One-credit graduate Math Methods: Ph 505

Date | Lectures | Assignments | Notes | |

09/28 | Complex numbers | HW 1 for 461 ; HW 1 for 561 | WS 1 | |

09/30 | Hyperbolic functions. | WS 2 | ||

10/02 | Series. | HW 2 (for both 461 and 561) | WS 3 | |

10/05 | Convergence of infinite series. | HW 3 for 461 ; HW 3 for 561 | WS 4 | |

10/07 | Power series. Taylor series. | HW 4 for 461 ; HW 4 for 561 | WS 5 | |

10/09 | Fourier series. | HW 5 for 461 ; HW 5 for 561 | WS 6 | |

10/12 | Matrices and vector spaces. | Problem #4 of HW#5 is due on Friday | WS 7 | |

10/14 | Eigenvalues and eigenvectors. Systems of linear equations. | HW 6 for 461 ; HW 6 for 561 | WS 8 | |

10/16 | Vector algebra. | WS 9 | ||

10/19 | Vector calculus: Cartesian coordinates. | HW 7 (for both 461 and 561) | WS 10 | |

10/21 | Vector calculus: cylindrical and spherical coordinates. | Midterm is set for Wednesday, November 4 (11 AM, Weniger 304). Ch.3,4,7,8,10,11,12. | Midterm is a closed book one: prepare your own formula sheet.No calculators. | |

10/23 | Vector calculus: generalized curvilinear coordinates. | HW 8 (for both 461 and 561) | WS 11 | |

10/26 | Line integrals.Green's theorem. Conservative fields. | WS 12 | ||

10/28 | Surface and volume integrals. | WS 13 | ||

10/30 | First-order ordinary differential equations. | WS 14 | ||

11/02 | Higher-order ordinary differential equations. | WS 15 | ||

11/04 | Midterm (11 am, Weniger 304) | |||

11/06 | Linear ODEs with variable coefficients. | HW 9 (for both 461 and 561) | ||

11/09 | Series solutions of ODEs: expansion about an ordinary point. | WS 16 | ||

11/11 | Series solutions of ODEs: expansion about regular singularity. | HW 10 (for both 461 and 561) | WS 17 | |

11/13 | Wronskian method of obtaining a second solution. Polynomial solutions. | |||

11/16 | Eigenfunction methods for ODEs. | HW 11 (for both 461 and 561) | WS 18 | |

11/18 | Special functions: Legendre functions and polynomials. | Read up on associated Legendre polynomials and spherical harmonics. | ||

11/20 | Special functions: Hermite polynomials. Gamma function. | HW 12 (for both 461 and 561) | Read up on Laguerre and associated Laguerre polynomials. | |

11/23 | Special functions: Bessel and spherical Bessel functions. Beta function. | Problem 20.4 of HW#12 is due next Monday. | WS 19 | |

11/25 | Partial differential equations: first and second order. | HW 13 (for both 461 and 561) | ||

11/30 | PDEs: diffusion-type problems and hyperbolic (wave) equations. | HW 14 (for both 461 and 561) | WS 20 | |

12/02 | Inhomogeneous PDEs. | Final exam: Thu Dec 10, 9:30 AM, Weniger 304. Prepare your formula sheet. Closed book, no calculators. |