Numerical Methods for Engineers and Scientists: An Introduction with Applications Using MATLAB
•
0 likes•412 views
This document contains a 35 slide presentation by Assistant Prof. Dr. Aydin Azizi on numerical methods and MATLAB. The presentation covers topics such as variables, vectors, matrices, arithmetic operations, random numbers, characters, logical expressions, loops, and more. Each slide provides an example and explanation of the concept being taught to help attendees learn how to use MATLAB for numerical methods.
More Related Content
Viewers also liked
Viewers also liked (20)
Similar to Numerical Methods for Engineers and Scientists: An Introduction with Applications Using MATLAB
Similar to Numerical Methods for Engineers and Scientists: An Introduction with Applications Using MATLAB (7)
Recently uploaded
Recently uploaded (20)
Numerical Methods for Engineers and Scientists: An Introduction with Applications Using MATLAB
- 1. This document is intended for internal use only and shall not be distributed outside of GUtech in Oman Numerical Methods for Engineers and Scientists Lecturer: Assistant Prof. Dr. AYDIN AZIZI
- 2. Slide 2 Copyright © 2014 John Wiley & Sons, Inc. All rights reserved. Third Edition Amos Gilat • Vish Subramaniam Numerical Methods for Engineers and Scientists
- 3. Slide 3 Lecturer: Assistant Prof. Dr. Aydin Azizi Introduction to MATLAB Lecturer: Assistant Prof. Dr. Aydin Azizi
- 4. Slide 4 Lecturer: Assistant Prof. Dr. Aydin Azizi Example of MATLAB Release 13 desktop Lecturer: Assistant Prof. Dr. Aydin Azizi
- 5. Slide 5 Lecturer: Assistant Prof. Dr. Aydin Azizi Variables – Vectors and Matrices – • ALL variables are matrices Variables •They are case–sensitive i.e. x X •Their names can contain up to 31 characters •Must start with a letter •Variables are stored in workspace e.g. 1 x 1 4 x 1 1 x 4 2 x 4 4239 6512 7123 3 9 2 3 4 Lecturer: Assistant Prof. Dr. Aydin Azizi
- 6. Slide 6 Lecturer: Assistant Prof. Dr. Aydin Azizi How do we assign a value to a variable? >>> v1=3 v1 = 3 >>> i1=4 i1 = 4 >>> R=v1/i1 R = 0.7500 >>> >>> whos Name Size Bytes Class R 1x1 8 double array i1 1x1 8 double array v1 1x1 8 double array Grand total is 3 elements using 24 bytes >>> who Your variables are: R i1 v1 >>> Lecturer: Assistant Prof. Dr. Aydin Azizi
- 7. Slide 7 Lecturer: Assistant Prof. Dr. Aydin Azizi How do we assign values to vectors? >>> A = [1 2 3 4 5] A = 1 2 3 4 5 >>> >>> B = [10;12;14;16;18] B = 10 12 14 16 18 >>> A row vector values are separated by spaces 54321A 18 16 14 12 10 B A column vector values are separated by semi–colon (;) Lecturer: Assistant Prof. Dr. Aydin Azizi
- 8. Slide 8 Lecturer: Assistant Prof. Dr. Aydin Azizi How do we assign values to vectors? • If we want to construct a vector of, say, 100 elements between 0 and 2 – linspace >>> c1 = linspace(0,(2*pi),100); >>> whos Name Size Bytes Class c1 1x100 800 double array Grand total is 100 elements using 800 bytes >>> Lecturer: Assistant Prof. Dr. Aydin Azizi
- 9. Slide 9 Lecturer: Assistant Prof. Dr. Aydin Azizi How do we assign values to vectors? If we want to construct an array of, say, 100 elements between 0 and 2 – colon notation >>> c2 = (0:0.0201:2)*pi; >>> whos Name Size Bytes Class c1 1x100 800 double array c2 1x100 800 double array Grand total is 200 elements using 1600 bytes >>> Lecturer: Assistant Prof. Dr. Aydin Azizi
- 10. Slide 10 Lecturer: Assistant Prof. Dr. Aydin Azizi How do we assign values to matrices ? Columns separated by space or a comma Rows separated by semi-colon >>> A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 >>> 987 654 321 Lecturer: Assistant Prof. Dr. Aydin Azizi
