# Syllabus for Calculus I (Math 165)

Chapter and Section references are to Thomas' Calculus, Early Transcendentals, 12th ed.

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 Wednesday evening February 21, 2018, 8:15pm-9:45pm. It will cover material through Section 3.8.