Professor's Notes

These lecture notes are provided for students in MAT141 Calculus I and are based on the presentation in Smith and Minton. They guide but do not necessarily correspond exactly to the classroom presentation.

• Polynomials and Rational Functions
• Inverse Functions
• Trigonometric and Inverse Trigonometric Functions
• Exponential and Logarithmic Functions
• Transformations of Functions
• A Brief Preview of Calculus (worksheet)
• The Concept of Limit
• Computation of Limits
• Continuity and its Consequences
• Limits Involving Infinity; Asymptotes
• Tangent Lines and Velocity
• The Derivative
• Computation of Derivatives: The Power Rule
• The Product and Quotient Rules
• The Chain Rule
• Derivatives of Trigonometric Functions
• Derivatives of Exponential and Logrithmic Functions
• Implicit Differentation
• Derivatives of Inverse Trigonometric Functions
• The Mean Value Theorem
• Linear Approximations and Newton's Method
• Indeterminate Forms and L'Hôpital's Rule
• Maximum and Minimum Values
• Increasing and Decreasing Functions
• Concavity and the Second Derivative Test
• Overview of Curve Sketching
• Optimization
• Rates of Change in Economics
• Antiderivatives
• Sums and Sigma Notation
• Area
• The Definite Integral
• The Fundamental Theorem of Calculus
• Applications of Integration