High School Calculus Honors

Segment One

Module 01 - Functions

• Course Introduction
• Introduction to Calculus
• Review of Function Terminology and More
• Graphing Calculators
• Compositions and Transformations of Functions
• Some Common Functions

Module 02 - Limits and Continuity

• Introduction to Limits
• Properties of Limits
• Limits Involving Infinity
• Continuity
• Application of Limits

Module 03 - Differentitiation

• The Derivative
• Rules of Differentitiation
• Trigonometric Derivatives and the Chain Rule
• Inverse Functions
• Exponential and Logarithmic Functions
• Dirivatives of Exponential, Logarithmic, and Inverse Trig Functions
• Implicit Differentitiation

Module 04 - Applications of Dervivatives

• Analyzing Functions Part I: Curve Sketching
• Analyzing Functions Part II: Maximums and Minimums
• Maximum and Minimum Problems
• Distance, Velocity, Acceleration, and Rectilinear Motion
• Related Rates
• The Mean-Value Theorem and L'Hopital's Rule
• Linearization

Segment 02

Module 05 -Integration

• Area Approximation and Riemann Sums
• Introduction to the Definite Integral
• The Fundemental Theorem of Calculus
• Integrals and Antiderivatives
• Integration by Substitution
• The Definite Integral

Module 06 - Applications of Integrals

• Finding the Area Under and Between Curves
• Volume by Disks (Slicing)
• Average Value of a Function and Rectilinear Motion Revisited

Module 07 - Differential Equations and More Riemann Sums

• Differential Equations--An Introduction
• Initial Value Problems and Slow Fields
• Numerical Approximation Methods and Integrals

Module 08 - Supplemental Topics

• Exlporing the Graphs of f, Prime, and f Double Prime
• Relative Rates of Growth
• Using Calculus with Data in a Table
• Functions Defined by Integral