Calculus
1. Limits and Continuity
2. Derivatives: Definition and Basic Rules
3. Derivatives: Chain Rule and Other Advanced Topics
4. Analyzing Functions
- 4.1 Intervals on which a function is increasing or decreasing
- 4.2 Relative (local) extrema
- 4.3 Absolute (global) extrema
- 4.4 Introduction to concavity and inflection points
- 4.5 Analyzing concavity and inflection points
- 4.6 Second derivative test
- 4.7 Sketching curves
- 4.8 Connecting f, f’, and f”
- 4.9 Solving optimization problems
1. Integrals Introduction
- 1.1 Introduction to accumulations of change
- 1.2 Approximation with Riemann sums
- 1.3 Summation notation review
- 1.4 Riemann sums in summation notation
- 1.5 Defining integrals with Riemann sums
- 1.6 Fundamental theorem of calculus and accumulation functions
- 1.7 Interpreting the behavior of accumulation functions
2. Exploring Bivariate Numerical Data
- 2.2 Fundamental theorem of calculus and definite integrals
- 2.3 Reverse power rule
- 2.4 Indefinite integrals of common functions
- 2.5 Definite integrals of common functions
- 2.6 Integrating with u-substitution
- 2.7 Integrating using long division and completing the square
- 2.8 Integration by parts
- 2.9 Integrating using linear partial fractions
- 2.10 Improper integrals