## Math 250/251## Downloads |

- A trigonometry fact sheet
- Partial fractions review notes
- formulas sheet for power series and Taylor/Maclaurin series

First Order Equations, Part 1 - including introduction and classifications of differential equations (updated 1-8-2016)

First Order Equations, Part 2 (updated 6-10-2017)

Review of Partial Differentiation (revised 7-27-2010)

Second Order Linear Equations, Part 1 - homogeneous equations (updated 6-24-2017)

Second Order Linear Equations, Part 2 - nonhomogeneous equations (updated 6-26-2014)

Mechanical Vibrations (updated 1-27-2016)

Higher Order Linear Equations (section 4.2) (updated 2-14-2016)

Laplace Transforms, Part 1 (sections 6.1 and 6.2) - introduction, solving initial value problems (updated 6-6-2017)

Laplace Transforms, Part 2 (sections 6.3 and 6.4) - piecewise continuous functions (updated 6-12-2016)

Laplace Transforms, Part 3 (section 6.5) - impulsive forcing functions (Revised 10-1-2014)

Table of basic Laplace Transforms

Systems of First Order Linear Equations (updated 6-9-2017)

Phase portraits; Nonlinear Systems (updated 7-13-2012)

Phase portrait reference chart -- a contribution of study-aid from a former student; it even has perforations for easy cut-and-paste onto 3x5 index cards.

Notes on Partial Differential Equations [Math 251 only]:

Part 1 (10.1 and 10.5) - introduction, separation of variables, 2-point boundary value problems, eigenvalues and eigenfunctions (updated 11-2-2014)

Part 2 (Fourier Series: 10.2, 10.3, and 10.4) - Fourier series, Fourier convergence theorem, even and odd periodic functions (updated 3-26-2013)

Fourier Series summary (the bare minimum version of part 2 above)

Part 3 (10.6 + summaries) - heat conduction problems, nonhomogeneous boundary conditions, steady-state solution (updated 11-17-2014)

Part 4 (10.7 and 10.8; incomplete optional topics section) - wave equations, Laplace/potential equation (updated 3-28-2016)

Study-aid: Summary sheet of common simple 2-point BVPs

Study-aid: (flash cards of) summary of solutions of heat conduction and wave equations' BVP

Send any question/comment about this page to: tseng@math.psu.edu

*Last modified: June 24, 2017*