College of the Holy Cross
Math 125: Calculus for Social Sciences I
Complete Schedule
Fall 2007

Topic: 1.1 Four Ways to Represent a Function

Chapter 1: Functions and Models
This chapter stresses the multiple representations of functions (verbal, numerical, visual, and algebraic). The content of this chapter should be familiar from your previous math courses, what may be new here is thie emphasis on the multiple ways in which we can represent functional relationships. We will not be studying sections 1.4 or 1.7 from this chapter.

Ahead of Time: Make sure this course is right for you. First read this course description. Then, visit the Department's website and carefully read through the descriptions of the various Calculus courses offered at Holy Cross by following the link for Introductory Courses and AP Credit. If you aren't sure if you're in the right course, please email me or stop by to see me as soon as possible.

Check this Out: Need extra help in Calculus? Free tutoring by math majors every Sun - Thurs night in Swords 302 from 7:00 - 9:00. Starts on Sunday.

Topic: 1.2 Mathematical Models: A Catalog of Essential Functions & 1.3 New Functions from Old Functions

Ahead of Time: Plan to read both your text in advance of each class meeting. Look ahead to see what section will be covered, and read through those sections beforehand. Take notes during class. After class, read through the sections again and fill in any gaps in your notes. The best students rewrite their class notes, incorporating material from the text and the lecture. These notes can really help when you study for the upcoming exams.

Assignment #1 Mathematical Autobiography Essay (up to 10 activity points)
DUE by 9 AM on Wednesday, Sept. 5 (see below for submission instructions)
This one to two page essay explores your relationship with mathematics. You choose the style of your paper -- it could recount a pivotal incident or influential person in your mathematical life, could be a poem, etc. Make it interesting to read! For full credit, it can't simply tell me about a favorite or horrendous math teacher...give me more! How did such an experience form your attitude about your engagement with mathematics?
SUBMISSION INSTRUCTIONS: You must submit this electronically. First type the paper in WORD and, if you wish, save it as a PDF document. Please spell-check and have a friend read it before you submit it to make sure that your prose makes sense. When you are ready to submit your paper, follow these instructions:

HOW TO SUBMIT ON BLACKBOARD: Many assignments this semester will be submitted to me electronically through Blackboard. To do so, write the document up in Word or save as a PDF file. Then log onto Blackboard by clicking the LOGIN box off of the main holycross webpage at http://www.holycross.edu. Then, choose the link for Tools. Click on Drop Box. Click on "send file" (not "add file") and you should be all set. The title or subject of your document must follow the format of "Last Name _ Assignment Number". For example, if I were going to submit this first assignment, I would title the document and the submission as "Roberts_#1". Keep a copy of what you submit, in case there is a problem. I know you may be nervous about this first electronic submission...so I will send you a confirmation email to let you know that I received it. Giveme 24 hours to send you the confirmation email, okay?

Check it Out: mathartfun.com This is an online store & gallery of Mathematical Art

Topic: 1.5 Exponential Functions

Assignment #2 Problem Set (up to 12 activity points)
DUE at the start of class at 12:30 place in the wooden assignment box that is located in the back of the classroom:
Section 1.1: # 2, 5-8, 16, 20, 24, 28, 42, 52, 64, 66, 70
If you click on the link above for Section 1.1, you can print out a form with the exercise problems and space in which to write your answers. Please use this form for your assignment. Turn it in with a cover sheet and the pages stapled (not paper-clipped) together. The cover sheet is available under the link for Course Materials.

Note: If you have questions on any of the homework problems, please put the problem number on the board at the beginning of class. If you see your problems already listed, please put a check-mark next to them, which indicates to me that more than one person has a question. I'll spend a few minutes at the beginning of each lecture addressing questions related to the homework assignments.

