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Calculus III utilizes previously learned techniques to solve problems in 3-dimentional space. Vectors are studied extensively, as well as surfaces, gradients, velocity, acceleration, and many other wonderful topics.

It is important to note that this course is not completely comprehensive to a typical Calculus III course in that several lessons are not included as evidenced by gaps in the section numbering in the table of contents.

- 11.1 Vectors in the Plane
- 11.6 Surfaces in Space
- 11.7 Cylindrical and Spherical Coordinates

- 12.1 Vector-Valued Functions
- 12.3 Velocity and Acceleration
- 12.5 Arc Length and Curvature

- 13.1 Introduction to Functions of Several Variables
- 13.2 Limits and Continuity
- 13.4 Differentials
- 13.5 Chain Rules for Functions of Several Variables
- 13.6 Directional Derivatives and Gradients
- 13.8 Extrema of Function of Two Variables
- 13.9 Applications of Extrema of Functions in Two Variables
- 13.10 Lagrange Multipliers

- 14.1 Iterated Integrals and Area in the Plane
- 14.3 Change of Variables: Polar Coordinates
- 14.4 Center of Mass and Moments of Inertia
- 14.5 Surface Area
- 14.6 Triple Integrals and Applications
- 14.8 Change of Variables: Jacobians

- 15.1 Vector Fields
- 15.3 Conservative Vector Fields and Independence of Path
- 15.5 Parametric Surfaces
- 15.6 Surface Integrals
- 15.7 Divergence Theorem

- 16.1 Exact First-Order Equations
- 16.2 Second-Order Homogeneous Linear Equations
- 16.3 Second-Order Nonhomogeneous Linear Equations
- 16.4 Series Solutions of Differential Equations