Math 250B - Spring 2010
Calculus and Differential Equations II
University of Arizona
Course Website
Basic Information
- Course Description: First order differential equations and modeling, approximations and series, second order differential equations, linear and nonlinear autonomous systems. The sequence MATH 250A-250B substitutes for the pair of courses MATH 129-254 or the pair MATH 129-355; however, MATH 250B alone does not substitute for MATH 254 or MATH 355.
- Location & Time: MWF 9:00-9:50 AM [ILC 125] AND T 2:00-2:50 PM [PSYCH 306; note room change!!]
(also see Thursday recitation times noted below)
- Instructor: Christopher Bergevin
Office: Math 321
Email: cbergevin [AT] math.arizona.edu
Office Hours: M 10-11, W 3-4 (in Math 321)
also by appointment; see TA office hours below as well
Phone: 520-626-0655
- Teaching Assistant: Joseph Padilla
Email: jrpadill [AT] email.arizona.edu
Office Hours: M and Th 2-3 (in the Math Center, Math 220)
Recitation: Thursday 5-6 (in Math 101) [tentative]
This is a more informal session where students can come and ask questions on concepts discussed in class,
homework, etc... (there will be computers in Math 101, so you can readily pull up questions with regard to WebAssign)
Students are strongly encouraged to come to recitation
- Texts - Note that two books are required for this course:
1. Calculus [Single Variable], Fourth Edition, by Hughes-Hallett et al. and published by Wiley
2. Differential Equations [Graphics, Models, Data], by D. Lomen and D. Loveock, published by Wiley
NOTE: You will need both books, as they will be used concurrently for 250A and will extend over into
250B (i.e., you will not need to purchase any additional texts for Spring 2010)
- Pre-Requisites - 250A. Credit allowed for only one of the following: MATH 250B, MATH 254, or MATH 355.
- Shortcut to updates re. HW assignments (see below). Quizzes/solutions will be posted on this page.
- 250A (Fall 2009) course webpage
In-Class Notes
This link leads you to the page housing pdf of the daily class notes. Updated regularly, so check back frequently.
Matlab
Over the course both semesters of Math 250, we will aim to make extensive use of computers to perform various types of calculations relevant to calculus and differential equations (e.g., numerically integrate a hard-to-solve ODE in order to obtain an approximate solution). The primary goal is two-fold. First, the computer can help provide insight and intuition into the underlying mathematical concepts encountered during the course. Second, you will essentially write your own programs, allowing you to directly specify the operations the computer performs. Ideally, the computer becomes less of a black box and more of a tool to extend your ability to essentially explore. While previous coding experience is not necessary, any you might have (e.g., Java, HTML) will likely be useful. Our primary means of interface to the computer will be via a well-known/developed package called Matlab.
In spirit, Math 250 is not promoting the specific use of Matlab per se. But it is a fairly high-level language (as opposed to something like assembly language, or the somewhat more accessible language C) and does much of the work for you 'behind the scenes'. Thus Matlab is a good candidate for folks relatively new to any type of programming. Furthermore, Matlab is widely-used and will thus likely be of great use to you in some form or another for future endeavors (e.g., there is a good chance you will see it in future classes, thus previous experience will likely be quite advantageous) . Thus time spent now learning its use will likely be time well spent.
Matlab is available for use on many computers around campus, including those found in the libraries as well as Math room 101. Furthermore, students with their own computer (PC, Mac or Linux) can download the full version of Matlab to their own computers via a license agreement the UofA has with the developer Mathworks. This is a very nice resource to have at your finger tips and are strongly encouraged to download the software for your own use. This link will take you the UofA page with information regarding how to download the software (you will ultimately need to use your Net ID and password to access the relevant material). It requires a bit of work/patience (plus memory; the entire package including all the 'toolboxes' is a few GB). A couple tips:
- Go to https://sitelicense.arizona.edu/matlab/index.php
- Hit
'Download Matlab Software' button
- Enter your NetID/password
- Read the instructions on the resulting page. You will ultimately Download
license.txt, which contains an activation key
- Go to www.mathworks.com (via step 1 of the presented instructions), and follow the
instructions given.
