# 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.

Deborah Hughes-Hallett, et al. Applied & Single Variable Calculus (custom edition), E-book packaged with WebAssign

### 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).

Math Club tutoring for **Spring 2016** will take place on **Tuesdays and Thursdays **from** 7-8:30pm** in **Cuneo Hall Room** **111**.

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.

## 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.