AHC Eng 179

1
ENGR 179EXCEL for Scientists and Engineers

• Lecture 2 Fall 2004
• Instructor
• Sherman Wiggin

2

• What is a derivative?
• The derivative is among the most useful
  mathematical entities used in defining
  engineering problems.  It is usually associated
  with a function.
• A function is a mathematical formula used to
  define or model behavior. 
• Derivatives also have a geometrical
  interpretation.  They represent the slope or the
  tangent at the point.

3
Making A Derivative Workbook
Typing in the Headers
Lets add a little more color to the sheet
4
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

5
Mathematical Entry Format
Now lets insert the function.
Next the analytical solution
6
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

7
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.

8
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.

9
Integral Workbook Using Numerical Methods
10
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.

11
The Inclined Plane Problem

• Normal Force
• Force Down the Plane
• Friction Force

12
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.