# MATH 132

**Review of **Chapters 5 & 6. *Definite and Indefinite Integrals* [1.5 to 2 Weeks]* (Prerequisite Material from MATH 131) 5*.1 – How Do We Measure Distance Traveled?

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

**5.2 – The Definite Integral**

5.3 – The Fundamental Theorem and Interpretations

5.4 – Theorems About Definite Integrals

properties of definite integrals; area between curves; using the definite integral to find an average

**Skip:**the subsection “Comparing Integrals”

**6.1 – Antiderivatives Graphically and Numerically**

6.2 – Constructing Antiderivatives Analytically

**Skip:**Sections 6.3-6.4

**Chapter 7. ***Integration* [1.5 to 2 Weeks]

7.1 – Integration by Substitution

7.2 – Integration by Parts

7.6 – Improper Integrals

consider only those where limits of integral are infinite

**Skip: **cases where value of integrand becomes infinite (pp. 398–400)

**Skip: **Sections 7.3, 7.4, 7.5 & 7.7

**Chapter 8. ***Using the Definite Integral* [2 Weeks]

8.6 – Applications to Economics

8.7 – Distribution Functions

8.8 – Probability, Mean, and Median

**Skip: **Sections 8.1–8.5

**Chapter 9. ***Functions of Several Variables* [2.5 to 3 Weeks]

9.1 – Understanding Functions of Two Variables

9.2 – Contour Diagrams

9.3 – Partial Derivatives

9.4 – Computing Partial Derivatives

9.5 – Critical Points and Optimization

9.6 – Constrained Optimization

**Chapter 11. ***Differential Equations* [3.5 Weeks]

11.1 – What is a Differential Equation?

11.2 – Slope Fields

11.3 – Euler's Method

11.4 – Separation of Variables

11.5 – Growth and Decay

11.6 – Applications and Modeling

11.7 – The Logistic Model

11.8 – Systems of Differential Equations

11.9 – Analyzing the Phase Plane (time permitting)

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.

Review of Material from MATH 131 | |
---|---|

5.1 | 1, 15, 25 |

5.2 | 4, 12, 29, 32 |

5.3 | 2, 6, 22, 30 |

5.4 | 14, 25, 46 |

6.1 | 3, 12, 16, 20, 22 |

6.2 | 21, 41, 46, 50, 60, 62, 65, 73 |

Chapter 7. Integration | |

7.1 | 4, 8, 12, 21, 25, 29, 36, 59, 77, 115, 138, 139 |

7.2 | 3, 5, 8, 10, 12, 20, 30, 38, 46, 54, 71 |

7.6 | 2, 4, 6, 10, 11, 12, 27, 35, 43 |

Chapter 8. Using the Definite Integral | |

8.6 | 1, 4, 8,10, 20, 21, 23, 28, 30, 32 |

8.7 | 1, 6, 7, 10, 11, 15, 16, 17, 21 |

8.8 | 2, 4, 6, 7, 8, 9, 10, 11, 12 |

Chapter 9. Functions of Several Variables | |

9.1 | 1, 3, 9, 11, 17 |

9.2 | 1, 2, 5, 10, 13, 20, 25, 27 |

9.3 | 1, 3, 5, 7, 8, 12, 18, 23, 24; Review: 15, 17 |

9.4 | 3, 4, 6, 8, 15, 23, 25, 29, 36; Review: 29, 34 |

9.5 | 1, 7, 8, 10, 11, 20, 21 |

9.6 | 2, 5, 8, 9, 11 14, 25; Review: 40 |

Chapter 11. Differential Equations | |

11.1 | 1, 2, 9, 11, 13, 16, 21, 26, 28 |

11.2 | 4, 13, 15, 17, 18 |

11.3 | 6, 7, 10, 11, 14 |

11.4 | 1, 2, 6, 8, 12, 16, 20, 22, 25, 44, 50 |

11.5 | 1, 2, 4, 9, 10, 14, 16, 22, 26, 30 |

11.6 | 1, 2, 9, 13, 14, 16, 19, 22, 26 |

11.7 | 10, 11, 12, 16, 18, 25, 28, 34 35 |

11.8 | 2, 3, 12, 14, 17, 19, 20, 22, 23, 24 |

11.9 | 1, 2, 5, 12, 20, 21 |

There is one required book for this course (which you may already own):

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. Print.

