# Math 165/166 - Calculus I/II

## Course Coordinator

Elgin Johnston (ehjohnst@iastate.edu)

## Catalog Description

MATHÂ 165. Calculus I.
(4-0) Cr. 4. F.S.SS. Prereq: Satisfactory performance on placement exam, 2 years of high school algebra, 1 year of geometry, 1 semester of trigonometry.
Differential calculus, applications of the derivative, introduction to integral calculus. Only one of Math 151 or 160 or the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.

MATHÂ 166. Calculus II.
(4-0) Cr. 4. F.S.SS. Prereq: Minimum of C- in MATH 165 or high math placement scores.
Integral calculus, applications of the integral, infinite series. Only one of MATH 151, MATH 160, the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.

## Textbook

Weir/Hass
Thomas' Calculus, Early Transcendentals, 12th Edition.
Pearson Publishing
ISBN: 9780321587992

## Syllabus

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

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

Chapter 1 is a review of high school mathematics; Math 165 begins with Chapter 2.

Course Chapter & Sections Topics Time
Math 165 Chapter 2 - Limits and Continuity 9 days
§2.1 - Rates of Change and Tangents
§2.2 - Limits of Functions and Limit Laws
§2.3 - Precise Definition of a Limit (Optional)
§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
§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 Trogonometric Functions
§3.10 Related Rates
§3.11 Linearization and Differentials

Chapter 4 - Applications of Derivatives 11 days
§4.1 - Extreme Values
§4.2 - Mean Value Theorem (Optional)
§4.3 - Monotonic Functions, First Derivative Test
§4.4 - Concavity
§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 Substituion
§5.6 - Substitution and Area Between Curves
Chapter 7 - Integrals and Transcendental Functions 3 days
§7.1 The Logarigthm Defined as an Integral (Optional)
§7.2 Exponential Change and Separable Differential Equations
§7.3 - Hyperbolic Functions (Optional)
§4.5 - L'Hôpital's Rule
§7.4 - Relative Rates of Growth (Optional)

Math 166 Chapter 6 - Applications of Definite Integrals 12 days
§6.1 - Volumes Using Cross-sections
§6.2 - Volumes Using Cylindrical Shells
§6.3 - Arc Length
§6.4 - Areas of Surfaces of Revolution
§6.5 - Work and Fluid Forces
§6.6 - Moments and Centers of Mass

Chapter 8 - Techniques of Integration 12 days
§8.1 - Integration by Parts
§8.2 - Trigonmetric Integrals
§8.3 - Trigonometric Substitutions
§8.4 - Integration of Rational Functions by Partial Fractions
§8.5 - Integral Tables and Computer Algebra Systems (Optional)
§8.6 - Numerical Integration
§8.7 - Improper Integrals

Chapter 10 - Infinite Sequences and Series 17 days
§10.1 - Sequences
§10.2 - Infinite Series
§10.3 - The Integral Test
§10.4 - Comparison Tests
§10.5 - The Ratio and Root Tests
§10.6 - Alternating Series, Absolute and Conditional Convergence
§10.7 - Power Series
§10.8 - Taylor and McLaurin Series
§10.9 - Convergence of Taylor Series
§10.10 - The Binomial Series and Applications of Taylor Series

Chapter 11 - Parametric Equations and Polar Coordinates 9 days
§11.1 - Parametrizations of Plane Curves
§11.2 - Calculus with Parametric Curves
§11.3 - Polar Coordinates
§11.4 - Graphing in Polar Coordinates
§11.5 - Areas and Lengths in Polar Coordinates

Math 165 Learning Objectives

Math 166 Learning Objectives

## Old Exams for Math 165

Midterm Fall 2013 Part I Part II
Midterm Fall 2014 Part I Part II
Midterm Spring 2015 Parts I and II
Final Fall 2013 Part I Part II
Final Spring 2014
Final Fall 2014 Part I Part II

## Old Exams for Math 166

Midterm Spring 2014 Part I Part II
Midterm Fall 2014 Part I Part II
Midterm Spring 2015 Part I Part II
Final Fall 2013
Final Spring 2014
Final Fall 2014

## Official Math Department Policies

The Math Department Class Policies page describes the official policies that all instructors have to follow. It covers rules on make-up exams, cheating, student behavior, etc.

## Students With Disabilities

If you have a documented disability and require accommodations, you should obtain a Student Academic Accommodation Request (SAAR) from the Disability Resources office (Student Services Building, Room 1076, 294-6624 or TDD 294-6335, disabilityresources@iastate.edu or accommodations@iastate.edu). Please contact your instructor early in the semester so that your learning needs may be appropriately met.