The TI-89 has many features that are particularly useful to ode and to calculus in general. These are taken directly from the ti89 manual which is a downloadable pdf file as well as the physical book which came with the calculator: ode features: Chapter 11 of the manual 1. First order systems of ode's. a. numerical methods for approximate solutions (Euler and RK) b. deSolve function for exact solutions 2. Non-trivial graphing choices: a. Single ode of 1st order. SLPFIELD or FLDOFF (DIRFLD causes an error) Can plot multiple integral curves on the same plot. b. Single ode of 2nd order, convert to a system of two 1st order odes. (Hint: y1(t) is the function and y2(t) is y1'(t), so y'' + y' + y = 0 becomes (let y2 be y' and y1 be y) y1'(t) = y2(t) and y2'(t) = - y2(t) - y1(t). Use DIRFLD for 2nd order ode or systems of 2 1st order ode's c. 3rd and higher require FLDOFF (field off) d. Initial conditons can be a set of values, or alternately use the ncurves variable in the window menu. You can also do it interactively. discrete system features: Chapter 9 of the manual. 1. graphing recursively defined sequences like u_n = n u_{n-1} u_1 = 1 2. TIME plots: n on x axis, u(n) on y axis 3. WEB plots: (u_{n-1}, u_n) 4. CUSTOM plots: you select the x and y axis You don't have to plot all of sequence, you can start/stop plotting earlier or plot just the even n. You can plot Line Dot Square or Thick. Systems of sequences (Custom for predator/prey -- rabbits eating banana) generating tables from sequences.