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Math 344: Calculus III

Table of Contents

Chapter 12 - Vectors and Geometry¶

12.1 3D Coordinates

12.2 Vectors

12.3 Dot Product

12.4 Cross Product

12.5 Lines and Planes

12.6 Quadratic Surfaces

Problem Set 1

Chapter 13 - Vector Functions¶

13.1 Vector Functions

13.2 Derivatives and Integrals

13.3 Arc Length and Curvature

13.4 Velocity and Acceleration

Chapter 14 - Partial Derivatives¶

14.1 Functions of Several Variables

14.2 Limits and Continuity

14.3 Partial Derivatives

14.4 Tangent Planes and Linear Approximations

14.5 The Chain Rule

14.6 Directional Derivatives and the Gradient

14.7 Maximal and Minimal Values

14.8 Lagrange Multipliers

Chapter 15 - Multiple Integrals¶

15.1 Double Integrals Over Rectangles

15.2 Double Integrals Over General Regions

15.3 Double Integrals in Polar Coordinates

15.4 Applications of Double Integrals

15.5 Surface Area

15.6 Triple Integrals

15.7 Cylindrical Coordinates

15.8 Spherical Coordinates

15.9 Change of Variables

Chapter 16 - Vector Calculus¶

16.1 Vector Fields

16.2 Path Integrals

16.3 Fundamental Theorem of Path Integrals

16.4 Green's Theorem

16.5 Divergence and Curl

16.6 Parametric Surfaces

16.7 Surface Integrals

16.8 Stoke's Theorem

16.9 Divergence Theorem

Additional Links and Resources¶

A web site that provides videos for linear algebra Linear Algebra

Another excellent series of videos by Grant Sanderson that explore the fundamental concepts of linear algebra. Several ideas, such as vectors, linear transformations, dot products, and cross products, are presented in a highly visual way to aid students' intuition and ability to visualize the objects considered.

A web site that provides videos for calculus Calculus

A wonderful series of short videos by Grant Sanderson that explore the fundamental ideas of calculus in a way that provides visualization and context for the primary concepts. If you find that there are some concepts from Calculus I or II that need a refresher, take a look at these videos.

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