Introduction To The Foundations Of Applied Mathematics Homework
MATH 543 APPLIED MATHEMATICS I
(2000-2017)
2017 Fall Semester
Math543: Applied Mathematics I
Text Books :
1. P. Dennery and A. Krzywicki, "Mathematics for Physicists", Harper and Row, 1967.2. F. B. Hildebrand, " Methods of Applied Mathematics", second edition, Prentice Hall.
3. Sadri Hassan, "Mathematical Physics: A Modern Introduction to its Foundations", Springer Verlag, New York, 1999.
4. J. David Logan, "Applied Mathematics", John Willey and Sons, Inc., New York, 1997 (Second Edition).
5. Haaser and Sullivan , "Real Analaysis", The University Series in Undergraduate Mathematics.
6. Richard Courant and David Hilbert, "Methods of Mathematical Physics", Vol 1, 2004 WILEY-VCH, Weinheim.
7. W. E. Boyce and R. C. DiPrima, " Elementary Differential Equations and Boundary Value Problems",
Sixth Edition, John Wiley and Sons, Inc.
some subjects in applied mathematics
Course Schedule
Tuesday 08:40-10:30 (SA-Z02)Thursday 10:40-12:30 (SA-Z02)
Exams
For previous exams see prev.exams(30%) First Midterm Exam 2007: pdf file , 2008 , 2010 , 2011 , 2012 , 2013 , 2014 , 2015 , 2017 , solution October 26, 2017
(30%) Second Midterm Exam 2006: pdf file , 2008 , 2011 , 2012 ( solution ), 2013 ( solution ), 2014 , ( solution ), 2015 ( solution ), 2017 ( solution ), November 30 , 2017
(40%) Final Exam 2007: pdf file , 2008 , 2010 , 2011 , 2012 ,2013 -Solution , 2015 -Solution , 2016-Solution , 2017-Solution , January xx, 2017
For exam results please see math543exams
In the exams you will be responsable from DK, Logan, Lecture notes
and the assigned exercises below
Lectures
1. Lecture 0 (some prelimineries)--[10 pages]2. Lectures 1 and 2-- [Function Spaces]
3. Lectures 3 and 4-- [Hilbert Spaces, Bases and Orthoganal Polynomials]
4. Lectures 5 and 6-- [Genralization of the Weirtstrass Theorem and Classical Orthogonal Polynomials]
5. Lectures 7 and 8-- [Second Order ODEs and Green's Function Method]
6. Lectures 9 and 10-- [Series solutions of DEs, Frobenius Method and Fuchsian DEs]
7. Lecture 10-- [Confluent Hypergeometric Equation is included]
8. Lecture 11 [Regular Perturbation Method]
9. Lecture 12 [Singular Perturbation Method]
Contents of Applied Mathematics I
For preparation read the last Chapter of Haaser and Sullivann "Real Analysis"Assigned Exercises
1. set 1 pdf file , ps file2. set 2 pdf file , ps file
3. set 3 pdf file , ps file
4. set 4 pdf file , ps file
1st exam pdf file
5. set 5 dvi file , ps file
6. set 6 dvi file , ps file
7. set 7 dvi file , ps file
2nd exam with solutions pdf file
8. set 8 dvi file , ps file
9. set 9 pdf file
10. set 10 pdf file
Final exam (pdf file)
Subjects covered
1. September 17Chapter III of Dennery, Chapter 5 (Hilbert Spaces) of Sadri Hassan
assigned exercises, set 1 pdf file ,
Homework Set 1 pdf file ,
2. September 24
assigned exercises, set 2, pdf file ,
3. October 1
Homework Set 2 pdf file ,
assigned exercises, set 3 pdf file
Spherical Harmonics in D Dimensions
Generating function of the Legendre Polynomials , Other generating functions
4. October 8
assigned exercises, set 4 pdf file
5. October 15
6. October 22
(2007)
7. November 29
First Midterm Exam pdf file (2006) ,
Homework Set 3 pdf file , assignaed exercises, set 5 pdf file
8. November 5
9. November 12
assigned exercises, set 6 pdf file ,
(Assigned exercises : Solve also the problems of the Sections 5.4-5.8 of Boyce and DiPrima)
10. November 19
(Assigned exercises : Solve also the problems of the Sections 5.4-5.8 of Boyce and DiPrima)
Second Midterm Exam pdf file
11. November 26
assigned exercises, set 7 pdf file
assigned exercises, set 8 pdf file
Homework Set IV: From set 7 Problems 12,13 and from set 8 Problems 2,3
(Due December 28)
12. December 3
Assigned exercises, set 9 pdf file
13. December 10
Second Midterm Exam pdf file
14. December 17
15. December 24
Assigned exercises, set 10 pdf file
end of the semester
16. December 28
Subjects to be covered
Ch.1. Function Space, Orthogonal Polynomials and Fourier Analysis (Dennery and Krzywicki)First Midterm
Ch.2. Ordinary Differential Equations (Dennery and Krzywicki)
Second Midterm
Ch.3. Perturbation Methods (Logan)
Final Exam
Ch.4. Calculus of Variations (Logan and Hildebrand)
Course Syllabus of Math543
02. Oct. 01 - Function Space
03. Oct. 08 - Function Space
04. Oct. 15 - Ordinary Differential Equations
05. Oct. 22 - Ordinary Differential Equations
06. Oct. 29 - Ordinar Differential Equations
07. Nov. 05 - Ordinary Differential Equations
08. Nov. 12 - Perturbation Methods
09. Nov. 19 - Perturbation Methods
10. Nov. 26 - Perturbation Methods
11. Dec. 03 - Perturbation Methods
12. Dec. 10 - Calculus of Variations
13. Dec. 17 - Calculus of Variations
14. Dec. 21 - Calculus of Variations
Last update May 2017
End of Applied1's Home Page
Math 451 Homework Assignments Spring, 2018
(Subject to change: check web page for each week’s assignment)
Office Hours: Tuesdays 2:30-3:00 p.m., and by appointment.
Book: Mark H. Holmes, Introduction to the Foundations of Applied Mathematics. Springer, 2009
Available as an ebook from the NCSU library.
Homework handed in should be written carefully.
HOMEWORK | |||
HW # | Due date | Problems | |
1/11 | Read sections 6.1 - 6.4 | ||
1 | 1/18 | Chap. 6: problems 6.1 - 6.5. Read sections 6.5-6.7. Hand in problems 6.2abcd, 6.5af. | |
2 | 1/25 | Read 6.6--6.8. Problems: 6.10, 6.11 | |
3 | 2/1 | Read sections 8.1 to 8.3. Problems,page 394: 8.1, 8.2 (a-d) | |
4 | 2/8 | Read sections 8.4 to 8.6. Problems, page 395: 8.6, 8.7. | |
2/15 | No homework due; get started on Chapter 9 reading sections 9.1, 9.2 | ||
5 | 2/22 | ||
6 | 3/1 | TEST 1old test for practice | |
7 | 3/5-9 | SPRING BREAK | |
3/15 | Read 8.11. Hand in at least 4 parts of the following: 8.14, 8.21(a), 8.22 - 8.24. | ||
8 | 3/22 | Read Chapter 9: | |
9 | 4/5 | | |
10 | 4/12 | Chapter 9, problems 9.4, 9.5, 9.6 | |
| 4/15 | |
Final Exam: Thursday, May 3rd, 1:00 - 4:00.
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