- 11. Slide 11 Lecturer: Assistant Prof. Dr. Aydin Azizi How do we access elements in a matrix or a vector? >>> A(2,3) ans = 6 >>> A(:,3) ans = 3 6 9 >>> A(1,:) ans = 1 2 3 >>> A(2,:) ans = 4 5 6 Lecturer: Assistant Prof. Dr. Aydin Azizi
- 12. Slide 12 Lecturer: Assistant Prof. Dr. Aydin Azizi Some special variables pi () inf (e.g. 1/0) i, j ( )1 >>> 1/0 Warning: Divide by zero. ans = Inf >>> pi ans = 3.1416 >>> i ans = 0+ 1.0000i Lecturer: Assistant Prof. Dr. Aydin Azizi
- 13. Slide 13 Lecturer: Assistant Prof. Dr. Aydin Azizi Arithmetic operations – Matrices Performing operations to every entry in a matrix Add and subtract>>> A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 >>> >>> A+3 ans = 4 5 6 7 8 9 10 11 12 >>> A-2 ans = -1 0 1 2 3 4 5 6 7 Lecturer: Assistant Prof. Dr. Aydin Azizi
- 14. Slide 14 Lecturer: Assistant Prof. Dr. Aydin Azizi Arithmetic operations – Matrices Performing operations to every entry in a matrix Multiply and divide>>> A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 >>> >>> A*2 ans = 2 4 6 8 10 12 14 16 18 >>> A/3 ans = 0.3333 0.6667 1.0000 1.3333 1.6667 2.0000 2.3333 2.6667 3.0000 Lecturer: Assistant Prof. Dr. Aydin Azizi
- 15. Slide 15 Lecturer: Assistant Prof. Dr. Aydin Azizi Arithmetic operations – Matrices Performing operations to every entry in a matrix Power >>> A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 >>> A^2 = A * A To square every element in A, use the element–wise operator .^ >>> A.^2 ans = 1 4 9 16 25 36 49 64 81 >>> A^2 ans = 30 36 42 66 81 96 102 126 150 Lecturer: Assistant Prof. Dr. Aydin Azizi
- 16. Slide 16 Lecturer: Assistant Prof. Dr. Aydin Azizi Performing operations between matrices >>> A=[1 2 3;4 5 6;7 8 9] A = 1 2 3 4 5 6 7 8 9 >>> B=[1 1 1;2 2 2;3 3 3] B = 1 1 1 2 2 2 3 3 3 A*B 333 222 111 987 654 321 A.*B 3x93x83x7 2x62x52x4 1x31x21x1 272421 12108 321 = = 505050 323232 141414 Arithmetic operations – Matrices Lecturer: Assistant Prof. Dr. Aydin Azizi
- 17. Slide 17 Lecturer: Assistant Prof. Dr. Aydin Azizi Roots- Logarithms
- 18. Slide 18 Lecturer: Assistant Prof. Dr. Aydin Azizi Random Number
- 19. Slide 19 Lecturer: Assistant Prof. Dr. Aydin Azizi Random Real Number
- 20. Slide 20 Lecturer: Assistant Prof. Dr. Aydin Azizi Random Integer Number
- 21. Slide 21 Lecturer: Assistant Prof. Dr. Aydin Azizi Practice
- 22. Slide 22 Lecturer: Assistant Prof. Dr. Aydin Azizi Characters and Encoding
- 23. Slide 23 Lecturer: Assistant Prof. Dr. Aydin Azizi Characters and Encoding
- 24. Slide 24 Lecturer: Assistant Prof. Dr. Aydin Azizi Characters and Encoding
- 25. Slide 25 Lecturer: Assistant Prof. Dr. Aydin Azizi Practice
- 26. Slide 26 Lecturer: Assistant Prof. Dr. Aydin Azizi Relational Expressions
- 27. Slide 27 Lecturer: Assistant Prof. Dr. Aydin Azizi Relational Expressions
- 28. Slide 28 Lecturer: Assistant Prof. Dr. Aydin Azizi Relational Expressions
- 29. Slide 29 Lecturer: Assistant Prof. Dr. Aydin Azizi Logical Operators
- 30. Slide 30 Lecturer: Assistant Prof. Dr. Aydin Azizi Logical Operators
- 31. Slide 31 Lecturer: Assistant Prof. Dr. Aydin Azizi Logical Operators
- 32. Slide 32 Lecturer: Assistant Prof. Dr. Aydin Azizi Truth Table for Logical Operators
- 33. Slide 33 Lecturer: Assistant Prof. Dr. Aydin Azizi Logical Error
- 34. Slide 34 Lecturer: Assistant Prof. Dr. Aydin Azizi Logical Error
- 35. Slide 35 Lecturer: Assistant Prof. Dr. Aydin Azizi Practice
- 36. Slide 36 Lecturer: Assistant Prof. Dr. Aydin Azizi While Loop count = 0; number = 8; while number > 3 number = number - 2 count = count+1 end
- 37. Slide 37 Lecturer: Assistant Prof. Dr. Aydin Azizi FOR Loop mat=rand(5,6) [r c] = size(mat) for i = 1:r for j = 1:c mat(i,j) = mat(i,j) * 2 end end
- 38. Slide 38 Lecturer: Assistant Prof. Dr. Aydin Azizi IF Loop x=rand(10,1); v = [ ] for i = 1:length(x) if x(i) > 0 v = [v i] end end