Course Information
I generally teach Honors Calculus I and Calculus II to high schoolers. In cases where the Calculus II students complete the course work before the end of the year, I offer choices as to what to do with the rest of the time. One of these is Calculus III. Generally, we are able to cover
- Course Overview – This is what I would handout on the first day of class. It contains a quick summary of the course, requirements.
- Course Plan – This is how I would break down my units in Calculus III and the number of days I reserve for specific topics for a semester of College.
- Supplement Plan – This is how I use Calculus III as a supplement to a Calculus II course with limited time. Based on four years of experience.
- Formula Sheets
Required Knowledge: Students engaging with Multivariable Calculus should be familar with the following concepts covered in the previous courses of Calculus I and II:
- Limits
- Derivatives
- Summation
- Integrals
- Series
- Differential Equations
To practice these concepts, see previous courses of Calculus I and Calculus II.
Table of Contents
Chapter 11: Parametric and Polar Equations – An Introduction to Alternate Coordinate Systems
- Parametric Equations
- Derivatives, Arclengths and Calculus with Parametric Equations
- Polar Equations
- Graphing Polar Equations
- Area and Arclength of Polar Equations
Chapter 12: Vectors – An Introductions to Vectors and Operations on Vectors
- Two Dimensional Vectors
- Three Dimensional Vectors
- The Dot Product
- The Cross Product
- Equations of Lines and PLanes
- Cylinderical and Spherical Coordinates
- Curvature
Chapter 13: Partial Derivatives – Using Derivatives in Multivariable Equations
- Functions of Several Variables
- Limits and Continuity of Several Variables
- Partial Derivatives
- Tangent Planes
- The Chain Rule
- The Gradient and Directional Derivatives
- Optimization of Several Variables
- Lagrange Multipliers
Chapter 14: Multiple Integrals – Using Integrals in More than Two Dimensions and with Alternate Coordinate Systems
- Integration of Several Variables
- Double Integrals in General Regions
- Double Integrals in Polar Coordinates
- Applications of Doulbe Integrals
- Triple Integrals
- Triple Integrals in Cylindrical Coordinates
- Triple Integrals in Spherical Coordinates
- Change of Variables
Chapter 15: Vector Calculus – Using the Techniques of Multivariable Calculus in Conjuction with Vectors
- Vector Fields
- Line Integrals
- The Fundemantal Theorem of Line Integrals
- Green’s Theorem
- Curl and Divergence
- Parametric Surfaces
- Surface Integrals
- Stokes’ Theorem
- Divergence Theorem