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# Math 181: Calculus II

### Course Prerequisites

A grade of C or better in MATH 180

### Course Description

Techniques of integration, arc length, solids of revolution, applications, polar coordinates, parametric equations, infinite sequences and series, power series. Course Information: Prerequisite(s): Grade of C or better in MATH 180. Class Schedule Information: To be properly registered, students must enroll in one Discussion/Recitation and one Lecture. Natural World – No Lab course.

4 hours

### Course Materials

#### Textbook

Calculus: Early Transcendentals by William Briggs and Lyle Cochran, 3rd edition, published by Addison-Wesley.

Note that a MyLabMath code is required for this course while the printed textbook is optional.

Chapters 6-10 are covered in Math 181.

#### MyMathLab Access Code

A MyLabMath code can be purchased online after registering for MyMathLab through Blackboard, or at the UIC bookstore, with or without the textbook. Make sure your MyMathLab code is linked to the Blackboard course.  The MyMathLab code includes an electronic version of the textbook, buying a physical copy is optional.

Students coming from Math 180 at UIC can use the same access code for Math 181, if it has not expired.

#### Worksheet Bundle

The worksheet bundle will be used in the problem solving sessions on Tuesdays and Thursdays. An electronic, printable copy of it can be found on the Blackboard site or by contacting any course instructor or TA. A physical copy can be bought directly at the UIC bookstore.

Check Blackboard for updated schedule and semester-specific information.

Sections Topics
Week 1

Sec 5.2-5.4
Review of Definite Integrals
Review of the FTC
Working with Integrals
Week 2

Sec 5.5, 6.1-6.3
Substitution
Velocity
Regions between Curves
Week 3

Sec 6.3, 6.5, 6.7
Volumes by Slicing
Length of Curves
Physical Approximations
Week 4

Sec 8.2-8.3
Integrtion by Parts
Trigonometric Integrals
Week 5

Sec 8.5, 8.9
Partial Fractions
Improper Integrals
Week 6

Review and Exam #1
Week 7

10.1-10.3
An Overview
Sequences
Infinite Series
Week 8

Sec 10.4, 10.7, 10.5
Divergence and p-test
Ratio Test
Comparison Tests
Week 9

Sec 11.1, 11.2
Approximating Functions with Polynomials
Properties of Power Series
Week 10

Sec 11.3
Review of Power Series
Taylor Series
Week 11

Sec 8.8, 11.4
Numerical Integration
Working with Taylor Series
Week 12

Sec 12.1, 12.2
Parametric Equations
Polar Coordinates
Week 13

Sec NH 9.1, NH 9.2
Linear Systems
Matrices
Week 14

NH 9.2, NH 9.3
Matrices
Linear Maps
Week 15 Review
Week 16
Finals' Week
Final Exam

The following topics are covered in Math 181
Section Topic(s)
5.2 Definite Integrals (Review)
5.3 FTC (Review
5.4 Working with Integrals (Review)
5.5 Substitution
6.1 Velocity and Net Change
6.2 Regions Between Curves
6.3 Volumes By Slicing
6.5 Length of Curves
6.7 Physical Applications
8.2 Integration By Parts
8.3 Trigonometric Integrals
8.5 Partial Fractions
8.8 Numerical Integration
8.9 Improper Integrals
10.1 An Overview of Sequences and Series
10.2 Sequences
10.3 Infinite Series
10.4 Divergence and p-test
10.7 Ratio Test
10.5 Comparison Tests
10.6 Alternating Series
11.1 Approximating Functions with Polynomials
11.2 Properties of Power Series
11.3 Taylor Series
11.4 Working with Taylor Series
12.1 Parametric Equations
12.2 Polar Coordinates
alternate text 9.1 Linear Systems
alternate text 9.2 Matrices
alternate text 9.3 Linear Maps