ENGR 179EXCEL for Scientists and Engineers

Lecture 2: Fall 2004

Instructor:Sherman Wiggin

What is a derivative?1. The derivative is among the most

useful mathematical entities used in defining engineering problems.  It is usually associated with a function.

2. A function is a mathematical formula used to define or model behavior. 

3. Derivatives also have a geometrical interpretation.  They represent the slope or the tangent at the point.

Making A Derivative WorkbookTyping in the Headers

Let’s add a little more color to the sheet

Building the Body of the Workbook

•Making a series of numbers

•Type in 2 to 3 of a set of numbers in this case 0, 0.1, 0.2.

•Then select all three cells and drag. The numbers will automatically increment by 0.1

Mathematical Entry FormatNow let’s insert the function.

Next the analytical solution

Mathematical Entry Format

•Next we need to put in the formulas for forward backward and central methods

•After doing this we will drag the formulas down the entire length of the time column

Graphing Results

•Now the results can be graphed to compare the accuracy of a given method

•We will select the data we want and then after creating the graph we can go back and alter one data series to create a combined chart. In this case line and bar graphs.

0.00

20.00

40.00

60.00

80.00

100.00

120.00

140.00

160.00

180.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

Series3

Series2

What is an Integral

1. Integrals can be considered as the inverse of the derivative. It is also a summation (addition) in the limit. 

2. It easiest shown to be equal to the area under the curve of a function.

Integral Workbook Using Numerical Methods

1e

Worksheet Set Up

• For this function the Left Rectangular Integration overestimates the value.

• The Right Rectangular Integration underestimates the value.

• The Trapezoidal method looks much like the rectangular method with the exception that only half of the first and last data points are used. This small modification can often produce large increases in accuracy.

4

0

xe dx

The Inclined Plane Problem

• Normal Force• Force Down the Plane• Friction Force

cosW sinW

N

; ;

coefficient of friction

angle of the incline plane

Normal Force

W mg m mass g gravity

N

Incline Plane Problem

• Motion is impending when the force down the plane is equal to the maximum static friction force.

• By graphing these values this point can be determined by the intersection of the two lines.