Math 180: Calculus I
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Course Information
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Course Prerequisites
One of:
- Grade C or better in Math 121
- Adequate score on the math placement test.
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.
Course Materials
Textbook
- Calculus: Early Transcendentals by William Briggs and Lyle Cochran, 3rd edition, published by Addison-Wesley.
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.
Discussion Worksheets and Guided Lecture Sheets Bundles
Discussion worksheets and Guided Lecture Sheets will not be provided in class. You can download the worksheets, or you can buy them from the bookstore. You can find the PDFs for the worksheets on Blackboard.
The guided lecture sheets will be used in the lecture, and the discussion worksheets will be used in the problem-solving sessions on Tuesdays and Thursdays.
Course Schedule
| 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 3.2 - 3.4 |
Rules of Differentiation
The Product & Quotient Rules |
|
Week 5
Sec 3.5, 3.6, 3.7 |
Derivatives of Trig Functions Derivatives as Rates of Change The Chain RuleDerivatives of Trig Functions |
|
Week 6
Sec 3.8, 3.11 |
Implicit Differentation Related Rates |
|
Week 7
Sec 3.9, 3.10 |
Derivatives of Log & Exp Functions Derivatives of Inverse Trig Functions |
|
Week 8
Sec 3.10, 4.1, 4.2 |
Derivatives of Inverse Trig Functions continued Maxima and Minima The Mean Value Theorem< |
|
Week 9
Sec 4.3, 4.4 |
What Derivatives Tell Us Graphing Functions |
|
Week 10
Sec 4.5 |
Optimization Problems |
|
Week 11
Sec 4.6, 4.7 |
Linear Approximation & Differentials L'Hopital's Rule |
|
Week 12
Sec 4.7, 4.9 |
L'Hopital's Rule
Antiderivatives |
|
Week 13
Sec 5.1, 5.2 |
Approximating Areas Under Curves
Definite Integrals |
|
Week 14
Sec 5.2, 5.3 |
Definite Integrals Fundamental Theorem of Calculus |
|
Week 15
Sec 5.4 |
Working with Integrals
Review for Final Exam |
|
Week 16
Finals' Week |
Final Exam |
List of Topics
| 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 |