Calculus 3 Multivariable Calculus Lectures and Problems

Introduction
0.1: Introduction to Multivariable Calculus 
0.2: Introduction to the Workbook 
0.3: College Learning vs. High School Learning 
0.4: Do these to succeed in this course 
0.5: Some Resources. Use These!

Chapter 1: The Geometry of R3
1.1: Basic Graphing in R 3 
1.2: Some Geometry and Topology in R 3
1.3: Functions, Limits and Continuity 
1.4: Graphing and Slices 
1.5: Vectors and Lines
1.6: Dot Products, Angles, Projections, Matrices 
1.7: Determinants and Cross Product 
1.8: Planes

Chapter 2: Parametric Curves and Surfaces
2.1: Parametric Curves
2.2: Calculus of Curves and Scalar Line Integrals
2.3: Coordinates: Polar, Cylindrical, Spherical
2.4: Parametric Surfaces

Chapter 3: Differential Calculus of Multivariable Functions
3.1: The Derivative
3.2: Tangent Planes and Approximations
3.3: Chain Rule
3.4: Directional Derivatives
3.5: Local Extrema
3.6: Global Extrema
3.7: Lagrange Multipliers

Chapter 4: Integral Calculus of Multivariable Functions
4.1: Double and Triple Integrals over Rectangular Regions
4.2: Double Integrals over General Regions
4.3: Triple Integrals over General Regions
4.4: Change of Variables
4.5: Polar and Cylindrical Coordinates
4.6: Spherical Coordinates
4.7: Surface Area and Surface Integrals

Chapter 5: Vector Calculus
5.1: Vector Fields
5.2: Vector Line Integrals and Work
5.3: Fundamental Theorem and Independence of Path
5.4: Surface Integrals of a Vector Field, Flux Integrals
5.5: Stokes’ Theorem
5.6: Green’s Theorem: Stokes’ Theorem for the Plane
5.7: Divergence Theorem