# MATH 131

Deborah Hughes-Hallett, et al. Applied & Single Variable Calculus for Loyola University Chicago with WebAssign Custom (WebAssign eBook).

Chapter 1: A Library of Functions
1.1    Functions and Change
1.2    Exponential Functions
1.3    New Functions from Old
1.4    Logarithmic Functions
1.5    Trigonometric Functions
1.6    Powers, Polynomials, and Rational Functions
1.7    Introduction to Continuity
1.8    Limits
Chapter 2: Key Concept: The Derivative
2.1    How Do We Measure Speed?
2.2    The Derivative at a Point
2.3    The Derivative Function
2.4    Interpretations of the Derivative
2.5    The Second Derivative
Chapter 3: Short-Cuts to Differentiation
3.1    Powers and Polynomials
3.2    The Exponential Function
3.3    The Product and Quotient Rules
3.4    The Chain Rule
3.5    The Trigonometric Functions
3.6    The Chain Rule and Inverse Functions
Chapter 4: Using the Derivative
4.1    Using First and Second Derivatives
4.2    Optimization
4.3    Optimization and Modeling
4.4    Families of Functions and Modeling
4.5    Applications to Marginality
4.7    L’Hopital’s Rule, Growth, and Dominance
Chapter 5: Using the Derivative
5.1    How Do We Measure Distance Traveled?
5.2    The Definite Integral
5.3    The Fundamental Theorem and Interpretations
Chapter 6: Constructing Antiderivatives
6.1    Antiderivatives Graphically and Numerically
6.2    Constructing Antiderivatives Analytically
6.3    [Optional] Differential Equations and Motion

Below are “core problems” that we expect students to be able to solve to ensure understanding of the material in the course syllabus. The problems are taken from Applied & Single Variable Calculus for Loyola University Chicago (packaged with WebAssign), 4th ed., Hughes-Hallett, Deborah, et al.

Chapter 1. A Library of Functions
1.1 1, 8, 13, 16, 23, 27, 31, 37, 41, 44, 59
1.2 2, 5, 6, 8, 10, 16, 17, 19, 22, 32, 42
1.3 8, 12, 13, 18, 24, 37, 38, 39, 43, 46, 50, 58, 66
1.4 2, 6, 10, 16, 24, 26, 30, 33, 39, 50, 52
1.5 6, 10, 12, 18, 20, 28, 30, 36, 38, 48
1.6 3, 6, 9, 12, 15, 17, 18, 32, 34, 40, 42
1.7 2, 4, 6, 20, 22, 32
1.8 2, 3, 12, 14, 22, 31, 42, 53, 56, 60, 63
Chapter 2. Key Concept: The Derivative
2.1 1, 3, 5, 6, 10, 14, 15, 16, 18, 19, 26, 28
2.2

1, 3, 4, 8, 10, 13, 16, 17, 26, 27, 31, 41, 45, 48

2.3 1, 2, 4, 12, 19, 21, 28, 40, 41, 43
2.4 2, 3, 7, 8, 10, 12, 13, 15, 20, 23, 29, 32
2.5 2, 3, 8, 9, 12, 14, 15, 24, 29, 30, 31
Chapter 3. Short-Cuts to Differentiation
3.1

6, 10, 11, 14, 18, 23, 25, 28, 30, 32, 35, 38, 45, 52, 62, 64, 65

3.2

2, 4, 6, 8, 10, 12, 13, 17, 24, 39, 40, 45, 47, 48

3.3

4, 6, 7, 10, 12, 16, 19, 20, 24, 28, 31, 43, 44, 46, 52, 65

3.4 2, 4, 7, 11, 16, 18, 26, 28, 30, 32, 45, 48, 57, 59, 61, 66, 68, 77, 91
3.5 4, 8, 10, 12, 16, 19, 22, 24, 26, 30, 36, 38, 45, 57
3.6

1, 2, 12, 13, 17, 22, 25, 26, 27, 28, 32, 37, 38, 39, 41, 51

Chapter 4. Using the Derivative
4.1

1, 5, 14, 16, 22, 23, 24, 25, 26, 27, 35, 38, 44

4.2

4, 6, 7, 8, 10, 13, 18, 19, 26, 31, 32, 33, 34, 38

4.3

4, 5, 6, 8, 10, 13, 17, 21, 24, 26, 35, 36, 42

4.4 3, 4, 16, 29, 30, 32, 34, 35, 36, 42, 51
4.5

1, 3, 4, 9, 10, 12, 13, 15

4.7 4, 5, 7, 14, 15, 21, 26, 31, 34, 38, 40, 49, 60, 68
Chapter 5. Using the Derivative
5.1

