MTH 226: Calculus III

Mathematics

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10.1: Curves Defined by Parametric Equations
Chapter 12: Vectors and the Geometry of Space
1.01: Vectors in the Plane
1.02: Exercises for Vectors in the Plane
1.03: Vectors in Space
1.04: Exercises for Vectors in Space
1.05: The Dot Product
1.06: Exercises for The Dot Product
1.07: The Cross Product
1.08: Exercises for The Cross Product
1.09: Equations of Lines and Planes in Space
12.5E: Exercises for Equations of Lines and Planes in Space
12.6: Quadric Surfaces
12.6E: Exercises for Quadric Surfaces
12.7: Cylindrical and Spherical Coordinates
12.7E: Exercises for Cylindrical and Spherical Coordinates
Chapter 12 Review Exercises
New Material
Chapter 13: Vector-valued Functions
13.1: Vector-Valued Functions and Space Curves
13.1E: Exercises for Section 12.1
13.2: The Calculus of Vector-Valued Functions
13.2B: The Calculus of Vector-Valued Functions II
13.2E: Exercises for Section 12.2
13.3: Motion in Space
13.3E: Exercises for Section 12.3
13.4: Arc Length and Curvature
13.4E: Exercises for Section 12.4
13.5: Acceleration and Kepler's Laws
13.5E: Exercises for Section 12.5
Chapter 13 Review Exercises
Chapter 14: Functions of Multiple Variables and Partial Derivatives
3.01: Introduction to Functions of Multiple Variables
3.02: Functions of Multiple Variables
3.03: Functions of Multiple Variables (Exercises)
3.04: Limits and Continuity
3.05: Exercises for Limits and Continuity
3.06: Partial Derivatives
3.07: Partial Derivatives (Exercises)
3.08: Tangent Planes, Linear Approximations, and the Total Differential
3.09: Tangent Planes, Linear Approximations, and the Total Differential (Exercises)
3.10: The Chain Rule for Functions of Multiple Variables
3.11: The Chain Rule for Functions of Multiple Variables (Exercises)
3.12: Directional Derivatives and the Gradient
3.13: Directional Derivatives and the Gradient (Exercises)
3.14: Taylor Polynomials of Functions of Two Variables
3.15: Taylor Polynomials if Functions of Two Variables (Exercises)
3.16: Optimization of Functions of Several Variables
3.17: Optimization of Functions of Several Variables (Exercises)
3.18: Constrained Optimization
3.19: Lagrange Multipliers
3.20: Exercises for Lagrange Multipliers
3.21: Differentiation of Functions of Several Variables (Exercise)
Chapter 15: Multiple Integration
4.01: Iterated Integrals and Area
4.02: Iterated Integrals and Area (Exercises)
4.03: Double Integrals Over Rectangular Regions
4.04: Double Integrals Part 1 (Exercises)
4.05: Double Integrals Over General Regions
4.06: Double Integrals Part 2 (Exercises)
4.07: Double Integration with Polar Coordinates
4.08: Double Integrals in Polar Coordinates
4.09: Double Integrals in Polar Coordinates (Exercises)
4.10: Triple Integrals
4.11: Triple Integrals (Exercises)
4.12: Triple Integrals (Exercises 2)
4.13: Triple Integrals in Cylindrical and Spherical Coordinates
4.14: Calculating Centers of Mass and Moments of Inertia
4.15: Change of Variables in Multiple Integrals (Jacobians)
4.16: Multiple Integration (Exercises)
4.17: Exercises for Chapter 14
Chapter 16: Vector Fields, Line Integrals, and Vector Theorems
5.01: Introduction to Vector Field Chapter
5.02: Vector Fields
5.03: Vector Fields (Exercises)
5.04: Line Integrals
5.05: Line Integrals (Exercises)
5.06: Conservative Vector Fields
5.07: Green's Theorem
5.08: Divergence and Curl
5.09: Surface Integrals
5.10: Stokes' Theorem
5.11: The Divergence Theorem
5.12: Vector Calculus (Exercises)
Review for Calculus III
Precalculus Review
z-Appendices
6.1: Table of Derivatives
6.2: Table of Integrals
6.3: Table of Laplace Transforms