Course Description

What is Calculus? What is a derivative? What is an integral? What do use them for?
This course will answer these questions with the basics of calculus and its application to mathematics and the world. Students will work with hands-on examples and problems.

Session Format: Sessions will be conducted as tutorial sessions for either help with a Calculus class they are taking or using this tutorial format as their primary instruction. Sessions will take place over Zoom. As primary instruction there will be quizzes and exams that will be hosted on the Moodle.

Session Times: To be negotiated with the student and parents.

Session Dates: August 31 – June 6

Text: For primary instruction: Calculus Volume 1 (OpenStax.Org)
https://openstax.org/details/books/calculus-volume-1

Other requirements: Access to various free online math tools and websites (e.g., the Desmos online graphing calculator, spinner apps, etc.). Students will engage in hands-on learning both in live sessions. Primary instruction sessions will assign homework to the student.

Limits

Limit of a Function
Limit Laws
Continuity
Precise Definition of a Limit

Derivatives

Definition of a Derivative
Derivative as a Function
Differentiation Rules
Derivatives as Rates of Change
Derivatives of Trigonometric Functions
The Chain Rule
Derivatives of Inverse Functions
Implicit Differentiation
Derivatives of Exponential & Logarithmic Function

Applications of Derivatives

Related Rates
Linear Approximations & Differentials
Maxima & Minima
The Mean Value Theorem
Derivatives and the Shape of a Graph
Limits of Infinity & Asymptotes
Applied Optimization Problems
L’Hopital’s Rule
Newton’s Method
Antiderivatives

Integration

Approximating Areas
The Definite Integral
The Fundamental Theorem of Calculus
Integration Formulas & the Net Change Theorem
Substitution
Integrals Involving Exponential & Logarithmic Functions
Integrals Resulting in Inverse Trigonometric Functions

Applications of Integrals

Areas between Curves
Determining Volumes by Slicing
Volumes of Revolution: Cylindrical Shells
Arc Length of a Curve & Surface Area
Physical Applications
Moments and Centers of Mass
Integrals, Exponential Functions, & Logarithms
Exponential Growth & Decay
Calculus of Hyperbolic Functions

*Sessions will not be held on the following dates:

• Nov 23-27 – American Thanksgiving Break
• Dec 21 – Jan 1 – Christmas Break
• Mar 22 – Mar 26 – Holy Week Break