D.
Calculus 3 Lecture 11.6: Cylinders and Surfaces in 3-D.
Calculus 3 Lecture 11.7: Using Cylindrical and Spherical Coordinates.
Calculus 3 Lecture 12.1: An Introduction To Vector Functions.
Calculus 3 Lecture 12.2: Derivatives and Integrals of Vector Functions.
Calculus 3 Lecture 12.3: Arc Length/Parameterization, TNB (Frenet-Serret) Intro.
Calculus 3 Lecture 12.3/12.5: TNB (Frenet-Serret) Frames, Curvature, Torsion, Encapsulation.
Calculus 3 Lecture 12.4: Velocity and Acceleration of Vector Functions.
Calculus 3 Lecture 13.1: Intro to Multivariable Functions (Domain, Sketching, Level Curves).
Calculus 3 Lecture 13.2: Limits and Continuity of Multivariable Functions (with Squeeze Th.).
Calculus 3 Lecture 13.3: Partial Derivatives (Derivatives of Multivariable Functions).
Calculus 3 Lecture 13.4: Finding Differentials of Multivariable Functions.
Calculus 3 Lecture 13.5: The Chain Rule for Multivariable Functions.
Calculus 3 Lecture 13.6: Finding Directional Derivatives and Gradients.
Calculus 3 Lecture 13.7: Finding Tangent Planes and Normal Lines to Surfaces.
Calculus 3 Lecture 13.8: Finding Extrema of Functions of 2 Variables (Max and Min).
Calculus 3 Lecture 13.9: Constrained Optimization with LaGrange Multipliers.
Calculus 3 Lecture 14.1: INTRODUCTION to Double Integrals (Background Info).
Calculus 3 Lecture 14.2: How to Solve Double/Repeated/Iterated Integrals.
Calculus 3 Lecture 14.3: Double Integrals over POLAR REGIONS.
Calculus 3 Lecture 14.4: Center of Mass (and Moments of Mass and Inertia) for Lamina in 2-D.
Calculus 3 Lecture 14.6: How to Solve TRIPLE INTEGRALS (Along with Center of Mass and Volume).
Calculus 3 Lecture 14.7: TRIPLE Integrals Over Regions with CYLINDRICAL or SPHERICAL Coord..
Calculus 3 Lecture 14.8: How to Change Variables in Multiple Integrals (Using the Jacobian).
Calculus 3 Lecture 15.1: INTRODUCTION to Vector Fields (and what makes them Conservative).
Calculus 3 Lecture 15.2: How to Find Divergence and Curl of Vector Fields.
Calculus 3 Lecture 15.3: How to Compute Line Integrals (Over Non-Conservative V.Fields).
Line Integrals on CONSERVATIVE Vector Fields (Independence of Path): Calculus 3 Lecture 15.4.
Green's Theorem: Calculus 3 Lecture 15.5.
Surface And Flux Integrals, Parametric Surf., Divergence/Stoke's Theorem: Calculus 3 Lecture 15.6_9.