Spreadsheet Tools for Engineers Using Excel CIVE 1331 Fall 2008 Hanadi Rifai

Chapter 1. Engineering Analysis and Spreadsheets

Engineering Analysis and Spreadsheets Engineering analysis is a systematic process for analyzing and understanding problems that arise in the various field of engineering To carry out this process, we use problem solving techniques Spreadsheet programs can be used to solve the problem once you have defined it and set it up properly

Spreadsheets allow you to: Import, export, store, process, and sort data Display data graphically Analyze data statistically Fit algebraic equations through datasets Solve single and simultaneous algebraic equations Solve optimization problems

Examples Book Example 1.1

General Problem Solving Techniques Think about the problem before you solve it Draw a sketch to visualize it Understand the overall purpose of the problem and its key points Ask yourself: what information is known? And what information must be determined? Ask yourself: what fundamental engineering principles apply?

General Problem Solving Techniques – Cont’d Think about how you will solve the problem Develop your solution in an orderly and logical manner Think about the solution: does it make sense? Make sure solution is clear and complete Problem solving is a skill that takes time and practice

Engineering Fundamentals Equilibrium (e.g., force, flux or chemical equilibrium) Conservation laws (mass, energy) Rate phenomena

Mathematical Solution Procedures Data Analysis Curve-fitting Interpolation Solving single algebraic equations Solving simultaneous algebraic equations Evaluating integrals Engineering economic analysis Optimization techniques

Chapter 2. Creating an Excel Worksheet

Spreadsheet Basics basically a table containing numeric or alphanumeric values Individual elements are called cells Cells can contain a number or text A cell reference is its column heading and row number, e.g., B3 Tabular collection of cells is called a worksheet Cells contain numbers resulting from formulas

Definitions Ribbon: upper portion of the window Title Bar: top line Office Button: replaced the File Menu Ribbon Tabs: below title bar, replaced menu headings Worksheet Tabs: beneath worksheet Scroll bars: horizontal and vertical Status bar: bottom line

Skills to learn in Excel Moving around the worksheet Entering data –2, -6, 3.33, 2.55e-12, -7.08e+6, 0.0, –$25, 50%, 5/24/2006, 7:20 PM, 19:20:00 Entering strings or label (text) Correcting errors Using formulas and functions Naming a cell or worksheet Saving, retrieving and printing worksheets

Operators in Excel Arithmetic: +, -, *, /, ^, % String: & Comparison: >, >=, Operator precedence: –1percentage (%) –2exponentiation (^) –3Multip/division (* and /) –4Add/subtract (+ and -) –5concatenation (&) –6comparisons (>, <, …) Operations carried out from left to right

Functions in Excel Function consists of a: –Function name –Arguments Example: SUM(C1,C2,C3) The function is the sum of cells C1,C2,C3

Examples Book Examples 2.4 &2.5

Chapter 3. Editing an Excel Worksheet

More skills to learn in Excel Selecting a block of cells Clearing a block of cells Copying to adjacent cells by dragging Copying to nonadjacent cells Moving a block of cells Undoing changes

Copying and Moving Formulas Relative vs. Absolute addressing A1+B1 vs. $A$1+$B$1 Moving a formula will not change cell addresses but copying does If an object cell is moved, the formula is changed to reflect the move C1=A1+B1 If A1 is moved to B5 then C1=B5+B1

Yet more skills to learn in Excel Inserting and deleting rows and columns Inserting or deleting cells Adjusting column width or row height Formatting data items Hyperlinks Displaying cell formulas

Chapter 4. Making Logical Decisions (If-Then-Else)

The IF Function Requires 3 arguments: logical expression, value for true, value for false =IF(C1>100, “Too Big”, “Ok”) Nested IF functions: =IF(A3<0, “Ice”, IF(A3<100, “Water”, “Steam”))

Example Book Example 4.2

Chapter 5. Graphing Data

Examples Book Examples 5.1&5.3

Chapter 6. Analyzing Data Statistically

Data Analysis - Statistics Engineers gather data to measure variability or consistency –Example: diameters of ball bearings off an assembly line –Another example: variation in sizes among customers to determine how many items of each size to manufacture Statistical data analysis tells us about data