Note: Homework strategy: Start early, never the night before the assignment is due! Try the problems on your own first. Try the odd problems that are adjacent to the ones assigned -- they have answers in the back of the book & in the Student Solution Book (if you purchased this) so you can see if you're understanding them. Then consult with your classmates. Receive free help at the Calculus Workshop in Swords 302 from Sunday-Thursday evenings from 7:00 - 9:00. Come to my office hours at any time or, if my office hours don't work with your schedule, email me for another appointment time.

Assignment #3 Activity Point Opportunity (up to 10 activity points)
DUE on Blackboard before midnight on Sunday night. This afternoon from 2:00 - 4:00, the Holy Cross students who conducted scientific research over the summer are presenting their results to the campus in a poster-session forum in the Hogan Ballroom. If you attend this session and submit a write-up about your experience, you can earn up to 10 activity points. Go to the poster session, walk around and pick out one poster that seems interesting to you. Ask the student some questions. Your write-up should be one to two pages in length. Half of it should be devoted to a description of the poster that you chose as interesting. The other half should be devoted to a personal response to the experience of attending this event. Submit this on Blackboard prior to the deadline.

HOW TO SUBMIT ON BLACKBOARD: Many assignments this semester will be submitted to me electronically through Blackboard. To do so, write the document up in Word or save as a PDF file. Then log onto Blackboard by clicking the LOGIN box off of the main holycross webpage at http://www.holycross.edu. Then, choose the link for Tools. Click on Drop Box. Click on "send file" (not "add file") and you should be all set. The title or subject of your document must follow the format of "Last Name _ Assignment Number". For example, if I were going to submit this first assignment, I would title the document and the submission as "Roberts_#1". Keep a copy of what you submit, in case there is a problem. I know you may be nervous about this first electronic submission...so I will send you a confirmation email to let you know that I received it. Giveme 24 hours to send you the confirmation email, okay?

Topic: Finish 1.5 Exponential Functions and begin 1.6 Inverse Functions & Logarithms

Ahead of Time: It's important to scroll ahead to see when problem sets are due, and get started on them early. This gives you the opportunity to ask questions in class, during office hours, or during the Calculus Workshop.

Topic: Finish 1.6 Inverse Functions & Logarithms

Note: If you have questions on any of the homework problems, please put the problem number on the board at the beginning of class. If you see your problems already listed, please put a check-mark next to them, which indicates to me that more than one person has a question. I'll spend a few minutes at the beginning of each lecture addressing questions related to the homework assignments.

Assignment #4 Problem Set (up to 30 activity points)
DUE at the start of class at 12:30 place in the wooden assignment box that is located in the back of the classroom:
1.2 #2, 4, 6, 8, 12, 18, 20
1.3 #2, 4, 6, 10, 16, 30, 32, 36 (The printout has additional problems #40, 42, 44, 50, 54 that are challenge problems. You don't have to do these problems, but if you do, they will be corrected for you. No credit for doing these challenge problems, it's just for you if you want to give them a try.)
If you click on the links or go under Course Materials on Blackboard, you can print out a form with the exercise problems and space in which to write your answers. Please use this form for your assignment. Turn it in with a cover sheet and the pages stapled (not paper-clipped) together. The cover sheet is available under the link for Course Materials.

Topic: Review for the Exam

Assignment #5 Problem Set (up to 38 activity points)
ASSIGNMENTS WITHOUT A COMPLETED COVER SHEET AND THAT ARE NOT STAPLED WILL NOT BE GRADED!!!
DUE at the start of class at 12:30 place in the wooden assignment box that is located in the back of the classroom:
Section 1.5: # 4, 8, 10, 14, 18, 20, 22 (For the intersection point, just give an approximation. It does not have to be correct to one decimal point), 26.
Section 1.6: # 4, 6, 10, 12, 14, 16 b), 18, 24, 26, 30, 34

EXAM 1 will cover Chapter 1 (we did not cover sections 1.4 or 1.7)

Stein 120 from 12:30 - 1:45. The exam will be administered by Professor C. Ballantine, who is capable of answering any questions you may have.

