1.
File management, navigation, etc.

Mastery expected by: First month of first semester

Sample worksheet
(to be created)

Sample problems / skills:
Create new workbook.
Open exisiting workbook from disk and from WWW.
Save workbook to disk and to network drive.
Close workbook and exit EXCEL.
Move between multiple worksheets in a workbook.
Print selection or entire worksheet.
Work on a network w/ limited writepermissions and multiple printers.
Know location and function of basic items on toolbars and pull down
menus.
Use onscreen help to find information.
Select (use mouse/arrow keys to "block") a cell or a region, possibly
disconnected (use CNTRL/SHIFT keys).
Edit the contents of a cell.
Copy, cut, paste and delete.
2. Worksheet formatting

Mastery expected by: first month of first semester??

Sample worksheet
(to be created)

Sample problems / skills:
Adjust row width and column height (important for "LONG" numbers)
Change format of cell contents (e.g. number of decimals displayed,
date format)
Change font (size, bold) of text (e.g. for worksheet titles, column
headers).
Change alignment, including text spanning multiple columns, and wrapped
text.
Manipulate cell borders for individual cells and for regions of cells.
Change color of cells (fill color).
3. Data points (x_{i},y_{i}),
statistics, plotting, and fitting curves

Mastery expected by: First month of first semester

Sample worksheet
(to be created)

Sample problems / skills:
Given a list of data points (pairs of numbers) on paper, manually enter
them into a worksheet.
Read in a text file containing a list of data points (pairs of numbers
w/ various separators).
Plot the data in appropriate styles, utilizing with the chart wizard.
Use of the SUM() function and basic statistic functions to calculate
the mean, median and std
Advanced skill: (optional)
Use builtin EXCEL tools to fit the data with appropriately chosen
families of curves.
4. Addresses, names, formulas, programming

Mastery expected by: optional in math: first semester??

Sample worksheet
(to be created)

Sample problems / skills:
Understand RC and A1 format, and toggle in between these.
Understanding the difference between relative and absolute addresses,
and their respective syntax in both RC and A1 formats.
Entering formulas into cells (use = sign), using relative addresses.
Using FILL DOWN / FILL RIGHT for formulas.
Copy, paste, and edit formulas.
Understand the difference between pasting (formulas) and pasting values
(PASTE SPECIAL).
Define and use names (for example for parameters in formulas).
Advanced skills: (optional)
Record and execute macros to automate basic, recurring manipulations
Create buttons to execute macros
Edit Visual Basic code
5. Functions y=f(x): Tables and graphs

Mastery expected by: precalculus, or first month of calculus I

Sample worksheet

Sample problems / skills:
Given a formula for a function create a two column table showing function
values
Working knowledge of builtin special functions, including PI()
and their syntax
(this includes knowledge of INSERT FUNCTION and HELP pages).
Use the chart wizard to graph the function using an appropriate styles.
Overlay multiple graphs and use first column for labeling the first
axis.
Advanced: (optional)
Use names to control parameters in formulas (e.g. y=a*x^2+b*x+c).
Finetune features of plots (e.g. spacing and lebeling of tickmarks,
colors of plots, etc.)
6. Numerical differentiation of y=f(x)

Mastery expected by: First half of semester, calculus I

Sample worksheet

Sample problems / skills:
Given a twocolumn table for a function, create a
third column for estimates of the derivative.
Create separate columns for forward, backward, and central difference
quotients.
Overlay plots of the original function and its derivative using appropriate
styles.
Advanced: (optional)
Given a formula for a function obtain improved numerical estimates
of the derivative by choosing smaller increments (e.g. use 2 columns each
for x_{i} and x_{i}+Dx, and
f(x_{i}) and f(x_{i}+Dx) (with
x_{i} spaced as usual, but Dx very small).
Working knowledge of numerical instability
Higher order difference quotients (directly estimate 2nd derivative
w/o first calculating 1st derivative)
7. Numerical integration of y=f(x)

Mastery expected by: Mid semester, calculus I

Sample worksheet
(to be created)

Sample problems / skills:
Given a twocolumn table for a function, create a
third column for estimates of antiderivative.
Overlay plots of function and the antiderivative in appropriate styles.
Advanced: (Mid semester calc II).
Working knowledge of higher order schemes like trapezoidal, midpoint and
Simpson's method
Use EXCEL to study the effects of choosing increments of different size.
Use EXCEL to study the convergenece rates of higher order schemes.
8. Euler's method for y'=f(x,y)

