MATHEMATICS
Calculus Honors
High School · 9 – 12 Courses
Calculus Honors
Overview
Study limits, continuity, differentiation, integrated algebraic, trigonometric, and transcendental functions, and the applications of derivatives and integrals.
Major Topics and Concepts
Functions
3- Graphing Calculators
- Compositions and Transformations of Functions
- Some Common Functions
Limits and Continuity
5- Introduction to Limits
- Properties of Limits
- Limits Involving Infinity
- Continuity
- Applications of Limits
Differentiation
7- 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
6- 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
6- 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
3- 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
3- Introduction
- Initial Value Problems and Slope Fields
- Numerical Approximation Methods with Integrals
Supplemental Topics
4- 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
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