# MATH 131

During the first week of classes, either Thursday for Tu/Th sections or Wednesday for MWF sections, **all students** enrolled in this course will take an assessment test. The assessment is part of a larger effort to reduce the number of withdrawals and low grades in our introductory math courses by identifying early on students who need assistance.

You may find **practice problems** by going to the web page http://webwork.math.luc.edu/webwork2/Math-lib/ and clicking on the "Guest Login" button and click the link that says "Practice." From there you can do the problems online and check your answers.

NOTE: the problems should be done without the use of any calculator as the actual assessment will follow the same format.

**Chapter 1 – A Library of Functions (1.5–2 weeks):**

1.1 – Functions and Change

1.2 – Exponential Functions

1.3 – New Functions from Old

**Skip:**the subsection on Shifts and Stretches and Odd and Even Symmetry.- Review of composite and inverse functions, framed in a practical, not merely algebraic, setting.

1.4 – Logarithmic Functions

1.5 – Trigonometric Functions

1.6 – Powers, Polynomials, and Rational Functions

**Skip:**the subsection on rational functions (pg 49-50).- Power functions, graph properties for both positive and negative exponents.
- Comparison of long-run behavior of exponentials and polynomials.

1.7 – Introduction to Continuity

**Skip:**the majority of the section.- Understand the graphical viewpoint of continuity. (are there holes, breaks, or jumps in the graph?)

1.8 – Limits

**Skip:**the subsection “Definition of Limit” (bottom of pg 58 – 59).**Skip:**the subsection “Definition of Continuity” (see comment on 1.7 above).- Understand the concept, notation, and properties of limits and one-sided limites at a point and limits at infinity.

**Chapter 2 – Key Concept – The Derivative (1.5 weeks)**

2.1 – How do we measure speed?

2.2 – The Derivative at a Point

- Emphasis on observing what happens to the value of the average rate of change as the interval gets smaller and smaller.
- Emphasis placed on visualizing the derivative as the slope of a tangent.

2.3 – The Derivative Function

- Focus on the conceptual and practical understanding of the derivative.
- Sketch the graph of
*f*’ given the graph of*f*.

2.4 – Interpretation of the Derivative

2.5 – The Second Derivative

**Chapter 3 – Shortcuts to Differentiation (2.5 weeks)**

3.1 – Powers and Polynomials

3.2 – The Exponential Function

- Emphasis on graphical, not epsilon-delta, definition of derivative.
**Add:**differentiation rule for y=ln(x), from section 3.6.

3.3 – Product and Quotient Rules

3.4 – The Chain Rule

3.5 – The Trigonometric Functions** **

**Chapter 4 – Using the Derivative (3 weeks)**

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 – Key Concept – The Definite Integral (2 weeks)**

5.1 – How Do We Measure Distance Traveled?

**Skip:**accuracy of estimates (pg 277)

5.2 – The Definite Integral

- Approximation using area and interpretation as accumulated change.

5.3 – The Fundamental Theorem and Interpretations

5.4 – Theorems About Definite Integrals

- Finding area between curves; using the definite integral to find an average.
**Skip:**the subsection “Comparing Integrals”

Chapter 6 – Constructing Antiderivatives (1 week)

6.1 – Antiderivatives Graphically and Numerically

6.2 – Constructing Antiderivatives Analytically

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.

(Instructors: the problems in **bold** were not available in WebAssign in the spring of 2015.)

Chapter 1. A Library of Functions | |
---|---|

1.1 | 1, 6, 8, 13, 16, 18, 22, 24, 37, 41, 42, 44, 52, 59 / 3, 39, 43, 45-48, 51, 55, 61, 63, 67 |

1.2 | 5, 8, 10, 13, 16, 17, 21, 22, 28, 31, 32, 35, 42 / 19, 25, 27, 29, 43, 45, 51, 57 |

1.3 | 8, 12, 18, 24, 36, 38, 43, 46, 49, 50, 57, 58, 64, 65, 66 / 19, 37, 39, 51, 53, 63, 71, 77 |

1.4 | 9, 10, 13, 14, 24, 26, 28, 32, 39, 42, 46, 47, 50, 53 / 15, 35, 37, 41, 43, 45, 65, 67 |

1.5 | 1, 6, 10, 15, 16, 20, 28, 36, 38, 41, 43, 48 / 29, 31, 33, 39, 42, 59, 61, 69 |

1.6 | 2, 6, 9, 12, 13, 15, 17, 18, 22, 33, 34, 40 / 23, 24-26, 27, 31, 35, 39, 45, 58-60 |

