Fall 2005 - PHYS 3390 - Mathematical Methods I

COURSE INFORMATION SHEET


COURSE
 DESCRIPTION
NAME
 PHYS 3390 - Mathematical Methods I - Fall 2005
LOCATION
 Room SETB 2.24; SETB Physics & Astronomy (UTB)
INSTRUCTOR
 Prof. Manuela Campanelli (Ph.D in Physics, Univ. of Bern CH)
Office: SETB 2.258
Phone: 882-6656
E-mail: manuela@phys.utb.edu
LEVEL
 Undergraduate sophomore and major in the Physics and Engineering Programs
PREREQUISITES / BACKGROUND Prerequisites: Calculus I, II, III
Corequisites: Linear Algebra, Differential Equations;
Background: In case you are missing all or part of this background material you will need the professor consent prior registering to this course. You can test your preparation taking the following: Quiz1.pdf
TEXT BOOK
 The required book is " Mathematical Methods in the Physical Sciences" by Mary L. Boas, 2nd Edition by John Wiley &  sons;
Remark: The 3rd edition has been adopted as required text book for this course. The 2nd edition is also accepted provided that the student completes the missing text with personal notes.
DESCRIPTION
 The course will focus on SELECTED topics from the following text book list:
Chapter  1- Infinite and Power Series;
Chapter  2 - Complex numbers;
Chapter  3 - Linear Equations, Vectors, Matrices and Determinants;
Chapter  4 - Partial Differentiation;
Chapter  5 - Multiple Integrals, Applications of Integration;
Chapter  6 - Vector Analysis;
Chapter  7 - Fourier Series;
Chapter  8 - Ordinary Differential Equations;
Chapter  9 - Calculus of Variations;
Chapter 10 - Coordinate Transformations; Tensor Analysis;
Cahpter 11 - Gamma, Beta and error functions; Asymptotic series; Stirling's formula; elliptic integrals and functions;
Chapter 12 - Series solutions  of differential equations; Legendre polynomials; Bessel functions; sets of orthogonal functions;
Chapter 13 - Partial Differential equations;
Chapter 14 - Function of a complex variable;
Chapter 15 - Integral Transforms.
Remark:  The course will not focus on mathematical proofs but on the theory and practical applications of the course topics.
SELECTED TOPICS
 Selected topics from the above description list will be covered in the following order:
Chapter   6 - Vector Analysis;
Chapter 10  (sec. 1-9) - Coordinate Transformations;
Chapter   7  - Fourier Series;
Chapter 13 (sec 1-4) - PDE's in cartesian coordinates;
Chapter 15 (sec 1-4) - Laplace/Fourier Transforms, Dirac Delta Function;
Chapter 12 (sec 1-11) - Legendre polynomials;
Chapter 13 (sec 1-4) - PDE's in Spherical Coordinates.
Remark: Students will be responsible of reviewing all background material, including material covered in Chapter 1-5.
CLASSES  Time:Tuesday (TU) and Thursday (TH) at 3:02 - 4:20 pm starting from August 24, 2005;
Room: SETB 2.236;
Remark: We will typically see material contained in one chapter of the book every 2-5 classes and problems associated to that chapter will be given to be turn at the end of each chapter as homework; Attendance in lecture will not be taken, but is highly recommended;.
OFFICE HOURS
 Time: TU, TH 11:00-13:30am, and by appointment.  
Room: SETB 2.258
COMPETENCIES
 Reading:  Each student is responsible for all the assigned reading. Reading in this course means the ability to analyze and interpret the printed material, including the ability to understand the assigned problems. You will not be able to understand the problems and the exams if you do not properly read the text. Not all material can be covered during classes so reading is considered an important part of this course.
Critical Thinking: Students must be able to read and analyze a stated problem, determine the solution required, identify the needed data, select the appropriate physics theory, apply proper mathematical calculations and ultimately reach the result. Students will be given to demonstrate these skills on course homework and examinations. Students should be able to make observations and draw conclusions based upon these observations. Laboratory excersices require demonstration of these skills.