- Activation
takes up to one business day.
- The
whole software package is very large. Make sure you have a high-speed
connection. You can safely omit all of the optional packages, i.e., select
'Custom installation' and download only MATLAB. This makes it more
manageable.
The needed syntax will be presented/discussed as we progress. Some basic Matlab links/codes are included below simply for reference to see how certain types of things are done:
- Series of tutorial videos via Mathworks designed specifically with students in mind. Use your Mathworks account log-in you created if you downloaded Matlab (otherwise you'll have to create one; it's free). Chances are if you watch these, you'll know more about the basic features than I do!
- This page from the Dept. of Mathematics at Clarkson University offers examples of many useful features, such as setting up loops and conditional statements. Make sure to also see the section on Executable Files to see the gist of creating .m files. It ain't perfect, but it will get you started.
- Yet another useful link. Simply typing 'matlab tutorial' into google will bring up all sorts of useful things.
- Very simple code (as a .m file) to take a specified function, generate a set of points and plot them to screen.
- Another simple code (.m file) that plots a linear combination of two sinusoids. Shows a few mor eof the bells and whistles with regard to plotting/visualizing data in Matlab.
- This code (.m file) demonstrates for loops, conditional statements and random number generation.
Matlab Projects (also see the Assignments page)
Special Note (for life science and integrated science students)
While our focus over the course of 250 is providing you with a firm mathematical foundation (in calculus and differential equations), we will draw some context from a number of real world applications as well. In particular, we will use numerous example stemming from the rapidly-evolving life sciences*, which provides diverse and rich examples of complex/nonlinear/statistical/etc.... types of problems. While students of any major can take this class (with regard to future math pre-requisites), we strongly encourage students in the life sciences (or even just an interest in the life sciences!) to take 250A&B as it will hopefully help to start illuminate the deep underlying connections between biology and mathematics (a useful perspective to have for your future endeavors!). These connections carry over to numerous other courses that will likely be of interest to you down the road (e.g., Math 363 and Physiology 472).
* - life sciences is a very broadly defined term and comprises many different fields of study, such as: molecular/cellular/micro/systems biology, biomedical engineering, bioinformatics, medicine, biophysics, etc... (just to list a few)
Note: There are a handful of links at the bottom of this webpage that might be of interest to those in the life sciences.
Several Important Dates
Weekly quizzes (M) - (typically on Fridays)
1.13.10 (W) - First day of classes
1.18.10 (M) - MLK Day (no class)
1.25.10 (M) - Last day to add a class
2.9.10 (T) - Drop date
3.9.10 (T) - Last day to drop with a W (see below)
3.13-21.10 (M-F) - Spring Break (no classes)
5.5.10 (W) - Last day of classes
5.14.10 (F) - 250B Spring 2010 FINAL EXAM
See below for exam dates. Note that there will be no makeups for missed exams!
Grades
There will be 650 total possible points in the course. Point breakdowns are as follows:
- Homework and Weekly Quizzes (100 points total; see HW section below)
- Reading & Discussion Assignments, Labs (50 points; see HW section below)
- Three mid-term exams (each worth 100 points, 300 points total)
- Final exam (200 points)
Final grades will be no lower than as listed below:
- 585 < points (90%-100%) = A
- 520 < points (80%-90%) = B
- 455 < points (70%-80%) = C
- 390 < points (60%-70%) = D
- points < 390 (0%-60%) = E
HW Assignments (WebAssign)
Click here on the ASSIGNMENTS link to get current info on assignments and WebAssign updates
Homework problems will be assigned regularly and graded. Some will be graded online (see below), others will have to be turned in and graded by hand. Weekly quizzes (likely every Friday typically) based on homework assignments will be given in class on a weekly basis. A final score, equivalent to 100 points, will be computed from the homework and quiz results. For each assignment, homework and quiz will each contribute to 50% of the homework score. Only the 10 best homework scores will be kept.