1.8 | 1.8 1, 2, 3, 12, 14, 22, 42, 56, 58, 62 / 5, 7, 15, 19, 25, 39, 59, 63, 93 |

Chapter 2. Key Concept: The Derivative | |

2.1 | 1, 3, 5, 6, 10, 14, 16, 18, 19 / 4, 7, 11, 12, 13, 20, 21, 23, 29, 31, 35 |

2.2 | 3, 4, 5, 10, 13, 15, 16, 17, 26, 31, 43 / 1, 7, 11, 12, 19, 21, 30, 35, 41, 47 |

2.3 | 1, 2, 4, 12, 19, 21, 28, 40, 41, 43 / 3, 16, 17, 18, 23, 37, 39, 53, 55, 59 |

2.4 | 2, 4, 7, 10, 12, 13, 15, 20, 28, 29, 32 / 5, 9, 17, 19, 25, 27, 37, 41, 43 |

2.5 | 2, 3, 4, 10, 12, 24, 29, 30, 31 / 1, 5, 15, 17, 23, 25, 27, 32, 37 |

Chapter 3. Short-cuts to Differentiation | |

3.1 | 6, 12, 14, 18, 22, 28, 30, 32, 38, 41, 43, 52, 57, 62, 64, 65, 69, 75, 504XP* / 3–5, 33, 35, 39, 47, 59, 61, 71, 73, 83, 87 |

3.2 | 2, 6, 8, 10, 15, 21, 24, 39, 40, 43, 47 / 17, 25, 29, 31, 35, 37, 41, 44, 53 |

3.3 | 3, 6, 10, 13, 21, 28, 31, 44, 45, 52, 56; Review: 7 / 11, 29, 41, 43, 47, 53, 58, 59 |

3.4 | 1, 4, 7, 19, 43, 45, 506XP*, 61, 66, 68, 77, 84, 85 / 35, 49, 53, 57, 69, 71, 87, 89 |

3.5 | 8, 10, 12, 16, 22, 31, 38, 48, 57, 506XP*, 60 / 45, 49, 58, 59 |

3.6 | 1, 12, 13, 18, 27, 36 |

3.9 | 2, 12, 20 / 3 |

Chapter 4. Using the Derivative | |

4.1 | 1, 5, 13, 14, 22, 24, 26, 27, 38, 44, 48 / 9, 11, 19, 21, 25, 29, 31, 33, 41 |

4.2 | 2, 4, 6, 8, 13, 18, 26, 30, 31, 32, 40 / 5, 11, 17, 29, 33, 37, 39, 41 |

4.3 | 5, 6, 8, 10, 17, 20, 33, 36, 38, 50, 53 / 13, 19, 21, 23, 39, 41 |

4.4 | 8, 16, 29, 35, 38, 40, 42, 51, 52 / 1, 5, 11, 19, 29, 33, 39, 41, 45, 49 |

4.5 | 1, 3, 4, 8, 11, 12, 13, 14, 18, 23 / 5, 9, 15, 17, 21 |

4.7 | 4, 5, 7, 18, 20, 21, 22, 68 |

Chapter 5. Key Concept: The Definite Integral | |

5.1 | 1, 2, 3, 6, 7, 15, 22, 23, 25, 28 / 9, 21, 27, 29, 31 |

5.2 | 4, 11, 12, 16, 18, 29, 30, 32, 36, 40, 8, 9 / 1, 3, 7, 13, 15, 17, 19, 21, 31, 33 |

5.3 | 1, 2, 4, 6, 8, 10, 12, 20, 22, 30 / 7, 11, 15, 19, 21, 23, 27, 33, 37 |

5.4 | 1, 2, 5, 10, 11, 21, 24, 32, 40, 41, 46, 13, 18 / 3, 7, 15, 25, 31, 35, 39–42, 43, 55 |

Chapter 6. Constructing Antiderivatives | |

6.1 | 3, 7, 8, 12, 14, 16, 19, 22, 25 / 9, 11, 15, 17, 21, 23, 29 |

6.2 | 2, 6, 7, 8, 14, 18, 20, 23, 36, 41, 44, 46, 50, 51, 55, 62, 65, 70 / 5, 13, 15, 27, 33, 39, 43, 47, 53, 59, 61, 71, 73, 77 |

* Indicates the question is an additional question coded in WebAssign but not contained in the printed text.

