TI-84 Plus CE field manual for IB Math
Euler's method
Use a sequence table to iterate Euler's method for a first-order differential equation.
Use Euler's method for y′=√tanxy, y(1)=1, with step size h=0.1, to approximate y(1.3).
Press and switch the graphing mode from FUNCTION to SEQ. Then press and set the sequence type to SEQ(n+1).
Use u ( ) for the x-values and v ( ) for the y-values. Set nMin=0, then enter u(n+1)=u(n)+0.1 and u(0)=1. For the y-recurrence, enter v(n+1)=v(n)+√tan(u(n))0.1v(n) and v(0)=1. Build the fraction with (F1) → 1: n/d, typing 0.1v(n) in the numerator and √(tan(u(n))) in the denominator. Type n with and the square root with .
Open table setup with and set both Indpnt and Depend to Ask. This is essential here: in Auto mode the table fills consecutive rows from n=0, and by n=6 it reaches x=1.6, past 2π, where tanx<0 and √tanx is non-real, so computing the next row throws a domain error. Ask mode lets you request only the row you need.
Clear out any old table rows: press (CATALOG), scroll down to ClrTable, and press twice to paste and run it. Leftover n values from earlier work are not recomputed when you switch to Ask, and can crash the table.
Press to open the table. Since 1.3 is three steps of size 0.1 from 1, type 3 in the n column and press . Move right to the v(n) column and press to calculate the y-value.
y(1.3)≈1.23 (the table shows 1.229343).
Your turn
Work each one on your calculator, then check the answer.
- 1
Use Euler's method with h=0.1 for y′=√tanxy, y(1)=2, to approximate y(1.2).
- 2
Use Euler's method with h=0.1 for y′=y√cosx, y(1)=1, to approximate y(1.4).
- 3
Use Euler's method with h=0.1 for y′=√1−x2y, y(0.6)=1, to approximate y(0.9).