1. Precalculus Review & Introduction to Calculus
Review of functions and function notation
Domain and range
Graphs and transformations
Polynomial, rational, exponential, and logarithmic functions
Basic trigonometric functions
Introduction to the idea of a limit
Average vs. instantaneous rate of change
Tangent lines
The derivative as a rate of change
2. Limits & Continuity
Evaluating limits graphically
Evaluating limits numerically
Basic limit laws
One-sided limits
Limits involving infinity
Continuity
Finding where a function is continuous/discontinuous
Simple applications of limits
3. Derivatives
Derivative from the definition
Basic derivative rules
Power rule
Constant, sum, and difference rules
Product rule
Quotient rule
Derivatives of exponential functions
Derivatives of logarithmic functions
Derivatives of basic trigonometric functions
Higher-order derivatives
4. Applications of Derivatives
Position, velocity, and acceleration
Increasing and decreasing functions
Relative and absolute extrema
Critical numbers
First derivative test
Concavity
Inflection points
Second derivative
Curve sketching
Optimization
Related rates (basic applications)
5. Introduction to Integration
Antiderivatives
Indefinite integrals
Basic integration rules
Initial-value problems
Area under a curve
Riemann sums conceptually
Definite integrals
Net area vs. total area
6. Fundamental Theorem of Calculus
Relationship between derivatives and integrals
Evaluating definite integrals
Accumulation functions
Finding total change from a rate
Average value of a function
Basic applications of the Fundamental Theorem
7. Techniques & Applications of Integration
u-substitution
Integrals involving basic exponential and logarithmic functions
Area between curves
Volumes using cross sections
Volumes using the disk/washer method
Basic applications of integration