PHYS 3392: Mathematical Methods II

COURSE INFORMATION SHEET



PHYS 3400
 Description
 Location/Time
COURSE
PHYS 3392 - Mathematical Methods II - Spring 2005
 UTB, SETB Physics & Astronomy; Room SETB 2.232.
DESCRIPTION
 Calculus of Variations (Chapter 9); Coordinate Transformations; Tensor Analysis (Chapter 10); Gamma, Beta and error functions; Asymptotic series; Stirling's formula; elliptic integrals and functions (Chapter 11); Series solutions  of differential equations; Legendre polynomials; Bessel functions; sets of orthogonal functions (Chapter 12); Partial Differential equations (Chapter 13); Function of a complex variable (Chapter 14); Integral Transforms (Chapter 15). Undergraduate Sophomore and Major Levels
PREREQUISITES & BACKGROUND
 Prerequistes/Background: Calculus I, II, Linear Algebra, Differential Equations, Mathematical Method II; or equivalently Charper 1-8.
Remark: 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
INSTRUCTOR              
 Prof. Manuela Campanelli (Ph.D in Physics, Univ. of Bern CH)
 Office: SETB 2.258
Phone: 574-6656
E-mail: manuela@phys.utb.edu
COURSE TOPICS
 The course will focus on Chapter 9 -15, in text book as following:

1) Coordinate Transformations; Tensor Analysis (Chapter 10)
2) Special Functions and Elliptic Integrals (Chapter 11-12)
3) Partial Differential equations (Chapter 13)
4) Function of a complex variable (Chapter 14)
5) Integral Transform (Chapter 15).
6) Calculus of Variations (Chapter 9) 		The course will not focus on mathematical proofs but on practical applications and calculations.

Students will be responsible of reviewing material in Chapter 1-4 as needed.
REQUIRED TEXT    
 " Mathematical Methods in the Physical Sciences" by Mary L. Boas, 2nd Edition by John Wiley &  sons


CLASSES
 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; The course will not focus on mathematical proofs but on practical applications and calculations. Attendance in lecture will not be taken, but is highly recommended;
First day of class: August 24th Tuesday and Thursday (10:50 am - 12:15 pm). Room SETB 2.232.
LAB
An weekly lab is associated to this course.  The lab will focus on the following topics: review of some of the topics related to the course, practical applications of all course materials though the use of Algebraic Manipulation Program such as Mathematica and/or Maple. Attendance to the lab is not required, but is highly recommended.
 

 Lab Instructor:
Napoleon Hernandez
Office: SETB 2.228
Phone: 574-6707
E-mail: nhernandez@phys.utb.edu
OFFICE HRS
 Instructors will be available after lecture and during office hours to answer any questions you might have on the problems;
 T, TH 2:00pm-4:30pm, and by appointment.  
Room SETB 2.258
EXAMS
 Open Book allowed; MidTerm and Final Exam will consist of written examinations based on problems similar to homework; Make-up exams and/or extra credit will not be given;
 MidTerm : Thursday October * (10:30 - 12:00 am). Room SETB 2.232.
Final : Tuesday December * (10:30 - 12:00 am). Room SETB 2.232.
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.
HOMEWORK
 Reading:  Each student is responsible for all the assigned reading.       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.
Problems: At least 10 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.
STUDENTS
 Eldib Moatez A.
Farrell, Alan C.
Orduna, Vilma N.
Sanchez, Patricia A.
Zuniga, Carlos A.

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, Jan 18)  Introduction and Syllabus;
Class 2 (TH Jan 20)
Class 3 (TU Jan 25)
Class 4 (TH Jan 27)
 LECTURES:Coordinate Transformations (Chapter 10);
 HOMEWORK #1 (due TU Feb 1):
1) Read Chapter 10
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 5 (TU Feb 1)
Class 6 (TH Feb 3)
  LECTURES: Gamma, Beta and error functions; Asymptotic series; Stirling's formula; elliptic integrals and functions (Chapter 11);
 HOMEWORK #2 (due TH Feb 10):
1) Read Chapter 11
2) Solve Problems: Sec3(7,15), Sec4(7), Sec7(1, 7), Sec8 (3), Sec10 (3,7,12), Sec11(5),Sec12(5,11, 13).
Class 7 (TU Feb 8)
Class 8 (TH Feb 10)
Class 9 (TU Feb 15)
Class 10 (TH Feb 17)
Class 11 (TU Feb 22)
 Class 12 (TH Feb 24)
 LECTURES: Series solutions  of differential equations; Legendre polynomials; Bessel functions; sets of orthogonal functions (Chapter 12);
 HOMEWORK #3 (due TU Mar 1):
1) Read Chapter 12
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),  Sec 13 (3),  Sec 14 (5),  Sec 16 (7),  Sec 20 (4, 7), Sec 21 (7, 14) .

Class 13 (TU Mar 1)
Class 14 (TH Mar 3)
  
 LECTURES: Partial Differential equations and review (Chapter 13);
 HOMEWORK #4 (due TU Mar 8):
1) Read Chapter 13,
2) Review ALL lab Projects, write a complete report
3) Solve  Problems:  Sec 2 (15),  Sec 3 (5), Sec 4 (3),  Sec 5 (2, 8),   Sec 6 (3),  Sec 7 (15)
Class 15 (TU Mar 8)):  Review
Class 16  (TH Mar 10):  MIDTERM #1:  Chapter 10 -12
No Class (Mar 14-19):  Spring Break
Class 17 (TU Mar 22)
 Class 18 (TH Mar 24)
Class 19 (TU Mar 29)

 LECTURES: Calculus of Variations (Chapter 9)
 HOMEWORK #5 (due TU Apr 5):
              1) Read Chapter 9
              2) Solve  Problems:  Sec 2 (2),  Sec 3 (13,18), Sec 4 (4,7),  Sec 5 (4, 8),   Sec 6 (3)
Class 20 (TH Mar 31)
Class 21 (TU Apr 5)
Class 22 (TH Apr 7)
Class 23 (TU Apr 12)
 LECTURES: Function of a complex variable (Chapter 14)
 HOMEWORK #6 (due Apr 14):
              1) Read Chapter 14
              2) Solve Problems:
Class 24 (TH Apr 14)
Class 25 (TU Apr 19)
Class 27 (TH Apr 21)
  LECTURES: Integral Transform (Chapter 15);
 HOMEWORK #7 (due Apr 28):
              1) Read Chapter 15
              2) Solve Problems:  Sec 2 (5,10,21,27), Sec 3 (3,9,19,18,28), Sec 4 (6,16,18,20), Sec 5 (5,13,17,20), Sec 6 (1,2)
Class 26 (TU Apr 26):
  LECTURE: Tensors (Chapter 10)
Class 27 (TH Apr 28):  Review and DEADLINE FOR ALL LATE HOMEWORK !
Class 28 (TU May 3)  FINAL EXAM: Chapter 9, 13, 14-15