Math 250A (Fall 2009) HW Assignments and WebAssign Updates
(this page will be continually updated as we progress though the semester)
- Final Exam (12.18.09) - (posted 12/9) Reminder that the final exam will be given on the morning of 12/18/09 (8-10 AM) in our regular classroom (ILC 125). Bring a calculator and make sure to arrive on time as you will likely need the full two hours. The exam will be cumulative and include all material covered throughout the semester. See the salient topics outlined below for each of the three class mid-term exams. Also, material covered in class since the third exam (i.e., sequences and their convergence, chaos in the logistic map, the Levins model for ecology) are all fair game for the exam.
- Quiz 12 solutions here
- HW due 12.5.09 (at 4:59 PM) - (posted 11/30) The new HW assignment is now posted. It covers sequences (see HH 9.1) as well as several ODE 'modeling' problems (see HH 11.5). Due to the late posting, the assignment will be due on Saturday (instead of Friday), but note that we will still have a quiz as usual on Friday morning (11/4) on this material.
- Exam III (11.25.09) - (posted 11/18) The following is a list of topics covered over the past few weeks that will form the basis for the third exam. Note that this list is not exhaustive (i.e., anything we covered in class or on the HW is fair game!). Furthermore, this material builds off that going into the first two exams (e.g., methods for solving integrals, etc.). So use it as a guide only (also including relevant book chapters to look at for reference, HH for the calculus book and LL for the ODE book):
- Existence and Uniqueness Theorem LL 2.4
- Phase-Line Analysis, Stability of Equilibria LL 2.1, 2.3, 2.5
- Bifurcations LL 2.6 (also see 10/28-30 and 11/18-20 class notes)
- Euler's Method HH 11.3, LL 3.3
- ODEs w/ Homogeneous Coefficients LL 4.2
- General Method for Linear First Order ODEs LL 5.1
- Applications of Linear ODEs (e.g., RL-circuit) LL 5.2
- Bernoulli Differential Eqns. LL 5.3
- Quiz 11 solutions here
- Lab III solutions here (please don't distribute!)
- Lab III The third project has been posted (pdf) and will be due Monday, 11/23/09 at 5:00. Note that this date is before the third in-class exam (on Wednesday 11/25), such that you will need not have to deal with the project over the holiday break! The sooner you get started on the project, the better. This projects builds off the foundation by the first lab and asks you to use Matlab to write a code that implements Euler's method to numerically solve ODEs.
- HW due 11.20.09 (at 4:59 PM) - (posted 11/13) The new HW assignment is now posted. It covers several 'older' topics, such as translating 'word problems' into ODEs and determining the qualitative behavior of ODE solutions. New material covers determining solutions to linear, first-order ODEs (see LL 5.1 for further reference in addition to the class notes). Remember, lab III is due on 11/23!
- Quiz 10 solutions here
- Quiz 9 solutions here
- (UPDATE: Due date extended) HW due 11.14.09 (at 4:59 PM) - (posted 11/6) The new HW assignment is now available. It covers several topics including ODEs w/ homogeneous coefficients (LL 4.2), linear first order ODES (LL 5.1), separable ODEs (LL 4.1; HH 11.4), and even deriving entries to the table of integrals (HH 7.3)! Also, you may need to review hyperbolic functions (see HH 3.8). Lastly, there are a few simple 'modeling' problems so help keep the applied perspective of ODEs in (at least) the back of your mind.
- Quiz 8 solutions here
- HW due 11.6.09 (at 4:59 PM) - (posted 10/28) The new HW assignment will be available Friday afternoon at 5 PM. Note that there is another (challenging) problem regarding Existence & Uniqueness, similar in spirit to last week. Look at the additional notes posted on the course webpage for additional background. Also covered on this assignment are Euler's method (see H.H. 11.3 and L.L. 3.3 for references) as well as finding derivatives of functions of more than one variable (as relevant for the Existence & Uniqueness theorem). Note that notationally, f_x (f with a small subscript x) means d/dx f(x,y). Similarly, f_y means d/dy f(x,y), f_xx means d^2/dx^2 f(x,y) [i.e., the second derivative], and f_xy means d/dy (d/dx f(x,y)).
- Quiz 7 solutions here
- HW due 10.30.09 (at 4:59 PM) - (posted 10/23) The new HW assignment is now available on WebAssign. One problem regarding Existence & Uniqueness is included and is somewhat more challenging than usual. Think about what we discussed in class and try to parse it up to make practical sense of what is being asked.
- HW due 10.23.09 (at 4:59 PM) - (posted 10/16) The sixth HW assignment will be available on WebAssign this afternoon at 5 PM. It covers further aspects of slope fields, notions of symmetries in ODEs and finally existence and uniqueness of solutions.