Notes about the exam: Graphing Calculators are not permitted; the department has some scientific calculators (TI-30Xa) for your use during the exam. If you want to bring your own scientific calculator, it must be pre-approved by your professor. You may bring one index card (3"x5") with notes into the exam (it's okay to write on both sides and your name should be on it). Please arrive five to ten minutes early so you aren't disrupting the exam by coming into the room late.

How to study for this test? First, use the resources that are available to you, such as your text book and lecture notes. The Review Exercises for Chapter 1 (page 83 - 85) are an excellent source of practice problems -- get together with someone else in the class after you've worked these problems to discuss your solutions and your approaches to the problems. You will have some multiple choice and true-false questions on the exam. If you have questions, please ask! You can also go to the Calculus Workshop for tutoring in the evenings (Sunday - Thursday from 7:00 - 9:00). The key is to work lots and lots of problems and to interact with other people to convince yourself that you are truly understanding the material. The Student Study Guide is an excellent resource; if you decided not to purchase the Study Guide, I have one in my office that you can borrow.

Chapter 2: Limits and Derivatives
The central concept of the semester is the notion of a derivative. In this chapter, this concept is motivated by introducting the idea of a limit.

Topic: 2.1 The Tangent & Velocity Problems & 2.2 The Limit of a Function

Assignment #6 (Due on or before 8:00 am on October 16) A response essay (up to 15 activity points)
Did you see the movie A Beautiful Mind? The movie portrays the life of a famous mathematician. It is reviewed by Lynne M. Butler for the professional mathematics community in the April 2002 Notices of the American Mathematical Society. For this assignment, read her review and submit a response essay that is your personal reaction to both the movie and her review. If you haven't seen the movie, it should be available in the Main Library here on campus.

Basic Instructions: Your response essay must be typed, one-and-a-half or double-spaced, size 12 font, no shorter than a page and a half, no longer than two pages. If you use any external references, please give proper citations in your paper. Submit this assignment electronically on Blackboard prior to 8:00 am on Oct 16.The title or subject of your document should follow the format of "Last Name _ Assignment Number" Do not use any special characters, such as #, in the title of the document you upload onto Blackboard.

Topic: 2.3 Calculating Limits Using the Limit Laws & 2.4 Continuity

Topic: 2.5 Limits Involving Infinity &

Topic: 2.6 Tangents, Velocities, and Other Rates of Change & 2.7 Derivatives

Assignment #7 Problem Set (up to 44 activity points)
ASSIGNMENTS WITHOUT A COMPLETED COVER SHEET AND THAT ARE NOT STAPLED WILL NOT BE GRADED!!!
DUE at the start of class at 12:30 place in the wooden assignment box that is located in the back of the classroom:
Section 2.1 #2,4,5,6 (even though 5 is an odd numbered problem with answers in the back of the book, it's important enough for you to do yourself)
Section 2.2 #2,4,6,8,10,16,22 (note that #28 is on the form, but you don't have to do it and won't receive credit for it...it's just extra practice)
Section 2.3 #2,6,8,10,16,20 (note that #26,36,40 are on the form, but you don't have to do these and won't receive credit for them...they're extra challenge problems that are optional)
Section 2.4 #4,6,8,10,16 (note that #18,26,32 are provided as optional challenge problems, but you don't have to do them and won't receive credit for them)

Topic: 2.8 The Derivative as a Function & 2.9 What does f' say about f?

Assignment #8 Water Tank Activity DUE (worth up to 15 activtity points)
Print out this worksheet and complete it. You will need to use graph paper. You may work with other students but must turn in your own work. Please add a cover sheet and list the names of all the people you worked with.

Check it Out: Flatland: The Movie
http://www.youtube.com/watch?v=C8oiwnNlyE4
This is a movie based on a famous book by Abbott that tries to explain how it is possible for dimensions higher than the 3d dimension to exist. A new movie is coming out that tries to explain this. If you enjoy this kind of thinking, explore on the internet under keywords "Flatland" and "Sphereland" and "Abbott".

