e MATH 487/ECE 493 Spring 2008
University of Illinois at Urbana-Champaign
University of Illinois at Urbana-Champaign
 

Math 487/ECE 493 Advanced Engineering Math

Spring 2008  Section Q13, Q14

12:00-13:20 TuTh

441 Altgeld Hall

Department of Mathematics

University of Illinois at Urbana-Champaign

Contents:

  1. Administrative Information 

  2. Description/Outline 

  3. Grading Policy

  4. Examinations

  5. Homework

  6. Handouts, Presentations, and Webpages

  7. Other Links

1.  Administrative Information

Instructors: Professor Stephen E. Levinson Professor Robert M. Fossum
Lectures: Tu/Th 12:00--13:20 441 Altgeld Hall
Office 2009 Beckman Institute 2021 Beckman Institute
Phone (217) 244-1262 (217) 244-3572
E-mail selevins at uiuc.edu rmfossum at uiuc.edu
Office Hours TBA (by appointment until further notice) TBA (by appointment until further notice)
Schedule:  
Class Time
Math 487 TuTh 12:00---13:20
Math 504 TuTh 9:00--10:20
PAML TBA
Huang Group Fri 16-18
Grader TBA

 

 

 

 

 

 

 

 

 

 

 

 

 

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2.  Textbook, Course Description, and Outline.

Textbook: Greenberg, Michael: Advanced Engineering Mathematics. 2nd Ed. Prentice Hall, Upper Saddle River, NJ 1998.

2.1 Course Description. The course will cover most of the material from Chapters 9 through 20 of the Greenberg text. An outline of material covered in a previous year can be found in this Outline.

2.2 Outline. For the first half the material will come from the part on Linear Algebra, in particular Chapters 8, 10, and 11. Then we will consider Chapters 13 through 16, getting to 16.7 to 16.10.

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3. Grading Policy: Homework (25%), Midterm Examination (25%), Final Examination (50%) (Currently subject to some modification.)

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4.  Examinations

Midterm Examination:

The midterm exam will be an 80 minute exam on the material that has been covered up to that point in the class. It will be given on Thursday 6 March 2008  during class. Sometime at the end of February there will be a practice exam posted.

Final Examination:

The Final Examination will be a three hour final given in 441 Altgeld Hall (unless changed) on Wednesday 7 May from 7 to 10 PM . (If there is a possibility that a conflict exam is required, please notify one of the instructors by 25 April. Normally Mathematics courses are not required to give conflict examinations since they are single section courses and their final examinations are given at the regularly scheduled time.)

The final examination will be comprehensive---covering all the material om the class.

Homework

Policy:

  • Homework will be assigned every Thursday to be due the following Thursday at the end of the class period.
  • Please submit your homework in a neatly written, stapled set of papers, with a clear indication of the problem being solved. The answer should, if possible, be given in a complete sentence. An example is "The lenght of the vector is 1." The papers should be turned in at the end of class. Every effort will be made to return homework within a week. Solutions will be posted on this webpage.
  • Please make sure your name and e-mail address are included on each solution set and on each page of the solution set.  Also make sure that the question as well as the asnswer is included.
  • You  may consult each other about the solutions but each student should submit a personal homework set.

Assignments:

(The page numbers refer to the pages in the Greenberg text)
  • Problem 456.7: We say the empty set is a basis of the zero vector space. The empty set has 0 elements. So a vector space with a basis with 0 elements has dimension 0. The empty set is linearly independent and it is the maximal linearly independent subset of the zero vector space. So the author's statement that the zero vector space has no basis is wrong.
  • Assignment 4. Due 14 Feb 2008. 456.1(i), 3(f), 6,8; 479.5; 486.10; 507.4, 507.9, 507.10, 530.7, 530.8, 530.9
  • Assignment 5. Read 13.1--13,4, 13.6, 14.1--14.5. Due 21 Feb 2008: 624.2(a), 624.3(d), 628.3(e), 654.5(a,c), 655.6(e), 655.7
  • Assignment 6. Due 28 Feb 2008. Read Chapters 15 and 16 and the Reviews. We will be most interested in getting to the Green's, Gauss', and Stoke's Theorems in Chapter 16.
  • Assignment 6. Due 28 Feb 2008. 711.3(a), 731.6, 746.8, 754.1.
  • Midterm on 6 Mar 2008. A practice exam and another practice exam .
  • Midterm on 6 Mar 2008. A practice exam answers and another practice exam answers .
  • Midterm on 6 Mar 2008. A Midterm exam answers .
  • Spring break from 15 Mar to 23 Mar 2008.
  • Assignment 7. Due 10 April 2008
    • p 216 #6a,b Legendre Polynomial Generating Function
    • p. 242 #5a 1/2 order Bessel Fnctns
    • p. 903 #8 Sturm Liouville Problem
    • p. 912 #6a,b,f Chebyshev Polynomials
  • Assignment 8. Due 17 April 2008
    • p. 1147 10 b,f and 11d,e differentiation, analyticity
    • p. 1194 4 d,g Cauchy's Theorem
    • p. 1205 1 d Cauchy's Integral formula
    • p. 1255 1 d,e Residue theorem
  • Assignment 9. Due 29 April 2008
    • p. 267 #2 (Extra Credit, Hint: see appendix A)
    • p. 1255 #5f, #10a Inverse Fourier and Laplace transforms
  • Last class Tues. April 29, Course review session.
  • Final Exam: Wed. May 7, 7 - 10 PM, AH441, One 8.5 X 11 crib sheet allowed.

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6.  Handouts, Presentations, and Webpage.

The Hilbert matrix and its determinant . Also the computation for n=1, 2, ... 11.