1, 2, 3, 4, 6, 8, 14, 15, 23, 25, 26, 28

5.2 4, 8, 12, 22, 24, 29, 30, 32, 36, 39, 40
5.3 1, 2, 3, 4, 5, 7, 8, 9, 10, 12, 14, 16, 18, 20, 22, 30
5.4 1, 2, 3, 4, 5, 6, 7, 8, 11, 14, 16, 19, 21, 24, 25, 26, 27, 28, 33, 46
Chapter 6. Constructing Antiderivatives
6.1 3, 7, 8, 12, 14, 15, 16, 19, 20, 25
6.2

1, 2, 4, 5, 6, 7, 8, 10, 11, 12, 14, 15, 16, 18, 20, 21, 26, 27, 28, 35, 36, 41, 44, 50, 53, 56, 70, 73

WebAssign is an online, interactive environment for teaching and learning. As part of the required text for MATH 131/132, you are asked to purchase an access code for WebAssign. This access code may be (re)used for MATH 131 and MATH 132 at no additional charge.

By department policy, all sections of MATH 131 and MATH 132 require online homework on "Core Problems; " this course component should count at least 5% towards students' final course grade. (The ground rules document provided by your instructor will have further details.)

You may begin using WebAssign on the first day of class. In order to access WebAssign after the 14-day grace period, you must purchase an access code as detailed below. If you purchased an access code in MATH 131 or MATH 132 for the Hughes-Hallett text in a previous semester, do not purchase a new code as the code you previously purchased remains valid.

Instructions for students to obtain the e-book and to use WebAssign: Once your instructor has uploaded the class roster to WebAssign, your personal class page will be activated. You will access it with your Loyola ID and password as detailed below. (Note to returning students: there is a change from previous semesters... you no longer need a class key to use WebAssign.)

1. Go to www.webassign.net/luc/login.html (Note the change in URL from previous semesters.)
2. Use the LOG IN @ LOYOLA UNIVERSITY CHICAGO button in the center of the page. The LOG IN button in the upper right-hand corner should NOT be used.
3. Selecting the Loyola login button will bring you to a standard Loyola login page, where you will enter your Loyola ID and password.
4. Successful login should bring you to a WebAssign home screen from which you can access any of your courses having a WebAssign component.
5. Select the desired course. If you have not already registered an access code for the course, a notice will be displayed with three choices:
• Enter an access code (purchased at the Loyola Bookstore or from the Cengage website),
• Purchase an access code (online from WebAssign), or
• Continue the free trial.
Select the appropriate choice to access the e-book and homework assignments.
6. If you purchased an access code for the Hughes-Hallett text in a previous semester, you do not need to purchase another code.
7. If at any time you run into technical difficulty using WebAssign, you can contact WebAssign directly by email or phone.  Visit https://webassign.com/support/student-support/ to get started.

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## Should you choose Math 161/162 or Math 131/132?

Any questions about placement in calculus or other 100-level courses that remain after reading that section should be directed to John Houlihan, Mathematics Placement Director. Please e-mail him to set up an appointment.

Math 161/162 (Calculus I, Calculus II) is a traditional calculus sequence covering all the basic topics of one-variable calculus. This sequence is a prerequisite for Multivariable Calculus (Math 263) as well as for almost all higher-level math courses. It is required for all students majoring in Chemistry, Engineering Science, Mathematics, Physics and Statistics. It is highly recommended, although not required, for students majoring in Biology, Computer Science and Economics.

Math 131/132 (Applied Calculus I, Applied Calculus II) is more of a survey sequence covering many of the basic topics in one-variable calculus as well as some topics in multivariable calculus and differential equations. It is a terminal sequence in that it does not satisfy the prerequisites of upper-level mathematics and statistics courses. Students who enjoyed mathematics in high school and earned ACT math scores of 28 and higher or SAT math scores of 610 and higher are encouraged to choose the Math 161/162 sequence.

### Center for Tutoring and Academic Excellence

The Center for Tutoring & Academic Excellence offers free collaborative learning opportunities that include small group tutoring and tutor-led study halls to Loyola students. To learn more or request tutoring services, visit the Center for Tutoring & Academic Excellence online at http://www.luc.edu/tutoring.

### Loyola Math Club Tutoring

The Loyola Math Club offers free tutoring to students in 100-level MATH courses (and others).

Math Club tutoring for Spring 2017 will take place Mondays and Thursdays from 7:00-8:30 pm in Dumbach 120. please contact Michael Serwetnyk (mserwetnyk@luc.edu) with any questions about tutoring.