MATH 1310: Calculus I

Functions and Models (Review)

• Four Ways to Represent a Function
• Mathematical Models: A Catalog of Esssential Functions
• New Functions from Old Functions
• Exponential Functions
• Exponential Functions
• Inverse Functions and Logarithms

Limits and Derivatives

• The Tangent and Velocity Problems
• The Limit of a Function
• Calculating Limits Using the Limit Laws
• The Precise Definition of a Limit
• Continuity
• Limits at Infinity
• Derivatives and Rates of Change
• The Derivative as a Function

Differentiation Rules

• Derivatives of Polynomials and Exponential Functions
• The Product and Quotient Rules
• Derivatives of Trigonometric Functions
• The Chain Rule
• Implicit Differentiation
• Derivatives of Logarithmic Functions
• Related Rates
• Linear Approximation and Differentials

Applications of Differentiation

• Maximum and Minimum Values
• The Mean Value Theorem
• How Derivatives Affect the Shape of a Graph
• Indeterminate Forms and L'Hôpital's Rule
• Summary of Curve Sketching
• Optimization Problems
• Antiderivatives

Integrals

• Areas and Distances
• The Definite Integral
• The Fundamental Theorem of Calculus
• Indefinite Integrals and the Net Change Theorem
• The Substitution Rule

Applications of Integration

• Areas Between Curves
• Volume by Slicing and/or Shells
• Average Value of a Function