Times are suggested based on a 15-week semester of 59 class meetings, allowing 9 days for review and exams.

Chapter & Sections | Topics | Time | |
---|---|---|---|

Weir, Hass Thomas' Calculus, Early Transcendentals, 12th edition Chapter 1 is a review of high school mathematics; Math 165 begins with Chapter 2. | Chapter 2 | Limits and Continuity | 9 days |

§2.1 | Rates of Change and Tangents | ||

§2.2 | Limit of a Function, Limit Laws | ||

§2.3 (Optional) | Precise Definition of a Limit | ||

§2.4 | One-Sided Limits | ||

§2.5 | Continuity | ||

§2.6 | Limits Involving Infinity, Asymptotes | ||

Chapter 3 | Differentiation | 16 days | |

§3.1 | Tangents and the Derivative at a Point | ||

§3.2 | The Derivative as a Function | ||

§3.3 | Differentiation Rules | ||

§3.4 | The Derivative as a Rate of Change | ||

§3.5 | Derivatives of Trigonometric Functions | ||

§3.6 | The Chain Rule | ||

§3.7 | Implicit Differentiation | ||

§3.8 | Derivatives of Inverse Functions and Logarithms | ||

§3.9 | Inverse Trigonometric Functions | ||

§3.10 | Related Rates | ||

§3.11 | Linearization and Differentials | ||

Chapter 4 | Applications of Derivatives | 11 days | |

§4.1 | Extreme Values | ||

§4.2 (Optional) | Mean Value Theorem | ||

§4.3 | Monotonic Functions, First Derivative Test | ||

§4.4 | Concavity | ||

§4.5 | L'Hôpital's Rule | ||

§4.6 | Optimization | ||

§4.7 | Newton's Method | ||

§4.8 | Antiderivatives | ||

Chapter 5 | Integration | 11 days | |

§5.1 | Area and Estimating with Finite Sums | ||

§5.2 | Sigma Notation and Limits of Finite Sums | ||

§5.3 | The Definite Integral | ||

§5.4 | The Fundamental Theorem of Calculus | ||

§5.5 | Indefinite Integrals and Substitution | ||

§5.6 | Substitution and Area Between Curves | ||

Chapter 7 | Integrals and Transcendental Functions | 3 days | |

§7.1 (Optional) | The Logarighm Defined as an integral | ||

§7.2 | Exponential Change and Separable Differential Equations | ||

§7.3 (Optional) | Hyperbolic functions | ||

§7.4 (Optional) | Relative Rates of Growth | ||

The Midterm Exam for Math 165 will be given

Document last modified on December 26, 2018