- Quiz 6 solutions here
- Exam II (10.14.09) - (posted 10/11) The following is a list of topics covered over the past few weeks that will form the basis for the second exam. Note that this list is not exhaustive (i.e., anything we covered in class or on the HW is fair game!) as it builds off the material going into the first exam. So use it as a guide only (also including relevant book chapters to look at for reference, HH for the calculus book and LL for the ODE book):
- Various methods of integration:
o Substitution
HH 7.1
o Integration by parts
HH 7.2
o Table of integrals
HH 7.3
o Long division, completing the square, and partial fraction decomposition
HH 7.4
o Trigonometric substitutions
HH 7.4
- Basic methods to solve ODEs via integration (e.g., separation of variables)
HH 11.4, LL 1.1, 2.1
- Using integrals to estimate areas and volumes via Riemann sums
HH 8.1
- Visualizing ODEs and slope fields
HH 11.2, LL 1.2, 1.3, 2.1, 3.2
- General vs. Unique solutions, initial conditions
HH 6.3, LL 2.1
- Logistic equation
LL 2.3
- Equilibria and stability
LL 2.1, 2.3
- Quiz 5 solutions here
- Lab II solutions here (please don't distribute!)
- HW due 10.09.09 (at 5:59 PM); Lab II due 10.19.09 (at 4:29 PM) - (posted 10/2)
- The fifth HW assignment will be available on WebAssign this afternoon at 5 PM. It covers further methods of integration (e.g., trig substitutions), solving ODEs given initial conditions, and slope fields. Helpful book chapters will be HH 7.4 and 11.2 as well as LL 1.3.
- Next, the second project has been posted (pdf) and will be due Monday, 10.19.09 at 4:29. Don't wait to the last minute! The sooner you get started on the project, the better. In addition to chapter LL 1.3, LL 3.2 will likely be of help. See the assignment for a description of software you will likely need (this will also be covered to some extent on Tuesday (10/6). The same strict deadline as was used for the first lab will also be enforced for this lab as well!
- Lastly, note that the second exam is scheduled for Wednesday, 10/14. Material from Lab II will be fair game for the exam (more specifics will follow next week).
- Quiz 4 solutions here
- Due 10.3.09 (at 5:59 PM) - (posted 9/27) This HW assignment covers several topics with regard to dealing with integral and differential equations:
1. Using Riemann sums to determine areas and volumes
2. Integration by parts
3. Separation of variables to solve ODEs
4. Using specified initial conditions to find unique solutions to ODEs
5. Using the table of integrals
6. Initials with regard to partial fraction decompositions
- Due 9.25.09 (at 11:59 PM) - (posted 9/18) The fourth HW assignment will be available on WebAssign this afternoon at 5 PM. It covers methods of integration, using the method of substitution, integration by parts and the table of integrals. This will be somewhat in the vein of review to some extent, though the problems may seem a bit harder than you came across before. The relevant book chapters are H.H. 7.1-7.3. Even though I will not be in class on 9/25, Prof. Joe Watkins will be covering for me and we will still have the quiz (based off the HW problems as usual).
- Exam I (9.16.09) - (posted 9/11) The first exam will be next week [NOTE: before Friday (9/18), the university drop date). Below is a brief outline of the salient topics covered over the first few weeks of the course that are fair game for the exam (also including relevant book chapters to look at for reference, HH for the calculus book and LL for the ODE book):
- Review of basic differential calculus
HH Ch.1-5
- Basic nature of ODEs and contexts they might be used in
HH 6.3, 11.1, 11.4-11.5; LL 1.1
- Identifying types of (first-order) ODEs
LL 1.1, 2.1, 5.1
- Translating 'word problems', considering dimensions of quantities
HH 6.3, 11.1, 11.4-11.5
- Solving ODEs of the form dy/dx = f(x)
LL 1.1
- Solving ODEs of the form dy/dx = g(y) [autonomous ODEs] such as y' = ay+b
HH 11.4-11.5; LL 2.1
- Determining whether a given functions satisfies a given ODE
HH 11.1
- Translating an ODE into a qualitative picture
HH 11.1, 11.4-11.5
- Numerical integration via Riemmann sums (LEFT, RIGHT, MID, TRAP)
HH 5.2, 7.5-7.6
- Quiz 3 solutions here
- Quiz 2 solutions here
- Lab I solutions here (please don't distribute!)
- Due 9.11.09 (at 11:59 PM) - (posted 9/4) The third HW assignment is now available on WebAssign. It covers basics of ODEs as well as numerical estimates of integrals. For reference, the following book chapters may provide a useful reference: HH-5.2,7.5,7.6 (Riemann sums), 11.1,11.4-11.6 (ODEs); LL-1.1 and 2.1. Also, the first Matlab project has been posted (pdf) and will be due Monday, 9/21/09 at 4:30. Don't wait to the last minute! The sooner you get started on the project, the better.
- Due 9.4.09 (at 6:30 PM) - (posted 8/28) Everyone now seems set up on WebAssign (good). Next week's assignment is a bit more meaty and basically comprises a review of material you should already know coming into 250A. If you are having troubles, try to work with other students in the class to discuss. Also, feel free to contact me of Joseph (our class TA). This assignment is a bit on the long side, so make sure to get an early start!
- Quiz 1 solutions here
- 8.24.09 - (posted 8/13) Now that class has started, the goal is to make sure you can get your account setup on WebAssign and log in, accessing the first HW assignment (due Friday, 8/28; is is really just to make sure that you obtain your WebAssign account and get basic familiarity with the interface). Contact me if you have troubles getting setup. Remember that the class key in arizona 6569 7717. See the main course webpage for info about logging in. Keep checking back for updates [the posting here will be a bit erratic at first until we get settled, at which point I'll aim to post on a regular/weekely basis]....