Mastery expected by: mid semester, calculus II

Sample worksheet
(to be created)

Sample problems / skills:
Given a formula for y'=f(x,y) and initial condition (x_{0},y_{0})
create a three column table to solve initial value problem.
Plot the solution curve (usually columns are not adjacent, use CNTRL key!).
Calculate and overlay several solution curves for different initial conditions.
(For autonomous differential equations, and those using measured data
compare the "7.Numerical integration of y=f(x)".)
Advanced: (optional, often only in mid semester of diff equns
course)
Implement a higher order scheme like RungeKutta 4th order
9. Functions z=f(x,y): Tables and graphs
(precalculus, first week of calculus III)

Mastery expected by: First week of calculus III

Sample worksheet
(to be created)

Sample problems / skills:
Given a formula for a function z=f(x,y), create a table of function
values using FILL DOWN / FILL RIGHT.
(Note: This requires facility with a mix of mixed relative and absolute
addresses, e.g. R7C[1] or A$1 and $A1.)
Usually the x and y values are displayed along the top row / leftmost column.
Use the chart wizard to graph function using appropriate styles
Advanced: (optional)
Use names to control parameters in formulas (e.g. z=a*x^2+b*x*y+c*y^2).
Finetune features of plots (e.g. spacing and lebeling of tickmarks, colors
of plots, etc.)
10. Partial derivatives numerically

Mastery expected by: First month of calculus III

Sample worksheet
(to be created)

Sample problems / skills:
Given a table of function values for z=f(x,y) with
x and y values listed along the top row / leftmost column, create new tables
approximating each first order partial derivative, again with x and y values
listed along top row / leftmost column.
Working knowledge of analogues of forward, backward and symmetric quotients.
Given a table of function values z=f(x,y) as above, create tables approximating
the second order partial derivaties z_{xx}, z_{yy}, z_{xy}
and z_{yx} by repeating the procedures for first order partials
twice.
Working knowledge of numerical instabilities.
Advanced: (optional)
Given a table of function values z=f(x,y) as above, directly create tables
approximating the second order partial derivaties z_{xx}, z_{yy},
and z_{xy} = z_{yx}without making intermediate tables
of first order partials, but by using appropriate second order divided
differences.
11. Double integrals

Mastery expected by: Middle of semester of calculus III

Sample worksheet
(to be created)

Sample problems / skills:
Given a table of function values for z=f(x,y) with
x and y values listed along the top row / leftmost column, find numerical
estimates for double integrals
over rectangular regions, giving careful attention to the number of
points used (e.g. usually include only one of either leftmost OR ritemost
datapoints etc.).
This includes working with iterated sums (displaying the intermediate
sums in added column or row (to the rite or to the bottom of the table),
and with
double sums.
Handson knowledge how to modify the procedure for integrals over less
regular shaped regions by changing the corresponding values in the table
for points outside the region to zero.
Advanced: (optional)
Modify the given formula by multiplying by an analytic representation of
the characteristic function for nonrectangular regions.
Naive adaptations of midpoint/trapezoidal and Simpson's Rule for each
of the iterated integrals.
Analysis of the resulting coefficients, and direct implementation of
higher order algorithms in double sums.
12. Numerical soln of PDEs

Mastery expected by: Optional in math, typical early in 2nd half
of calc III
a. parabolic/hyperbolic PDEs: (optional,typically
mid semester calculus III)

Sample worksheet
(to be created)

Sample problems / skills:
Set up a worksheet with values of independent variables listed in top
row and left most column, and boundary values given on rows/columns bounding
the region where to solve the PDE.
Combine the difference scheme for numerical differentiation (compare
partials) and linear extrapolation (compare Euler's
method) to numerically solve the PDE over a rectangular region by using
filldown and fillright commands.
A handson knowledge of numerical stability, in partical the need for
small timesteps to avoid blowups.
Setup
for heatequation example, Sample
solutions.
b. elliptic PDEs (rarely covered in
intro level courses, special project calc III)

Sample worksheet
(to be created)

Sample problems / skills:
Set up a worksheet with values of independent variables listed in top
row and left most column, and boundary values given on rows/columns bounding
the region where to solve the PDE.
Combine the difference scheme for numerical differentiation (compare
partials) and linear extrapolation (compare Euler's
method) to numerically solve the PDE over a rectangular region by using
filldown and fillright commands to map the formula over the region, followed
by iteration .
A handson knowledge of numerical stability.