Mathematical Methods: Syllabus

Lectures: Monday & Wednesday, 1.40pm - 2.55pm. Location: HBH 423 + Zoom (dual delivery).
 
Office Hours: Monday, 12.00pm - 1.30pm (HBH 310) & Friday, 4.00pm - 5.30pm (Zoom).
 
Required Text: Mathematical Methods for Physicists, by George Arfken and Hans Weber (Sixth Edition, Elsevier: AW below). The 7th edition of this book, Arfken, Weber & Harris (AWH below) can also be used, and corresponding Chapters are listed below. The structure of the course more closely approximates the 6th Edition chapters, and is supplemented by other texts, as indicated.
 
Teaching Assistant: Yi Xu (yx51 at rice.edu). All homeworks will be emailed directly to Yi as single PDF file submissions (CCing Dr. Baring). He will grade them and forward to Prof. Baring for final appraisal and return.
  



                            AW/[AWH] (or MW)     APPROX NUMBER       APPROX
         TOPIC                   CHAPTER          OF LECTURES        DATES


  Preliminaries                                                       8/22
  Complex Variables           6,7 [AWH 11]            2.5       8/22, 8/24, 8/29
  Introduction to Numerics     AW App 1,2             1.5          8/29, 8/31
  Ordinary Differential      8, MW1 [AWH 7]            3        9/7, 9/12, 9/14
     Equations (ODEs)
  Series and Summation         5 [AWH 1]              1.5          9/19, 9/21
  Integral Evaluation             MW3                 1.5          9/21, 9/26
  Numerical Integration        AW App 2                1              9/28
  Fourier Series/Transforms  14,15 [AWH 19,20]         1              10/3
  Integral Transforms        15, MW4 [AWH 20]          1              10/5


                       Midterm Recess, October 10 - 11



  Dispersion Relations         7 [AWH 12]              1             10/12  
  Vectors and Matrices       3, MW6 [AWH 2,3]          1             10/17
  Matrix Numerics                -                    0.5            10/19
  Tensors                      2 [AWH 4]              1.5         10/19, 10/24


            	   Take-Home Mid-Term Exam, due 3pm October 22



  Special Functions         9-13 [AWH 13-15,18]       3.5    10/26, 10/31, 11/2, 11/7
  Orthogonal Polynomials    9-13 [AWH 13-15,18]       1.5          11/7, 11/9
  Partial Differential        8, MW8 [AWH 9]           2          11/14, 11/16
    Equations (PDEs) and BVPs
  Eigenfunctions               9 [AWH 6,8]             1             11/21
  Integral Equations         16, MW9 [AWH 21]          2          11/28, 11/30


                Take-Home Final Exam, due before 5pm on December 13

Lecture/date allocations for the material are approximate, and may be modified as the semester progresses.

Special Needs? Any student with a documented disability needing academic adjustments or accommodations is requested to speak with Dr. Baring during the first two weeks of class. All discussions will remain confidential. Students with disabilities should also contact Disability Resource Center in Room 111 of the Allen Center.
 
Other texts: