| MAT 201 Calculus I |
| Course Outline |
| Chapter 1: Limits |
| Introduction to Limits |
| Rigorous Study of Limits |
| Limit Theorems |
| Limits Involving Trigonometric Functions |
| Limits at Infinity; Infinite Limits |
| Continuity of Functions |
| Chapter 2: The Derivative |
| Two Problems with One Theme |
| The Derivative |
| Rules for Finding Derivatives |
| Derivatives of Trigonometric Functions |
| The Chain Rule |
| Higher-Order Derivatives |
| Implicit Differentiation |
| Related Rates |
| Differentials and Approximations |
| Chapter 3: Applications of the Derivative |
| Maxima and Minima |
| Monotonicity and Concavity |
| Local Extrema and Extrema on Open Intervals |
| Practical Problems |
| Graphing Functions Using Calculus |
| The Mean Value Theorem for Derivatives |
| Solving Equations Numerically |
| Antiderivatives |
| Introduction to Differential Equations |
| Chapter 4: The Definite Integral |
| Introduction to Area |
| The Definite Integral |
| The First Fundamental Theorem of Calculus |
| The Second Fundamental Theorem of Calculus & Method of Substitution |
| The Mean Value Theorem for Integrals & the Use of Symmetry |
| Numerical Integration |
| Chapter 5: Applications of the Integral |
| The Area of a Plane Region |
| Volumes of Solids: Slabs, Disks, Washers |
| Volumes of Solids of Revolution: Shells |
| Length of a Plane Curve |
| Work and Fluid Force |
| Moments and Center of Mass |
| Probability and Random Variables |