Topic: Review for the second exam.

Assignment #6 DUE (Due on or before 8:00 am on October 16) A response essay (up to 15 activity points)
Did you see the movie A Beautiful Mind? The movie portrays the life of a famous mathematician. It is reviewed by Lynne M. Butler for the professional mathematics community in the April 2002 Notices of the American Mathematical Society. For this assignment, read her review and submit a response essay that is your personal reaction to both the movie and her review.

Basic Instructions: Your response essay must be typed, one-and-a-half or double-spaced, size 12 font, no shorter than a page and a half, no longer than two pages. If you use any external references, please give proper citations in your paper. Submit this assignment electronically on Blackboard prior to 8:00 am on Oct 16.The title or subject of your document should follow the format of "Last Name _ Assignment Number" Do not use any special characters, such as #, in the title of the document you upload onto Blackboard. If you are using the VISTA operating system and could save your document in Windows XP form, it'll have the extension .doc and I can read it from any computer. I can read .docx files from my work computer, though, so you'll be okay.

Assignment #9 Problem Set (up to 64 activity points)
ASSIGNMENTS WITHOUT A COMPLETED COVER SHEET AND THAT ARE NOT STAPLED WILL NOT BE GRADED!!!
DUE at the start of class at 12:30 place in the wooden assignment box that is located in the back of the classroom:
Section 2.5 #4, 6, 8, 20, 24 (Optional Challenge Problems #28 (use squeeze theorem),34,40 (many possible answers))
Section 2.6 #2,6,8,12,14,16 (Hints:#6 x^3 + 1 = (x+1) (x^2 -x +1); #8 do long division to simplify the rational function; #12 get common denominator) (Optional Challenge Problems #18,24)
Section 2.7 #2 (you'll need to do #1 first separately), 4,6,12,16,20,28,30,34 (these last three problems are very important)
Section 2.8 #2,4,8,12,20,30,32,38,50 (please note that problem #3 is a really great problem)
Section 2.9 #2,4,6 (Optional Challenge Problems 8,12,18,26 )

Assignment #TALK (up to 10 activity points) Teacher Education Program: Info. Session
You may attend up to three lectures or events this semester and earn activity points. I will list the eligible talks in the schedule. If you choose to attend and write me a one page letter about the event and what you took away from the experience, then you can earn up to 10 activity points. You may either submit your written response on Blackboard (follow the instructions from earlier in the semester) or you can turn in a hard-copy print out. Your write-up is due within two days of attending the event.

Information Session for all students interested in Teacher Education: Wednesday October 17, 2007 in Hogan 305, 6.30-7.15pm

Education is ALIVE and WELL at Holy Cross!! The Education division would like to encourage all students who are interested in considering teaching as a career to attend this meeting. The Holy Cross Teacher Education Program (TEP) offers a series of courses and experiences that lead undergraduate students to become licensed by the Commonwealth of Massachusetts to teach in high and middle schools. The following majors can apply: Biology, Chemistry, Classics, Mathematics, Physics, History, English, Spanish, and French. We also offer pre-practicum experiences and courses for students interested in a teaching career - but not necessarily obtaining licensure while at Holy Cross. Come along and learn how you can take courses that will excite you about teaching, prepare you for TEP licensure, prepare you for grad school teacher licensure, or simply provide you with opportunities to work in schools.

Deadline for application for the Holy Cross TEP program acceptance this semester is November 2nd
Applications can be downloaded from: http://www.holycross.edu/departments/education/website/tep_application_page.htm

If you have any further questions please contact Professor Bev Bell via phone #3058 or email bbell@holycross.edu

EXAM 2 will cover Chapter 2

Notes about the exam: Graphing Calculators are not permitted; the department has some scientific calculators(TI-30Xa) for your use during the exam. If you want to bring your own scientific calculator, it must be pre-approved by your professor. You may bring one index card (3"x5") with notes into the exam (it's okay to write on both sides and your name should be on it).

