# PH461/561: Math Methods

## Fall 2010

PH461/561 serves as a capstone undergraduate course and introductory graduate level course. Graduate students taking PH561 should also enroll in the companion one credit class PH505. In Fall 2010 these courses are being taught by Prof. Ethan Minot.

## Calendar

1M 9/27Complex numbersCh 3 HW #1
2W 9/29Hyperbolic functionsCh 3
3F 10/1SeriesCh 4 hw 1 soln
4M 10/4Series convergenceCh 4Including power seriesHW #2
5W 10/6Application of Power Series: Taylor seriesCh 4
6F 10/8Fourier seriesCh 4 hw2 soln
7M 10/11MatricesCh 8eigenvectors & eigenvaluesHW #3
8W 10/13MatricesCh 8approaches to solve linear equations
9F 10/15Vector Algebra -worksheet_2.dochw3 soln
10M 10/18Review of worksheet 2Chpt 8 Rank, orthonormal basisHW #4
11W 10/20Vector CalculusChpt 10Cartesian Coordinates
12F 10/22Vector CalculusChpt 10Numerical method ∇²Φ=0, cylindrical coordshw4 soln
13M 10/25Vector CalculusChpt 10Curvilinear coordinates
14W 10/27MIDTERM - - Midterm
15F 10/29Ordinary Diff. Eqns.Chpt 14Separable variable, Exact, Inexact-
16M 11/1Ordinary Diff. Eqns.Chpt 14Homogeneous, Isobaric, Bernoulli'sHW #5
17W 11/3Ordinary Diff. Eqns.Chpt 15worksheet3.doc, Euler's ODE method, Higher Order: n lin. ind. solns.
18F 11/5Ordinary Diff. Eqns.Chpt 15Complementary, Particular, Guessing y_c and y_p hw5 soln
19M 11/8Ordinary Diff. Eqns.Chpt 15Method of variation of parametersHW #6
20W 11/10Power series solns of ODEsChpt 16Special 2nd order Ord. Diff Eqs, Wronskian, Series Solution
21F 11/12Power series solns of ODEsChpt 16Recursion relationhw6 soln
22M 11/15Power series solns of ODEsChpt 16 & 18Legendre Eqn., Series solution about regular singular point, indicial eqnHW #7
23W 11/17Special functionsChpt 18Generating functions, Bessel functions
24F 11/19 hw7 soln
25M 11/22 -worksheet_4.docHW #8
26W 11/24Partial Differential EquationsChpt 20
27F 11/26THANKSGIVING HOLIDAY -
28M 11/29Partial Differential EquationsChpt 20 -
29W 12/1Partial Differential EquationsChpt 20 -
30F 12/3Review for final - ph461exercises.pdfhw8 soln

## Syllabus

• Complex numbers
• Manipulating complex numbers
• Functions of complex numbers
• Hyperbolic functions
• Series
• Convergence of series
• Taylor series expansions
• Fourier series
• Matrices and vector spaces
• Eigenvalues and eigenvectors
• Vector algebra
• Vector calculus
• in cartesian coordinates,
• in cylindrical coordinates
• in spherical coordinates
• Line integrals
• Conservative fields
• Surface and volume integrals
• Differential Equations
• First-order ordinary differential equations (ODEs)
• Higher-order ODEs
• Series solutions of ODEs
• Eigenfunction method for ODEs
• Special functions
• Legendre
• Hermite
• Gamma
• Bessel
• Beta
• Partial differential equations (PDEs)
• First order PDEs
• Second order PDEs
• Diffusion equation