Contents

• Introduction to Differential Calculus
• Functions
  • Introduction to Functions
  • Function Notation
  • Combining Functions
  • Composite Functions
  • Graph of Functions
  • Vertical Line Test
  • Evaluating Functions From a Graph
  • Odd and Even Functions
• Limits and Continuity
  • Introduction to Limits
  • Properties of Limits
  • Limits at Infinity
  • One-Sided Limits
  • Infinite Limits
  • Limits of Functions with Absolute Value
  • Continuity
• The Derivative
  • Introduction to Derivatives
  • Notation of Derivatives
  • Slope of a Curve
  • Rate of Change
  • Average and Instantaneous Velocity
• Algebraic Functions
  • Differentiation and its Rules for Algebraic Functions
  • Higher Order Derivatives
  • The Chain Rule
  • Implicit Differentiation
• Polynomial Curves
  • Tangents and Normals to Plane Curves
  • Equation of Tangent and Normal Lines
  • Increasing and Decreasing Functions
  • Maxima and Minima
  • Concavity and the Second Derivative Test
• Applications of Derivatives
  • Introduction to Applications of Derivatives
  • Optimization
  • Related Rates
• The Differential
  • Differentials
  • Approximate Formula
• Introduction to Integral Calculus
  • Introduction and History of Integral Calculus
  • The Essence of Integral Calculus
  • Definite and Indefinite Integrals
  • Antiderivatives
• General Power Rule
  • Properties and the General Power Rule for Integration
• Exponential and Logarithmic Functions
  • Exponential Functions
  • Logarithmic Functions
  • Derivatives of Exponential and Logarithmic Functions
  • Integral of Exponential and Logarithmic Functions
• Trigonometric Functions
  • Angles
  • Basic Trigonometric Functions
  • Evaluating Trigonometric Functions
  • Trigonometric Identities
  • Derivatives of Trigonometric Function
  • Integral of Trigonometric Functions
• Integration by Parts
  • Integration by Parts
    • Tabular Integration by Parts
• The Definite Integral
  • Introduction to Definite Integrals
  • Properties of Definite Integrals
• Plane Areas
  • Introduction to Plane Areas
  • Area Under a Curve
  • Area Between Curves