Chapter 3: Differentiation Rules
The sections we will cover in this chapter represent the core material for the course. We will not be covering some of the applications in section 3.3. We will not cover 3.6 and we will only use the differentiation formulas in 3.7 (we won't derive them). We will not cover section 3.8.

Topic: 3.1 Derivatives of Polynomials & Exponential Functions & 3.2 The Product & Quotient Rules 

Check it Out: The Dot and the Line: A Romance in Lower Mathematics

This won an Academy Award in 1965 for Best
Animated Short Film. Enjoy!

http://www.youtube.com/watch?v=OmSbdvzbOzY

You can read more about it at Wikipedia: http://en.wikipedia.org/wiki/The_Dot_and_the_Line

Assignment #TALK (up to 10 activity points) Mathematics/Computer Science Career Night
You may attend up to three lectures or events this semester and earn activity points. I will list the eligible talks in the schedule. If you choose to attend and write me a one page letter about the event and what you took away from the experience, then you can earn up to 10 activity points. You may either submit your written response on Blackboard (follow the instructions from earlier in the semester) or you can turn in a hard-copy print out. Your write-up is due within two days of attending the event.

What in the world does an actuary really do? How could a degree from Holy Cross prepare you to become a software engineer? Have you considered becoming a math teacher?

If you would like to learn more about careers in actuarial science, software engineering and high school teaching this is the program for you!

Mathematics/Computer Science Career Night
Tuesday, October 23
Swords 359
7:00 PM
Students from all classes and majors are welcome!What in the world does an actuary really do?

Topic: 3.3 Rates of Change in the Natural and Social Sciences & 3.4 Derivatives of Trigonometric Functions

Assignment #10 Optional Activity Point Assignment (up to 34 activity points)
DUE at the start of class at 12:30 place in the wooden assignment box that is located in the back of the classroom:
Chapter 2 Review Problems

Check it Out: http://www.youtube.com/watch?v=UTby_e4-Rhg

Topic: 3.5 The Chain Rule

Assignment #11 Optional Activity Point Assignment (up to 38 activity points)
3.1 # 2, 4, 8, 10, 14, 16, 20, 22, 24 , 28 (Optional: 30, 32, 48, 58)
3.2 # 2, 4, 6, 8, 10, 14, 16, 20, 22 (Optional: 24, 28, 32, 36, 40, 42)

Topic: 3.5 The Chain Rule

Assignment #12 Optional Activity Point Assignment (up to 20 activity points)
3.3 # 2, 4, 8, (Optional: 16, 18, 24, 26, 32)
3.4 # 2, 10, 14, 18, 32 - (#32 is worth 4 points) (Optional: 40, 42)

Note: Tomorrow (Weds. Nov. 7) is the last day to withdraw from the course. If you are considering withdrawing from the course, you should plan to speak with me and your class dean right away!

Assignment #13 (Due Nov. 13 by 8:00 am) A response essay (worth up to 20 points)
Read this recent article about Math Education in America from the NY Times and submit a response essay on Blackboard. What do you think?

Chapter 4: Applications of Differentiation
Now that we understand the concept of a derivative and how to compute them, we can explore the applications of differentiation. We'll pick and choose applications from this chapter on which to focus our attention. My choices will reflect the fact that this is a terminal math course (i.e. you won't be continuing in mathematics) and that you are probably going to major in Economics and/or Accounting. We will cover sections 4.2, 4.3 and 4.7

Topic: 4.1 Related Rates (with some comments about implicit differentiation, which you can read more about in section 3.7)

Assignment #14 Optional Activity Point Assignment (up to 28 activity points)
Solution template is available under Course materials on Blackboard.
3.5 # 4, 6, 8, 10, 12, 16, 18, 36, 42
3.7 # 2, 4, 6, 10, 14

Assignment #TALK (up to 10 activity points) Environmental Studies Seminar TOMORROW
You may attend up to three lectures or events this semester and earn activity points. I will list the eligible talks in the schedule. If you choose to attend and write me a one page letter about the event and what you took away from the experience, then you can earn up to 10 activity points. You may either submit your written response on Blackboard (follow the instructions from earlier in the semester) or you can turn in a hard-copy print out. Your write-up is due within two days of attending the event.

