Math 2250 (ODEs and Linear Algebra), Fall 2009

 

Dr. Jimmy Dillies
Office & office hours: Thu 11:00AM - 12:00PM in LCB 114
webpage: http://www.math.utah.edu/~dillies
email: dillies@math.utah.edu

Details: days, time and rooms

Class:
M,W,F 8:35-9:25AM ST 104
T 8:35-9:25AM JFB 103

Prerequisites

MATH 1210/1220 and MATH 2210 or PHYS 2210 or 3210, MATH 1250/1260; 1270/1280. Fulfills Quantitative Reasoning (Math & Stat/Logic).

Syllabus

This is a hybrid course which teaches the allied subjects of linear algebra and differential equations. These topics underpin the mathematics required for most students in the Colleges of Science, Engineering, Mines & Earth Science.

Text

C. Henry EDWARDS & David E. PENNEY, Differential Equations & Linear Algebra, 3rd edition, ISBN 13 978 0 13 605425 2

Homework

Homework will be assigned weekly (on Fridays) and will be due the following Friday, at the beginning of class. The assignments will be posted online (see bottom of the page). Feel free to work with your classmates. Nevertheless, if you work in groups, write up your own answers: homeworks will be graded individually. Important: when submitting a homework, follow these guidelines! No late homework will be accepted.

Maple Projects

Four Maple projects will be assigned during the semester.

Exam Schedule

All exams are closed-book. No calculators are allowed. The final exam is comprehensive.

Make-up Policy

I follow the department's policy to not offer make-up midterms. The grade of an exam missed for a valid reason will be the weighted average of the other exam's scores.

Help

You can get help from a Tutor at the Math Center, located on the first floor between the two Math buildings (JWB and LCB). The hours are Monday-Thursday 8am-8pm and Friday 8am-6pm.

Grade

Your final score will consist in a weighted average of your homeworks (30%), exams (25%), projects (20%) and final exam (25%). When computing your homework average, your lowest homework grade will be dropped. Idem for Maple projects. You can track your scores on WebCT/Blackboard.

Disability

Students with documented disabilities or other special needs that require special accomodation must register with the Center for Disability Services. After that, contact me at least a week before each exam; we will need to have received confirmation from the Center for Disability Services.

Lecture Notes

Problem Session

Homework Assignments

  1. (due Fri Aug 2) : read the homework guidelines.
  2. (due Fri Sep 4) :
    1.1 # 1, 10, 15, 23, 27, 29, 34, 35, 45
    1.2 # 1, 6, 16, 17, 19, 21, 24 (note g=32ft/sec^2), 37
    1.3 # 1 (pick 3 points), 2 (pick 3 points), 12, 15, 16, 26, 27
    1.4 # 1, 6, 12, 15, 20, 29, 30, 31, 35, 38, 40
  3. (due Fri Sep 11) :
    1.5 # 7, 13, 16, 17, 20, 28, 33, 35, 40, 41
    1.6 # 1, 5, 9, 13, 17, 21, 28, 29, 30, 33, 36, 40, 66, 67
  4. (due Fri Sep 18):
    - Practice your integration : http://www.math.dartmouth.edu/archive/m11f97/public_html/integrals.html. You do not have to submit those but I strongly encourage you to do them!
    2.1 # 5, 11, 13, 27 (check the definition of doomsday)
    2.2 # 7, 9
    2.4 # 1, 4
  5. (due Fri Sep 25) :
    3.1 # 1, 3, 11, 17, 22, 25, 27
    3.2 # 1, 3, 6, 13, 25, 27, 28
    3.3 # 1, 4, 7, 10, 18, 32
    3.4 # 2, 5, 7, 9, 12, 13, 23, 34, 35, 36
  6. You do not need to return this assignment.
    3.5 # 9, 12, 17, 30
    3.6 # 2, 3, 4
  7. (due Fri Oct 23)
    3.5 # 2, 13
    3.6 # 3, 5, 51, 53, 64
    3.7 # 1, 5, 8, 13, 19, 37
    4.1 read page 236 then do # 31, 32, 33, 35, 41
  8. (due Fri Oct 30) 4.2 # 1, 3, 7, 12, 28, 30
    4.3 # 3, 7, 8, 13, 24, 25
    4.4 # 3, 4, 5, 6, 9, 10, 12, 16, 20, 29
    4.5 # 1, 2, 5, 14, 18
  9. (due Fri Nov 6)
    4.6 # 1, 2, 3, 6, 13, 17, 24, 27, 34
    4.7 # 1, 5, 9, 30
    5.1 # 3, 10, 33, 35, 37, 39, 41, 43, 44
    5.2 # 13, 15
    5.3 # 2, 4, 6, 10, 12, 14, 21, 24, 27, 30, 33
  10. Review problems for linear algebra (you do not have to submit those)
    1) Write (3,2,1) as linear combination of (1,-1,1), (2,0,0) and (0,1,1).
    2) What are the coordinates of (4,4) in the basis e=<(1,1),(4,-4)>?
    3) Using the same basis e as in 3), what vector has coordinates e(v)=(1,1)?
    4) In R^2 give a set of vectors which
    i) span R^2 but are not lin. indep.
    ii) are lin. indep. but do not span R^2.
    iii) are neither spanning R^2 nor lin. indep.
    iv) form a basis of R^2
    5) Check whether (1,2,0,1); (0,1,1,1); (2,0,-4,3) are lin. indep.
    6) Let A be the matrix
    0 1 0 0
    2 0 2 0
    0 -2 0 0
    Find a basis for C(A). What is the dimension of C(A)? What is the dim of ker(A).
    Find a basis of ker(A). Check the rank-nullity theorem.
    7) Find a matix such that det(A)=2 and det(A^2)=0.
    8) What is the rank of the matrix B:
    2 3 0 1
    1 1 1 1
    3 4 1 2
    9) Find a vector orthogonal to (1,0,1) and (0,1,0).
    10) Let V=<(1,1,1)>, find a basis of V^perp.
    11) Show that T(f):=f-f' is a linear map. What is its kernel?
    12) Show that V={(x,y,z) s.t. x-y=z} is a vector space. [hint, it's a subset of R^3]
    13) Is the set W={(x,x+1)} a lin. subspace of R^2? Justify.
    14) Compute det(C) using el.op., C=
    1 0 0 0
    34 0 0 5
    4 0 0 4
    0 1 0 1
    15) det(AB)=24, if det(B)=det(A)+5 what is det(A) if you know that it is a negative number?
    16) Consider the linear map A:R^2->R^2 where A=
    1 2
    0 2.
    What is the area of the image of the triangle of summits (0,0), (1,0) (1,1) ?
  11. (do not submit) 5.2 # 7, 8
    5.3 # 21, 23, 25, 26, 33
    5.5 # 1, 3, 5, 9, 11, 13, 19,20, 26, 31, 33, 36
  12. (due Fri Nov 20) []
    10.1 # 1, 2, 7, 11, 20, 23, 26, 28, 30
    10.2 # 2, 4, 16, 17, 19, 21, 25