Table of Contents
 Part I • Prologue

Part II • Foundations
 Radical Functions
 Composite Functions
 Even and Odd Functions
 Inequalities on a Number Line
 Graphing Polar Curves
 Polar Coordinates
 Evaluating Limits Using Algebraic Techniques
 Limits of Trigonometric Functions
 Euler’s Number as a Limit
 OneSided Limits
 Limits at Infinity and Unbounded Limits
 Properties of Limits
 Limits in a RealWorld Context
 Continuity at a Point
 Classifying Discontinuities
 Continuity of Functions
 Horizontal and Vertical Asymptotes of a Function

Part III • Derivatives and Integrals
 The Differentiability of a Function
 Rate of Change and Derivatives
 Definition of the Derivative
 Power Rule of Derivatives
 Combining the Product, Quotient, and Chain Rules
 The Product Rule
 The Quotient Rule
 Differentiation of Trigonometric Functions
 Differentiation of Reciprocal Trigonometric Functions
 Implicit Differentiation
 Critical Points and Local Extrema of a Function
 Absolute Extrema
 Second Derivative Test for Local Extrema
 Inverse of a Function
 The Fundamental Theorem of Calculus: Evaluating Definite Integrals
 Properties of Definite Integrals
 Definite Integrals as Limits of Riemann Sums
 Average Value of a Function
 The Fundamental Theorem of Calculus: Functions Defined by Integrals
 L’Hôpital’s Rule
 Indeterminate Forms and L’Hôpital’s Rule
 Differentiation of Exponential Functions
 Differentiation of Logarithmic Functions
 Logarithmic Differentiation
 Integration by Parts
 Reduction Formulae for Integration

Part IV • Infinite Sequences and Infinite Series
 Taylor Series
 Taylor Polynomials Approximation to a Function
 Representing Sequences
 Convergent and Divergent Sequences
 Recursive Formula of a Sequence
 Monotone Convergence Theorem
 Partial Sums
 Infinite Geometric Series
 The nth Term Divergence Test
 Operations on Series
 Power Series and Radius of Convergence
 Operations on Power Series
 Differentiating and Integrating Power Series
 The Argument of a Complex Number
 Quadratic Equations with Complex Coefficients
 Part V • Epilogue