Friday, November 2, O'Neil 112, 12:15 - 1:30.
Tim Pruinton and Beth Lambert from the Massachusetts State Riverways Program to campus to discuss Dam Removal and River Restoration.

Topic: Review for the exam & more on related rates, if you don't keep me busy with questions!

Good practice problems: Chapter 3 Review #1 - 18, 32, 33, 47, 48, 49-56, 60

Assignment #TALK TOMORROW (up to 10 activity points) Education Graduate School Fair
You may attend up to three lectures or events this semester and earn activity points. I will list the eligible talks in the schedule. If you choose to attend and write me a one page letter about the event and what you took away from the experience, then you can earn up to 10 activity points. You may either submit your written response on Blackboard (follow the instructions from earlier in the semester) or you can turn in a hard-copy print out. Your write-up is due within two days of attending the event.

Wednesday, November 14
Hogan Jenks Suite B/C
7:00 PM

Representatives will be available to speak with you about graduate programs in these fields.
Counseling
Elementary Education
Middle School Education
High School Education
Special Education
Urban Education

The following institutions will be represented at this event. Assumption , Brandeis, Brown , Clark , Harvard, Lesley, UMass Amherst

Assignment #TALK (up to 10 activity points) Your Professor's Research in the Grand Canyon
You may attend up to three lectures or events this semester and earn activity points. I will list the eligible talks in the schedule. If you choose to attend and write me a one page letter about the event and what you took away from the experience, then you can earn up to 10 activity points. You may either submit your written response on Blackboard (follow the instructions from earlier in the semester) or you can turn in a hard-copy print out. Your write-up is due within two days of attending the event.

Tuesday, Nov. 20
Stein 133
9:00 - 9:50 (don't be late!)
I will be giving a power point presentation about the research that I did for the Grand Canyon National Park. You will learn about the kind of research that an applied mathematician does. It is designed for a general audience, so you will be able to understand most everything. The photography is spectacular. I hope you can come!

Exam 3 will cover Chapter 3 (note we only covered sections 3.1 - 3.5 plus part of 3.7)

Notes about the exam: Graphing Calculators are not permitted; the department has some scientific calculators(TI-30Xa) for your use during the exam. If you want to bring your own scientific calculator, it must be pre-approved by your professor. You may bring one index card (3"x5") with notes into the exam (it's okay to write on both sides and your name should be on it).

Topic: 4.2 Maximum and Minimum Values of Functions & 4.3 Derivatives and the Shapes of Curves

Template to practice sketching functions.

Assignment #15 Optional Activity Point Assignment (up to 12 activity points)
4.1 #4, 10 12 (problem set was handed out in class on Nov. 8...if you don't have it, make one up yourself)

Topic: 4.7 Application to Busines and Economics

Topic: 4.7 Application to Busines and Economics

Topic: 4.7 Application to Busines and Economics

Review Session

Monday Dec 10 in HAB103 from 10-11 and from 1-2
Wednesday Dec 12 in O'Neil 101 from 10-11 and from 1-2

FINAL EXAM 8:30 AM - 11:30 AM in O'Neil 101
This is a comprehensive Final Exam that covers every section we've covered this semester. The material we covered from Chapter 4 will be represented more on this exam...20% will be for each of Chapters 1, 2, and 3 and 40% of the final will be on the Chapter 4 material.