High School: pre-Calculus, Calculus, AP Calculus
College: Pre-Calculus, Calculus I
The following is a list of typical topics covered
| |
- Introduction
- Real numbers
- Mathematical induction
- Some inequalities
- Integral Calculus
- Functions
- Area as a set function & step functions
- Integrals of step functions
- Integrals of general functions
- Integrals of monotonic functions
- Integrals of powers & polynomials
- Properties of the integral
- Applications of Integration
- Area between two graphs
- Integrating trig functions
- Integrals in polar coordinates
- Calculation of volume
- Work & average value
- Indefinite integrals
- Continuous Functions
- Limits of functions
- Continuity
- Properties of limits
- Composite functions & continuity
- Intermediate value theorem
- Inverse functions
- Extrema & uniform continuity
- Differential Calculus
- Differentiating a function
- Algebra of derivatives
- The derivative as a slope
- The chain rule
- Applications of the chain rule
- Extreme values of functions
- The mean value theorem
- First & second derivative tests
- Curve sketching
| |
- Integration & Differentiation
- Derivative of indefinite integrals
- Primitive functions
- Integration by substitution
- Integration by parts
- Logarithm, Exponential, & Trig Functions
- Definition of logarithm as an integral
- Differentiation & integration formulas
- Exponential function
- Differentiation & integration formulas
- Inverse trigonometric functions
- Sequences
- Basic Definitions
- Limit of a Sequence
- Special Limits
- Challenging Limits
- Stirling's Formula
- Series
- Characteristics of Series
- Convergence of Series
- Geometric Series
- Root & Ratio Tests
- Limit & Continuity
- Basic Definitions
- Basic Properties
- Limits & Infinity
- Continuity
- Intermediate Value Theorem
- Bisection Method
- Power Series
- Geometric Series
- Power Series
- Radius of Convergence
- Taylor Series
| |
|
