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# Math 180: Calculus I

### Course Prerequisites

One of:

Prerequisites are enforced throughout all sections of the course without exceptions.

### Course Description

Differentiation, curve sketching, maximum-minimum problems, related rates, mean-value theorem, antiderivative, Riemann integral, logarithm, and exponential functions. Course Information: Prior credit in MATH 165 or MATH 170 will be lost with subsequent completion of MATH 180. Prerequisite(s): Grade of C or better in MATH 121 or appropriate performance on the department placement test. Class Schedule Information: To be properly registered, students must enroll in one Discussion/Recitation and one Lecture. Natural World – No Lab course.

### Credit Awarded

4 hours (some exceptions noted below)

Prior credit in MATH 165 or MATH 170 will be lost with subsequent completion of MATH 180.

### 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.

### 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 below or on the Blackboard site. A physical copy can be bought directly at the UIC bookstore.

Sections Topics
Week 1

Sec 2.1 - 2.3
The Idea of Limits
Definitions of Limits
Techniques of Computing Limits
Week 2

Sec 2.3 - 2.5
Techniques for Computing Limits
Infinite Limits
Limits at Infinity
Week 3

Sec 2.6, 3.1-3.2
Continuity
Introducing the derivative
Working with Derivatives
Week 4

Sec 3.3 - 3.5
Derivatives of Trig Functions
The Chain Rule
Derivatives as Rates of Change
Week 5

Sec 3.8
Review and Exam 1
Implicit Differentiation
Week 6

Sec 3.9-3.11
Derivatives of Log & Exp Functions
Derivatives of Inverse Trig Functions
Related Rates
Week 7

Sec 4.1-4.3
Maxima and Minima
The Mean Value Theorem
What Derivatives Tell Us
Week 8

Sec 4.3-4.5
Graphing Functions
Optimization Problems
Week 9

Sec 4.5-4.6
Review and Exam 2
Linear Approximation and Differentials
Week 10

Sec 4.7, 4.9
L'Hopital's Rule
Antiderivatives
Week 11

Sec 5.1, 5.2
Approximating Areas Under Curves
Definite Integrals
Week 12

Sec 5.3, 5.4
Fundamental Theorem of Calculus
Working with Integrals
Week 13

Sec 13.1, 13.3
Vectors in the Plane
Dot Products
Week 14

Sec 13.3
Dot Products
Week 15 Review for Final Exam
Week 16
Finals' Week
Final Exam

The following topics are covered in Math 180
Section Topic(s)
2.1 The Idea of Limits
2.2 Definitions of Limits
2.3 Techniques for Computing Limits, Squeeze Theorem
2.4 Infinite Limits
2.5 Limits at Infinity
2.6 Continuity
3.1 Introducing the Derivative
3.2 Working with Derivatives
3.3 Rules of Differentiation
3.4 The Product & Quotient Rules
3.5 Derivatives of Trigonometric Functions
3.6 Derivatives as Rates of Change
3.7 The Chain Rule
3.8 Implicit Differentiation
3.9 Derivatives of Logarithmic & Exponential Functions
3.10 Derivatives of Inverse Trigonometric Functions
3.11 Related Rates
4.1 Maxima and Minima
4.2 The Mean Value Theorem
4.3 What Derivatives Tell Us
4.4 Graphing Functions
4.5 Optimization Problems
4.6 Linear Approximation & Differentials
4.7 L'Hôpital's rule
4.9 Antiderivatives
5.1 Approximating Areas Under Curves
5.2 Definite Integrals
5.3 Fundamental Theorem of Calculus
5.4 Working with Integrals
13.1 Vectors in the Plane (time permitting)
13.3 Dot Products (time permitting)