Study Scope and Sequence
Module 01: Functions
- Introduction to Calculus
- Review of Function Terminology
- 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
- Applications of Limits
Module 03: Differentiation
- The Derivative
- Rules of Differentiation
- Trigonometric Derivatives and the Chain Rule
- Inverse · Exponential and Logarithmic Functions
- Derivatives of Exponential, Logarithmic, and Inverse Trig Functions
- Implicit Differentiation
Module 04: Applications of Derivatives
- Curve Sketching
- Maximums and Minimums
- Applied Maximum and Minimum Problems
- Distance, Velocity, Acceleration, and Rectilinear Motion
- Related Rates
- The Mean-Value Theorem and L’Hopital’s Ryler
- Linearization
Module 05: Integrations
· Area Approximation and Riemann Sums
· Introduction to the Definite Integral
· The Fundamental Theorem of Calculus
· Integrals and Anti-derivatives
· Integration by Substitution
· The Definite Integral
Module 06: Applications of Integrals
· Finding the Area Under and Between Curves
· Volume by Discs (Slicing)
· Average Value of a Function and Rectilinear Motion Revisited
Module 07: Differential Equations
· Introduction to Differential Equations
· Initial Value Problems and Slope Fields
· Numerical Approximation Methods with Integrals
Module 08: 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