Computer Literacy: Students in this course should be able to use computers to solve simple mathematical problems. The students use computers of the laboratory activities both to collect the data and the analyze and solve assigned problems. Students will learn how to use programs for Algebraic manipulation Algebraic Manipulation Program such as Mathematica and/or Maple to solve selected problem. Successful completion of these lab activities indicate that the students have gained this competency. Students should be able to locate material relevant to the course on the course's own web site and using the world wide web search engines such as google .
HOMEWORK Assigned Reading and Problems associated to each chapter will be given to be turn the day after the end of each chapter. Homework is very important for this course. Students need to solve many problems in order to master this material and learn good problem-solving techniques. Late homework will not be accepted (except in very exceptional cases).
You are strongly encouraged to work together on the problems using the collaborative learning technique.  Group of students can meet and work together on problems provided that they do not copy but learn and solve together the problems. You will discover that, in the process of explaining physics to one another, you obtain a better understanding of the material yourself.
LABORATORY Time: TH at 4:25 - 7:05 pm starting from August 24, 2005;
Room: SETB 2.218 (SPS lab);
Description: PHYS 3391 - Laboratory for Mathetmatical Methods - is associated to this course. The laboratory will be held twice a week and will focus on:
1) Review of topics related to the course ranging from Chapter 1-5:
    Chapter 3 - Vector and Vector Operations, Matrices and Determinants;
    Chapter 4 - Partial Diffrentiation:
    Chapter 5 -  Multiple Integrals;
    Chapter 1 - Infinite Serioes, Power Series;
    Chapter 8 - Ordinary Diffrential Equations;
    Chapter 2 - Complex Numbers
2) Practical applications of all course materials and sample problems;
3) The use of Algebraic Manipulation Program such as Mathematica and/or Maple to solve selected problems;
Instructor: Alan Farrell (Phone: 882-6655; Email: farrell@phys.utb.edu);
Remark: The lab is a very important component of this course; attendance to the lab will be taken;
EXAMS
 MidTerm and Final Exam will consist of written examinations based on problems similar to homework and laboratory problems; Make-up exams and/or extra credit will not be given;
MidTerm : TBA Room SETB 2.24.
Final : TBA  Room SETB 2.24.
GRADES
 Your final grade will be based on homework (25%), lab (25%), midterm (25%) and final (25%).
Four  homework  sets, extracted among all homeworks, will contribute to the 25% of the grades.
Letter grades will be assigned to number grades as follows: A: 90-100, B: 80-89, C: 70-79, D: 60-69, F: 0-59.
STUDENTS
 Names:
1) Bonilla, Peter N
2) Grimaldo, Nazul H.
3) Lara, Gerardo R.
4) MacHuca, Luis A.
5) Martinez, Pedro,
6) Oropeza, Grabriela
7) Ramos, Jose M.
8) Resendez, Joe
9) Rodriguez, Maria G.
10) Sanchez, Juan C.
11) Elias, Juan C.
12) Oscar Guerra
13) Marc Cenac
Remark: Students with disabilities, including learning disabilities, who wish to request accommodations in this class, should notify the Disability Services Office early in the semester so that the appropriate arrangements may be made. In accordance with federal law, a student requesting accommodations must provide documentation of his/her disability to the Disability Services counselor. For more information visit Disability Services in the Lightner Center, call 956-882-7374 or e-mail DisabilityServices@utb.edu

