f(x) = Sin x
Derivative
nth Derivative
f[x_]:=Sin[x]
f'[x]
or D[f[x],x]
f'[x]
or D[f[x],cfw_x,2]
D[f[x],cfw_x,n]
xn
ex
Ln x
Logba
Sin x
Cos x
Tan x
Cot x
Arcsin x
Arccos x
Arctan x
Sinh x
Cosh x
f(1)+f(2)+.+f(n)
f(1)+f(2)+.+f(n)
f(x) dx
x^n
Exp(x)
or E^x
TI-89 Commands
-1. Exact vs. Approximate
MODE F2
Use the arrow keys to move up and down until you hit
Exact/Approx.AUTO
CURSOR RIGHT ARROW
Get a menu with 3 options:
1. AUTO
2. EXACT
3. APPROXIMATE
Move the cursor up and down to select EXACT.
You can also
HW 2: Due September 9, 2015
1.
The recursion for Midpoint Method for solving the IVP y' = f(t, y) with y(t 0) = y0 is given by the formula
yi+1 = yi + h*f(t + h/2, yi + 0.5h*f(ti, yi)
Write a Mathematica code for the Midpoint Method. Use your code to appr
Comparisons of Series
We will continue considering the convergence and divergence of series with
positive terms. However, many series are a bit more complicated than some of our
basic rules and one slight variable adjustment may make a rule or method
ina
Conics
This is meant to be a brief review of the basic sketches, equations, etc. for geometric
shapes called conic sections, or conics. These are parabolas, circles, ellipses, and
hyperbolas.
Conic sections (or simply conics) are the curves formed by th
Ratio and Root Tests
We discuss two tests in this section that are particularly useful for innite series
which converge rapidly. Series involving factorials, powers, roots, and infinite
products are ofthis type. The tests typically do NOT work on innite
Representing Functions By Power Series
We will begin to develop power series for non-algebraic functions. There are
several strategies for developing these power series and we will look at a variety of
these strategies and then generalize the process in
HW 1: Due September 2, 2015
Let dy/dt = y + (2et + 3)y with y(0) = -1.
a. Estimate y(0.5) using Euler's method. Get 2 estimates using h = 0.1 and h = 0.5.
b. Suppose that the estimate that you got for a given h-value in (a) is Y and exact is the exact val