Calculus Honors

Study limits, continuity, differentiation, integrated algebraic, trigonometric, and transcendental functions, and the applications of derivatives and integrals.

Major Concepts:

Functions

• Introduction to Calculus
• Graphing Calculators
• Compositions and Transformations of Functions
• Some Common Functions

Limits and Continuity

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

Differentiation

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

Applications of Derivatives

• Analyzing Functions: Curve Sketching
• Analyzing Functions: Maximums and Minimums
• Distance, Velocity, Acceleration, and Rectilinear Motion
• Related Rates
• The Mean-Value Theorem and L’Hôpital’s Rule
• Linearization

Integration

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

Applications of Integrals

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

Differential Equations and More Riemann Sums

• Introduction
• Initial Value Problems and Slope Fields
• Numerical Approximation Methods with Integrals

Supplemental Topics

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