There is one required book for this course:

Hughes-Hallett, Deborah, et al. *Applied & Single Variable Calculus for Loyola University Chicago with WebAssign Custom* (packaged with WebAssign). 4th ed. ISBN-13: 9781118762202. Hoboken, NJ: Wiley, 2009.

**Textbook Notes:** (1) The cover of the physical book reads "Applied Calculus" (not the longer name above), and has the Loyola crest at the bottom. (2) This is a custom text, that can only be purchased via one of the methods below.

- From the University Bookstore ($190.25, includes Math 131 and Math 132 access to WebAssign).
- Directly through the publisher (Wiley) website ($152.95 plus $4 shipping charge, includes Math 131 and Math 132 access to WebAssign). It will take about 3 days from order date for students to receive a softcover book by mail.
- Visiting the WebAssign website ($89.70 per semester for ebook and WebAssign access). Students who purchase “materials” through WebAssign
**will not**receive a copy of the softcover text. The ebook is only accessible after signing into WebAssign (it cannot be downloaded onto an a device such as Kindle or iPad).

**WebAssign Notes:** (1) WebAssign charges** by the semester.** This means, e.g., students choosing textbook option 3 and would pay an additional $89.70 the following semester to either retake Math 131 or take Math 132. (2) There is a fourth textbook option, but it is *not recommended:* students may find cheap copies of the *Applied* Hughes-Hallett text and the *Single Variable* Hughes-Hallett text, from which the above textbook is built, then purchase WebAssign access (homework only) for $44.95. (3) Whether you have purchased an access code or not, you have immediate and free access to register for your class WebAssign page. **Free trial access expires two weeks after the semester begins.**

This semester, Loyola is running a cross-section discussion session, listed in LOCUS as MATH 131D.

MATH 131D: Thursdays 4:00 – 5:30 in Mundelein 204

This is a non-credit and ungraded supplement to your standard 131 section, led by Aleksandr Goltsiker. The discussion section is intended to be a forum in which students can go over problems and course material. Registration in LOCUS is recommended but **not required** for students to participate.

### 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 Math 131 (and other courses). Further details regarding the important information of where and when will be posted once announced.

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 is active for up to one year, so you may be able to reuse your access code (at no additional cost) if you have enrolled in either course the previous semester.

**NOTE:** Many sections of MATH 131/132 use WebAssign as a required homework component of the final course grade, so even if your instructor this semester does not, it may still be prudent to purchase an access code.

Follow the steps below to register for your section in WebAssign:

- From www.webassign.net, click on “I have a Class Key” in the “Account Log In” box (https://www.webassign.net/v4cgi/selfenroll/classkey.html) and enter
**luc ABCD WXYZ**(where ABCD WXYZ is an eight-digit number provided to you by your instructor). - See WebAssign Support for help getting started.
- For roster management purposes, it would be helpful if you choose your LoyolaID when setting up your WebAssign account.

**NOTE:** Students may register for their WebAssign course immediately, even without an access code. Open enrollment closes two weeks after the semester begins.

### Installing Mathematica (free!)

Mathematica is a powerful computing environment that is designed for use in engineering, mathematics, finance, physics, chemistry, biology, and a wide range of other fields. Loyola students and faculty can download and install the latest copy of Mathematica for free. You must be logged on to Loyola VPN, and then visit the following ITS webpage, https://digitalmedia.luc.edu/News/NewsItem/View/4/mathematica-version-9-downloads-available.

### Wolfram Demonstrations Project

From the Wolfram Demonstrations Project. ". . . the Wolfram Demonstrations Project is an open-code resource that uses dynamic computation to illuminate concepts in science, technology, mathematics, art, finance, and a remarkable range of other fields.

Its daily growing collection of interactive illustrations is created by Mathematica users from around the world who participate by contributing innovative Demonstrations."

Click on the link to go to the home page of the Wolfram Demonstrations Project.

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

Any questions about placement in calculus or other 100- and 200-level courses which remain after reading this section should be directed to Professor John Del Greco, Assistant Chair. Please e-mail him to set up an appointment.

**Math 161-162** (Calculus I, Calculus II) is a **traditional** calculus course 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 Mathematics, Statistics, Physics and Chemistry. It is highly recommended, although not required, for students majoring in Economics, Computer Science and Biology.

**Math 131-132** (Applied Calculus I, Applied Calculus II) is more of a **survey** course 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 course 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.

#### Advanced Placement Credit:

For information about advanced placement in Calculus or Statistics click on this link.

## Other Useful Loyola Sites

- Sakai (Online Course Materials)
- Tutoring Center
- Get
*Wolfram Mathematica* - WebWork