Schedule (subject to change)

DateTopicsAssignments Due
Week 1L101.05 MReview
Equations of Mathematical Physics
Real series		 
 L201.07 WVector calculus HW1 (01.08.09)HW1 soln
Week 2L3 01.12 MComplex Variables
Formalism		 HW2 HW2 soln
 L401.14 WTransformationsHW3 soln
Week 3L5 01.15 TH(contd.)  
 L601.21 WContour integration
Taylor series		HW4 soln
Week 4L7 01.26 MLaurent series
Calculus of residues		 HW5 soln
  01.28 WSnow day 
Week 5L8 02.02 M(contd.) HW6 soln
 L902.04 WTake-Home Exam 1: SolnTake-Home Exam 1
HW7 soln(due THU)
Week 6L10 02.09 MReview  
  02.11 WExam 1 
Week 7L11 02.16 MPartial Differential Equations
Formalism		  
 L1202.18 WSeparation of variablesHW8 soln
Week 8L13 02.23 MSturm-Liouville theory HW9 soln
 L1402.25 WGreen's functionHW10 soln
Week 9L15 03.02 MSeries solution HW11 soln
 L1603.04 W(contd.)HW12 soln
Week 10L17 03.09 M(contd.) HW13 soln
 L1803.11 WReview 
Week 11 03.19 HTake-Home Exam 2  

Syllabus

  1. Review
    1. Equations of Mathematical Physics
    2. Real series
      1. Cauchy criterion
      2. Convergence tests: positive series
        1. necessary condition
        2. comparison
        3. d'Alembert-Cauchy ratio
        4. Cauchy root
        5. Cauchy-Maclaurin integral
        6. Kummer's
        7. Raabe's
        8. Gauss's
      3. Convergence tests: alternating series
      4. Absolute convergence
      5. Uniform convergence
        1. Weierstrass M test
        2. Abel's test
        3. Properties
  2. Vector Calculus
    1. Differential operators
    2. Theorems
      1. Gauss
      2. Stokes
      3. Green
      4. Helmholtz
    3. Curvilinear coordinates
    4. Curvilinear differential operators
    5. Conservative fields and potentials
  3. Complex Variables
    1. Formalism
      1. Cauchy-Riemann conditions
      2. Analytic functions
      3. Examples
    2. Conformal transformations
    3. Contour integration
      1. Cauchy integral theorem
      2. Cauchy integral representation
      3. Derivatives
    4. Series
      1. Taylor series
      2. Laurent series
    5. Calculus of residues
  4. Partial Differential Equations
    1. Classification
    2. Separation of variables
  5. Ordinary Differential Equations
    1. Sturm-Liouville theory
    2. Green's function
    3. Series solution
    4. Special functions