**Students that have taken Math 131 **in Fall 2013 and purchased a new copy of the text bundled with WebAssign access code do not need to purchase any additional materials.** **

**Otherwise,** the required text above is a customized text that students can only purchase by one of the following methods:

- From the University Bookstore (http://www.luc.edu/info/bookstore.shtml). ($190.25, includes Math 131 and Math 132 access to WebAssign)
- Directly through the publisher (Wiley) website. www.wiley.com/WileyCDA/Section/id-817162.html. It will take about 3 days from order date for students to receive a softcover book by mail. This should not present a problem, as students will have two weeks of open access to WebAssign. ($152.95 plus $4 shipping charge, includes Math 131 and Math 132 access to WebAssign, 20% discount from bookstore price).
- Visiting WebAssign’s website (http://www.webassign.net). Students will need the Class Key which will be of the form luc #### ####. Students who purchase “materials” through WebAssign will not receive a copy of the softcover text. Instead students can purchase access to homework and an electronic version of the full text that can only be accessed online after signing into WebAssign (it cannot be downloaded onto an a device such as Kindle or iPad).
**Note WebAssign charges by the semester.**This means if a student purchased WebAssign access to Math 131directly through WebAssign for $89.70 in the previous semester, they will still need to pay an additional $89.70 for WebAssign access to Math 132 again this semester. ($89.70 per semester for WebAssign, no physical textbook.)

**We stress** that the required Math 132 text has been customized specifically for use at Loyola University Chicago. There are several publisher versions of calculus texts by the same author that students are certain to come across if they search Amazon or elsewhere online. Although these may be cheaper, any such versions (new or old) are different than the required text, and thus not a substitute.

WebAssign access is required for the course. Students who experience delays or difficulties in getting their textbooks or setting up their WebAssign accounts need not fall behind. **Free trial access** to this homework and eBook system has been arranged. Trial access to WebAssign **expires on January 24.**

This semester, Loyola is running a cross-section discussion session, listed in LOCUS as MATH 132D.

MATH 132D: Mondays 4:00 – 5:30 in Mundelein 204

This is a non-credit and ungraded supplement to your standard 132 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 132 (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.

### Chapter 6

6.1: 2, 4, 5, 6, 12, 16, 19, 21

6.2: 1, 2, 4, 5, 8, 11, 12

6.3: 2– 6, 12, 14, 15

6.4: 2, 3, 5, 10, 11, 17, 18

### Chapter 7

7.1: 4, 9, 16, 17, 23, 24, 32, 37, 43, 56, 59, 65

7.2: 1– 40 multiples of four (i.e. 4, 8, 12 . . .), 41, 43

7.3: 1– 19 multiples of three, 23, 28, 32, 34, 37, 38, 41, 44

7.4: 1, 4, 5, 14, 15, 21, 24

7.5: 2, 3, 7, 10, 11, 14, 17, 18, 24– 27

### Chapter 8

8.1: 1, 3, 5, 6, 10, 14

8.2: 1, 2, 4, 8, 10, 11, 12 , 14

8.3: 2, 4, 6, 8, 9

### Chapter 9

9.1: 2, 3, 4, 10, 17

9.2: 2, 4, 5– 8, 18, 23, 25

9.3: 1, 8, 12, 17, 18, 20, 24

9.4: 1, 2, 8, 10, 14, 16, 18, 22, 30

9.5: 2, 5, 9, 14, 16, 18, 20

9.6: 2, 8, 11, 15, 19, 22

### Chapter 10

10.1: 1, 2, 5, 8, 10, 11, 12, 13

10.2: 2, 3, 7, 12, 13, 14, 16, 21, 22

10.3: 1, 2, 4, 5, 6, 12, 13

10.4: 1, 2, 10, 13, 14, 17

10.5: 1, 4, 8, 10, 14, 16, 19, 23

10.6: 1–3, 6, 7, 8, 14–16

10.7: 3, 4, 6, 8, 9, 10, 12

Focus on Theory: Separation of Variables: 1, 2, 6, 7, 9, 12, 13, 15, 20

Some instructors may be using WeBWorK for required, online homework submission (instead of WileyPLUS). Your instructor will provide you with the required username and password needed to login to your section's page. You can view the list of available courses/sections for which WeBWorK will be used this semester be clicking on any of the WeBWorK hyperlinks.

### 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*for***free***through myITS - WebWork