Online homework will be assigned and collected via WebAssign. Here is some WebAssign information that you will probably find useful. Using WebAssign will allow you to gain important practice in terms of solving problems and gaining insight into the nature of the material. These assignments will be supplemented with quizzes given in class each week.
Here is what you will need when you log on to webassign for the first time:
- Your username is your email prefix (i.e. everything in your email address before the @)
- The institution is 'arizona'
- The password should be the same as you used last semester
- The class key is: arizona 7954 6042
You will need an access code for Webassign. This code either comes with your textbook (Hughes-Hallet book, if you purchase it at the UofA bookstore) or is available online on the webassign page. It costs 19.95 (per semester).
This link has helpful WebAssign tips.
Exams (tentative dates; potentially subject to change)
Exam 1: Monday, Feb.8, 2010
Exam 2: Monday, Mar.8, 2010
Exam 3: Monday, Apr.12, 2010
*** Final Exam *** : Friday, May 14, 8-10 AM
Location: ILC 125 [tentative]
More details can be found on the HW assignment page.
- A graphing calculator is an important tool that will be used in this course. Students are expected to have a working calculator for each quiz and exam. No calculator swapping is permitted during testing periods.
- The University's Exam regulations for final exam week will be strictly followed, in particular those regarding students with multiple exams on a single day.
- This link provides an overview of the guidelines the actual final exam (e.g. tips for how to prepare, what you will/will not be allowed to bring, etc.).
- This website link provides a study guide for the MATH 129 final exam and sample test questions. Highly recommended you look it over and spend some time on these problems.
During the exams, all electronic devices (particularly cell phones) must be turned off. Silence and vibration modes are not allowed. While calculators are allowed for the exam, you can not swap a calculator with another student.
As indicated in the course policy below, no makeup exams will be given. It is very important that you are present in class for the three exams and the final (as these determine more than 80% of your final grade!). Exceptions in extreme cases may be granted, but only upon prior approval.
Course Policy
- Attendance: Students are expected to attend every scheduled class, and to be familiar with the
University Class Attendance policy as it appears in the General Catalog. It is the student's responsibility to keep informed of any announcements, syllabus adjustments, or policy changes made during scheduled classes. Students may be administratively dropped if they miss more than three classes and/or the first class on 8/24.
- Homework: Homework
problems will be assigned regularly and graded online (see me for
passcodes). Quizzes based on homework assignments will be given in
class on a regular basis. A final score, equivalent to 100 points, will
be computed from the online and quiz results. For each assignment,
online and quiz will each contribute to 50% of the homework score. Only
the 10 best homework scores will be kept.
- Calculator:
A graphics calculator is an important tool that will be used in this
course. Students are expected to have a working calculator for each
test and exam. No calculator swapping is permitted during testing
periods.
- Tests: There will be three tests and a final exam. The test schedule is indicated above. There will be no make-up tests. The University has scheduled the final exam for Friday, May 14 from 8-10 AM The University's Exam regulations for final exam week
will be strictly followed, in particular those regarding students with
multiple exams on a single day. Each exam will be worth 100 points and
the final exam worth 200 points.
- Grades: [see separate section above]
Incomplete Grades: The grade of I will be awarded if all of the following conditions are met:
- The student has completed all but a small portion of the required work.
- The student has scored at least 50% on the work completed.
- The student has a valid reason for not completing the course on time.
- The student agrees to make up the material in a short period of time.
- The student asks for the incomplete before grades are due, 48 hours after the final exam.
For general information on grades and the grading system, see the University Policy.
Classroom Conduct: Students at The University of Arizona are expected to conform to the standards of conduct established in the Student Code of Conduct. Prohibited conduct includes:
- All forms of student academic dishonesty, including cheating, fabrication, facilitating academic dishonesty, and plagiarism.
