Worksheet 1 [pdf] [tex] - ordinary differential equations, population models
Worksheet 2 [pdf] [tex] - families of solutions to 1st order equations, direction fields, examples: mixing, interest, radioactive decay
Worksheet 3 [pdf] [tex] - exact equations, separable equations, uniqueness theorem
Worksheet 4 [pdf] [tex] - exact equations, separable equations, the brachistochrone and other examples
Worksheet 5 [pdf] [tex] - integrating factors, homogeneous equations
Worksheet 6 [pdf] [tex] - classification of equations, Newton's law of cooling and other examples
Worksheet 7 [pdf] [tex] - computer lab: using dfplot and Maple's dsolve
Worksheet 8 [pdf] [tex] - definitions, organize methods, Newton's second law, falling objects, existence and uniqueness theorem, mixing problem
Worksheet 9 [pdf] [tex] - practice exam
Worksheet 10 [pdf] [tex] - reduction of order, solution basis, Wronskian, principle of superposition, linear dependence/indepednece
Worksheet 11 [pdf] [tex] - reduction of order, solution basis, Wronskian, principle of superposition, linear dependence/indepednece
Worksheet 12 [pdf] [tex] - computer lab: constant coefficient equations, Euler equations, variation of parameters, Taylor series
Worksheet 13 [pdf] [tex] - variation of parameters, higher order equations
Worksheet 14 [pdf] [tex] - undetermined coefficients, limiting behavior of constant coefficient equations
Worksheet 15 [pdf] [tex] - computer lab: oscillator - damped/undamped, forced/free
Worksheet 16 [pdf] [tex] - undetermined coefficients
Worksheet 17 [pdf] [tex] - Laplace transform
Worksheet 18 [pdf] [tex] - springs, strings, Laplace transform
Worksheet 19 [pdf] [tex] - springs, eigenfunctions, energy, phase plane
Worksheet 20 [pdf] [tex] - practice exam
Worksheet 21 [pdf] [tex] - taylor series review: convergence, indexing
Worksheet 22 [pdf] [tex] - taylor series review: convergence, solving ode's
Worksheet 23 [pdf] [tex] - talyor series solutions, Airy's equation, computer lab
Worksheet 24 [pdf] [tex] - singular points - regular/irregular, Bessel equations
Worksheet 25 [pdf] [tex] - time-independent Schroedinger equation for a simple harmonic oscillator potential
Worksheet 26 [pdf] [tex] - partial differential equations, separation of variables, heat equation, time-dependent Schroedinger equation
Worksheet 27 [pdf] [tex] - function inner product, Fourier series, the space l2
Worksheet 28 [pdf] [tex] - Fourier series, orthogonality, computer lab
Worksheet 29 [pdf] [tex] - computer lab: Fourier series, Legendre polynomials
Worksheet 30 [pdf] [tex] - practice exam
Worksheet 31 [pdf] [tex] - separation of variables, heat equation: homogeneous ends, insulated ends, Bar-Wellington problem, Fourier series
Worksheet 32 [pdf] [tex] - wave equation, Fourier series, separation of variables
Worksheet 33 [pdf] [tex] - wave equation
Worksheet 34 [pdf] [tex] - practice with various pde's: heat, wave, and Laplace's equations
Worksheet 35 [pdf] [tex] - practice with various pde's: heat, wave, and Laplace's equations
Worksheet 36 [pdf] [tex] - Laplace's equation, Dirichlet problem, Fourier series
Worksheet 37 [pdf] [tex] - Laplace's equation: Dirichlet problem, Neumann problem, wave equation, heat equation
Worksheet 38 [pdf] [tex] - practice exam