1. ECIV 301 Programming & Graphics Numerical Methods for Engineers Lecture 4 Programming and Software EXCEL and MathCAD

2. Last Time Software Packages Users StandardPower Limited to standard software capabilities Write your own macros and/or software

3. Last Time Computer Implementation Algorithm Flowchart Pseudocode Computer Program

4. Last Time Algorithms & Flowcharts Algorithm The step by step procedure that describes the implementation of a solution strategy. Flowchart The visual representation of an algorithm.

5. Last Time Pseudocode and Computer Code Computer Code Set of Instructions in a computer language that direct the computer to perform a certain task. Pseudocode Set of code-like instructions that express the flowchart in a narrative form

6. Last Time Programming Topics Simple Information Specification –Constants, variables, type declarations Advanced Information Representation –Arrays, data structures, records Mathematical Formulas –Operators, priority rules, intrinsic functions Input/Output Logical Representation –Sequence, selection and repetition Modular Programming –Functions and Subroutines

7. Last Time Logical Representation Sequence Computer code is to be implemented one instruction at a time Analytic Solution Enter g,m,c Enter time t Evaluate v Print t,v

8. Last Time Logical Representation Selection Computer code flow is split into branches based on a logical decision. Enter g,m,c Check if m=0 Print Error Message OK to continue

9. Last Time Logical Representation Repetition Implement instructions repeatedly

10. Last Time Modular Programming Module is a self contained and independent code segment Modules are designed to perform a specific, well designed task Functions return a single result Subroutines return several results

11. Example Consider Quadratic Equation With closed form solution

12. Example If a,b,c are given Compute x 1 and x 2 What Do I Need?

13. Example Ask user to input a,b,c Check if a=0 –Linear equation, this solution does not apply Check if a=0 and b=0 –Trivial Solution Check if b 2 -4ac=0 –Double Real Root

14. A Simple Model FuFu FDFD FiFi

15. Analytic vs Numerical Solution Start from Governing Equation Derivative = Slope

16. Analytic vs Numerical Solution Use Finite Difference to Approximate Derivative vivi titi t i+1 v i+1 True Slope Approximate Slope

17. Analytic vs Numerical Solution

18. Numerical Solution Slope New Value Old ValueStep Size Euler Method

19. Analytic vs Numerical Solution Algorithm 1.Input a sequence of time nodes i.e. Start Time, End Time, Time Step 2. Input model parameters i.e. m, c 4. Input initial velocity i.e. v(t=0) 3. Input forcing function i.e. g

20. Algorithm 5. Check if m=0 avoid division by 0 6. For each time node evaluate 7. Other secondary checks…

21. Excel and MathCAD EXCEL MathCAD-IMathCAD-II

22. Project # 1 – DUE 9/12/03 This is a group project. You form your own teams. Each team should consist of UP TO THREE students. Consider the parachutist problem. Write an Excel Spreadsheet solution using Visual Basic macros to calculate terminal velocities numerically for each of the following cases: Mass in the range of 0-100 Kg with step 10 For each mass vary the drag coefficient c in the range 0 to 20 with step 2 Plot the terminal velocity as a function of drag coefficient for each mass