Data Characteristics Mean or average: expected behavior Median: a value such that half the data values lie above and half lie below 8, 10, 12, 14, 16, 18, 22, 25, 29 5, 8, 12, 16, 18, 22, 27, 29 Mode: value that occurs the most in a data set 10, 5, 8, 9, 3, 10, 7Mode is 10 Median is 17

More Data Characteristics Min and Max: smallest and biggest value in a dataset Variance: an indication of the degree of spread in the data s 2 = 1/(n-1)*  (x i -x m ) 2 where x m is mean and the summation is for all I from 1 to n The greater the spread in the data, the larger the variance Standard deviation: square root of the variance

Example Book Example 6.1

Histogram or relative frequency plot Describes how data are distributed within their range Cumulative distribution allows us to estimate the likelihood that a data value associated with an item drawn at random is less than or greater than a specified value

How to construct a histogram Subdivide the range of the data into a series of adjacent equally spaced intervals 1 st interval begins at smallest value Last interval extends to or beyond the largest data value (the max) Fixed interval width Detemine how many values fall in each interval f i = n i /n where n i is the # of points in the ith interval

Examples Book Examples 6.3, 6.5, & 6.6

Chapter 7. Fitting Equations to Data

Fitting Equations to Data Statistics and Histograms analyze a set of single-value data: x 1, x 2, etc. Engineers need to analyze two-value or paired (x,y) data Different Methods: –Linear Interpolation –Fitting data with a curve

Linear Interpolation P1P1 P2P2 y1y1 y2y2 x1x1 x2x2 x y y – y 1 y 2 -y 1 x – x 1 x 2 -x 1 =

Example Book Example 7.2

Curve Fitting Fitting a line or curve through pairs of data Concept is to represent data with an equation (y = f(x)) Fit does not have to be exact Goal is to minimize the error somehow between the line and the data (error between y i and y)

Error in Curve Fitting For each data point P i = (x i, y i ), the error is the difference between y i and F(x i ) or the calculated value of y i e i = y i – f(x i ) Strategy is to pick a function f(x i ) that minimizes e i

Straight Line Fit Method of Least Squares Y = ax +b –Two unknowns: a and b have to be chosen carefully to minimize the sum of the squares of the errors –Equations 7.7 and 7.8 in book –Two equations in 2 unknowns (a, b)

Examples Book Examples 7.5 & 7.6

Chapter 9. Transferring Data

Even more skills to learn in Excel Importing/exporting data from text files Transferring data from and to Word or PowerPoint Transferring graphs to Word or PowerPoint

Chapters 11. Solving Single Equations

Algebraic Equations Linear – none of the unknowns are raised to a power or appear as arguments in a trig function, a log function, a square root etc. Nonlinear – harder to solve

Finding Numerical Solutions Using Excel Goal Seek Solver

Examples Book Examples 11.5 & 11.7

Chapters 12. Solving Simultaneous Equations

n-linear Equations in n unknowns a 11 x 1 + a 12 x 2 +a 13 x 3 +….+a 1n x n = b 1 a 21 x 1 + a 22 x 2 + a 23 x 3 +….+a 2n x n = b 2 …. a n1 x 1 + a n2 x 2 + a n3 x 3 +….+a nn x n = b n a ij ’s and b’s are known x i ’s are unknown i = row j = column

Matrix Is a two dimensional array of numbers Elements characterized by a row number and a column number A matrix with one column is called a vector System of equations on previous slide can be written as: AX = B

Example 12.1 Writing a System of Simultaneous Equations in Matrix Form

Matrix Operations You can add, subtract, and multiply a matrix by a scalar Matrices can be added if they have same number of rows and columns A, B are m x n matrices then C = A + B is an m x n matrix

Matrix Multiplication Matrices can also be multiplied A is an m x n matrix can be multiplied by B if B is an n x p matrix The result, matrix C will be an m x p matrix Example 12.2 in book

Special Matrices The identity matrix I and the inverse matrix A -1 I is a square matrix (n x n) and has the important property: –IA = AI = A Inverse matrix (n x n) has the important property: –A -1 A = A A -1 = I

Examples Book Examples 12.7 & 12.8