Calculus 3

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.

Chapter 11 – VECTORS AND THE GEOMETRY OF SPACE

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

Chapter 12 – VECTOR-VALUED FUNCTIONS

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

Chapter 13 – FUNCTIONS OF SEVERAL VARIABLES

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

Chapter 14 – MULTIPLE INTEGRATION

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

Chapter 15 – VECTOR ANALYSIS

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

Chapter 16 – ADDITIONAL TOPICS IN DIFFERENTIAL EQUATIONS

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

Calculus 3

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