Table of Contents
 Defining Limits
 Evaluating Limits
 Continuity
 Defining Derivatives

Differentiation Rules
 Power Rule of Derivatives
 The Product Rule
 The Quotient Rule
 Differentiation of Trigonometric Functions
 The Chain Rule
 Differentiation of Reciprocal Trigonometric Functions
 Second and HigherOrder Derivatives
 Implicit Differentiation
 Differentiation of Exponential Functions
 Differentiation of Inverse Functions
 Differentiation of Logarithmic Functions
 Derivatives of Inverse Trigonometric Functions
 Combining the Product, Quotient, and Chain Rules

Applications of Differentiation
 Rate of Change and Derivatives
 Related Time Rates
 Equations of Tangent Lines and Normal Lines
 Linear Approximation
 Critical Points and Local Extrema of a Function
 The Extreme Value Theorem and Rolle’s Theorem
 The Mean Value Theorem
 Increasing and Decreasing Intervals of a Function Using Derivatives
 Convexity and Points of Inflection
 Second Derivative Test for Local Extrema
 Absolute Extrema
 Interpreting Graphs of Derivatives
 Graphing Using Derivatives
 Optimization: Applications on Extreme Values
 Applications of Derivatives on Rectilinear Motion
 L’Hôpital’s Rule
 Comparing Rate of Growth of Functions
 Indefinite Integrals
 Definite Integrals
 Fundamental Theorem of Calculus

Integration Skills
 Integration by Substitution: Indefinite Integrals
 Integration by Substitution: Definite Integrals
 Integrals Resulting in Logarithmic Functions
 Integrals Resulting in Inverse Trigonometric Functions
 Integration by Parts
 Integration by Partial Fractions with Linear Factors
 Improper Integrals: Infinite Limits of Integration
 Improper Integrals: Discontinuous Integrands
 Applications of Integration
 Differential Equations
 Parametric Equations
 Polar Coordinates
 VectorValued Functions
 Infinite Series
 Power Series
 Taylor and Maclaurin Series