• 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 write-permissions and multiple printers.

Know location and function of basic items on toolbars and pull down menus.
Use on-screen 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 (xi,yi), 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

Use built-in EXCEL tools to fit the data with appropriately chosen families of curves.

• 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).

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 built-in 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.

Use names to control parameters in formulas (e.g. y=a*x^2+b*x+c).
Fine-tune 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 two-column 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.

Given a formula for a function obtain improved numerical estimates of the derivative by choosing smaller increments (e.g. use 2 columns each for xi and xi+Dx, and f(xi) and f(xi+Dx) (with xi 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 two-column table for a function, create a third column for estimates of antiderivative.
Overlay plots of function and the antiderivative in appropriate styles.

Working knowledge of higher order schemes like trapezoidal, mid-point 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 (x0,y0) 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 Runge-Kutta 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

Use names to control parameters in formulas (e.g. z=a*x^2+b*x*y+c*y^2).
Fine-tune 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 zxx, zyy, zxy and zyx by repeating the procedures for first order partials twice.
Working knowledge of numerical instabilities.
Given a table of function values z=f(x,y) as above, directly create tables approximating the second order partial derivaties zxx, zyy, and zxy = zyxwithout 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.
Hands-on 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.

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 fill-down and fill-right commands.
A hands-on knowledge of numerical stability, in partical the need for small time-steps to avoid blow-ups.
Set-up for heat-equation 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 fill-down and fill-right commands to map the formula over the region, followed by iteration .
A hands-on knowledge of numerical stability.