- Interfering
with University or University-sponsored activities, including but not
limited to classroom related activities, studying, teaching, research,
intellectual or creative endeavor, administration, service or the
provision of communication, computing or emergency services.
- Endangering,
threatening, or causing physical harm to any member of the University
community or to oneself or causing reasonable apprehension of such
harm.
- Engaging in harassment or
unlawful discriminatory activities on the basis of age, ethnicity,
gender, handicapping condition, national origin, race, religion, sexual
orientation, or veteran status, or violating University rules governing
harassment or discrimination.
Students found to be in violation of the Code are subject to disciplinary action.
Academic Integrity: Students are responsible to be informed of University policies regarding the Code of Academic Integrity.
Students found to be in violation of the Code are subject to sanctions
that will be determined by the severity of the infraction. The Code of
Academic Integrity will be enforced in all areas of the course,
including projects, tests, and homework.
Students Who Require Reasonable Accommodations Based on Disability:
Students planning to use accommodations for this course should
privately identify themselves to their instructor within the first few
days of class. These students must also provide the instructor with a
letter of identification from the Disability Resource Center. This
letter should include information about any accommodation that will be
needed for the class, including accommodations for test taking.
Students are also invited to discuss specific issues with the course
instructor during regular office hours or by appointment.
Withdrawal Dates: - Last day to drop courses resulting in deletion of course enrollment from record: Tuesday, Feb. 9.
- Withdrawal
deadline (instructor's signature on a Change of Schedule form is required; student must have a passing grade to get a W): Tuesday, Mar. 9. The University allows withdrawals after this date, but only with the Dean's signature. Late withdrawals will be dealt with on a case by case basis, and requests for late withdrawals with a W without a valid reason may or may not be honored.
Helpful Slides
Below are class slides (in pdf form) created by Prof. Jim Cushing for Math 250A (Fall 2007). That class has parallels to those here for 250A (Fall 2009) and thus these slides cover much of the same material we do. You are encouraged to look these over as a supplement to your class notes and readings from the book. You will likely find them of great help in learning this material. As the semester progresses, I will continue to post relevant slides here for you to view.
- Integration I (7.1) - basics on integration
- Integration II (7.2) - integration by parts
- Integration III (7.3, 7.4) - partial fraction decomposition, table of integrals
- Integration IV (7.5, 7.6) - estimating integrals numerically
- Integration V (7.5, 7.6, 7.7) - improper integrals
- Integration VI (7.7, 7.8) - improper integrals
- Integration VII (7.8, 8.5) - improper integrals & applications (physics)
- Integration VII (8.1) - applications (geometry)
- Integration VIII (8.2) - applications (arc length)
- Sequences & Discrete Dynamical Systems (9.1)
- Convergence of Sequences and Limits, Geometric Series (finite) (9.1, 9.2)
- Infinite Series & Convergence (9.2)
- Convergence Tests for Infinite Series (9.3)
- Power Series, Taylor Polynomials (9.5, 10.1)
- Taylor Polynomials/Series (10.1, 10.2)
- Taylor Series & Applications (10.2, 10.3)
Useful Links
Of interest to those in the life sciences.....
- Overview of the Bio2010 report (Transforming
Undergraduate Education for Future Research Biologists). Provides some interesting ideas about the need for and how to go about evolving biology education.
[from this link you can access the entire report in pdf format]
- An article by Bialek and Botstein that provides a compelling argument about the need for changes in undergraduate life science education.
- Interesting article discussing to what extent biology education should strive to incorporate computer science (and mathematics) [posted 7.31.09]
- This link takes you to the homepage of Prof. Leah Edelstein-Keshet. There are numerous resources here that will likely be of great value to students in the life sciences and mathematics. In particular, see the links for the UBC calculus online: Math 102 & 103.
Javelina (Tayassu tajacu)