Topic outline
Pre-requisits for Calculus
* Lines
* Functions & Their Graphs
* Exponential & Logarithmic Functions
* Trigonometric Functions
Limits & Their Properties
1.1 A Preview of Calculus
1.2 Finding Limits Graphically and Numerically
1.3 Evaluating Limits Analytically
1.4 Continuity and One-Sided Limits
1.5 Infinite Limits
Differentiation
2.1 The Derivative and the Tangent Line Problem
2.2 Basic Differentiation Rules and Rates of Change
2.3 Product and Quoitent Rules and Higher-Order Derivatives
2.4 The Chain Rule
2.5 Implicit Differentiation
2.6 Related Rates
Applications of Derivatives
3.1 Extrema on an Interval
3.2 Rolle's Theorem & The Mean Value Theorem
3.3 Increasing & Decreasing Functions & The First Derivative Test
3.4 Concavity & The Second Derivative Test
3.5 Curve Sketching
3.6 Optimization
Antiderivatives and Indefinite Integration
4.1 Antidervatives and Indefinite Integration
4.2 Integration by Substitution
4.3 Sigma Notation
4.4 Riemann Sums and Area Under the Curve
4.4a Finding Exact Area Under the Curve
4.4b The Definite Integral as Area
4.5 The Accumulation Function
4.6 The Fundamental Theorem of Calculus
Exponential & Other Transcendental Functions