Note: This information sheet will be updated periodically and can be subject to changes (especially in the part of the homework assignements). Any comment or suggestion should be addressed directly to the Instructor .

HOMEWORK  Reading and Homework problems are assigned at the end of each Thursday's class, and are due at the beginning of next Tuesday's class.  

Class 1 (TU, Aug 24)  Introctuction and Syllabus
Class 2 (TH Aug 26)
 Class 3 (TU Aug 30)
Class 4 (TH Sept 01)
Class 5 (TU Sept 06)
Class 6 (TH Sept 08)
Class 7 (TU Sept 13)
Class 8 (TH Sept 15)
  HOMEWORK # 1:
1) Read Chapter 6, Review Chapter 3 and Chapter 5;
2) Solve Problems:
Chapter 6: Sec 3 (7,17,19), Sec 4 (2,8), Sec 6 (10,14),  Sec 7 (13), Sec 8 (4,18), Sec 9 (10), Sec 10 (2, 15), Sec 11 (15, 20)
Suggested review Problems:
Chapter 3: Sec2(4,14), Sec3(4,7, 14,15,23), Sec4(5,8,15,21,26), Sec5(4,,9,18,,21, 31,45), Sec6(2,10, 13,21), Sec7(1,4,11,14), Sec8(5,12,20,26), Sec9(4,10,16).
Chapter 5: Sec1,2 (11,21,31,39,45); Sec 3 (1, 13, 21, 26, 31); Sec 4 (5,11,14,21); Sec5 (3,5,14
Class 9 (TU Sept 20)
Class 10 (TH Sept 22)
Class 11 (TU Sept 27)
Class 12 (TH Sept 29)
HOMEWORK #2:
1) Read Chapter 10 (sec 1-9);
2) Solve Problems: Sec1(5), Sec 3(9), Sec4(7,10, 17,29,37),Sec5(6,13),Sec8(1,3,9,14),Sec9(4,9,13,16,21).
Class 13 (TU Oct 04)
Class 14 (TH Oct 06)
Class 15 (TU Oct 11)
Class 16 (TH Oct 13)
 HOMEWORK #3:
1) Read Chapter 7; Review Chapter 1;
2) Solve Problems: Sec 2 (10,13), Sec 4 (13,15), Sec 5 (2, 7), Sec 6 (2, 7), Sec 7 (12), Sec 8 (7,11), Sec 9 (5, 11), Sec 10 (4), Sec 11 (7); Lab: Sec 2 (20), Sec 3 (6)
 
Class 17 (TU Oct 18) MIDTERM 1 
Class 18 (TH Oct 10)
Class 19 (TU Oct 25)
Class 20 (TH Oct 27)		 HOMEWORK #4:
1) Read Chapter 8;
3) Solve  Problems:  Sec 1 (3), Sec 2 (6,12), Sec 3 (8,13), Sec4 (9,18), Sec 5 (5,9,18,20,21,24,35), Sec 6(3,18,22,25,34, Sec 7 (1,8,16), Sec 8 (3,28)
Class 21 (TU Nov 01 )
Class 22 (TH Nov 03)
Class 23 (TU Nov 08)
 HOMEWORK #5:
1) Read Chapter 13 (sec 1-4);
3) Solve  Problems:  Sec 2 (15),  Sec 3 (5), Sec 4 (3),  Sec 5 (2, 8),   Sec 6 (3),  Sec 7 (15);
Class 24 (TH Nov 10)
Class 25 (TU Nov 15)		 HOMEWORK #6:
              1) Read Chapter 15 (sec 1-4)
              2) Solve Problems:  Sec 2 (5,10,21,27), Sec 3 (3,9,19,18,28), Sec 4 (6,16,18,20);
Class 26 (TH Nov 17)
 Class 27 (TU Nov 22) 		 HOMEWORK #7:
1) Read Chapter 12  (sec 1-11)
2) Solve Problems:  Sec 1 (3), Sec 2 (3), Sec 5 (3,12), Sec 6 (6), Sec 8 (5), Sec 9 (11), Sec 11 (4) .
Holiday (Nov 23-26) HOMEWORK: review all material
Class 28 (TU Nov 29):
Class 29 (TH Dec 01):
 HOMEWORK #7:
1) Read Chapter 12  (sec 1-11)
2) Solve Problems:  Sec 1 (3), Sec 2 (3), Sec 5 (3,12), Sec 6 (6), Sec 8 (5), Sec 9 (11), Sec 11 (4) .
Class 30 (TU Dec 06): FINAL EXAM