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EECS 1541 Introduction to Computing for the Physical Sciences Winter 2015

EECS 1541 Introduction to Computing for the Physical Sciences Winter 2015. EECS 1541 -- Introduction to Computing for the Physical Sciences. Introduction – Course Overview. Instructor : John Lam Office : Lassonde Building 1012G E-mail : johnlam@cse.yorku.ca

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EECS 1541 Introduction to Computing for the Physical Sciences Winter 2015

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  1. EECS 1541 Introduction to Computing for the Physical Sciences Winter 2015

  2. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – Course Overview Instructor:John Lam Office:Lassonde Building 1012G E-mail:johnlam@cse.yorku.ca Lecture: Tuesday & Thursday 2:30 – 3:30pm Office hours:Wednesday & Thursday 3:30pm – 4:30pm 2

  3. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – Course Overview Course website:http://www.eecs.yorku.ca/course_archive/2014-15/W/1541/ • There are 8 labs in total (3% each) • Labs start next Tuesday (Jan 13) • 2 term tests (20% each) • Final exam (36%) Please setup your CSE account and have it ready by next Tuesday! 3

  4. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – Course Overview How to do well in the course? • Do all the labs (3% each!) • Attend lectures • Do not skip the tests • Read the text and study lecture notes 4

  5. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB • This is an introductory course on computing for physical sciences using MATLAB • What is MATLAB (MATrix LABoratory)? • Software program for technical computing, it combines computation, visualization and programming. 5

  6. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB • Computation:computes value from complex equations; solving a single equation or a system of equations • Visualization: plots different types of 2-D graphs, 3-D contours • Progamming:creates conditional statements or small programs such as using “if-statement”, “while-loop”, “for-loop”, etc. 6

  7. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB • Computation:computes value from complex equations; solving a single equation or a system of equations • Visualization:plotting different types of 2-D graphs, 3-D contours Progamming: create conditional statements or small programs such as using if-loop, while-loop, for-loop 7

  8. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 1) • Recall that a linear equation with slope m and y-intercept b is given by: • Suppose the y-intercept b is zero and the slop is 3/2, and we want to plot the equation for -3 ≤ x ≤ 3: 8

  9. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 1) 9

  10. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 1) 10

  11. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 1) • Suppose a parabola w is plotted on the same graph with the previous linear function and we want to determine the x-coordinates of the intersection points 11

  12. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 1) Can we determine the exact x-coordinate? Approx. x = 2.4 x = 0 12

  13. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 1) • Alternatively, we can equate the two equations and solve for x from MATLAB to determine the exact points: 13

  14. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 1) Solutions: x = 0 or 9/4 (i.e. 2.25) 14

  15. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB Computation: computes value from complex equations; solving a single equation or a system of equations • Visualization:plotting different types of 2-D graphs, 3-D contours • Progamming:create conditional statements or small programs such as using if-loop, while-loop, for-loop 15

  16. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 2) • A periodic symmetrical square wave can be represented by the Fourier Series representation: • Let’s plot the above series that consists of the first 3 terms for 0 ≤ x≤ 2π: 16

  17. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 2) 17

  18. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 2) • We can see that the graph is not really a perfect square wave, this is because we only used 3 of the terms in the Series. • We can increase the “resolution” of the square wave by including more terms in the Series. • Instead of typing each term into MATLAB, we can use a “for-loop” to create the series to include “n” terms in the Series: 18

  19. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 2) A “for-loop” is used to implement the Series 19

  20. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 2) 20

  21. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 2) • We can put the 2 graphs on the same plot for comparison. 21

  22. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 2) • Essentially, the Fourier Series consists of terms with different frequencies. Fundamental component • The first term is called fundamental component and the rest of the terms are called the harmonics. • We are interested to see the amount of harmonics in this series. 22

  23. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 2) 23

  24. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 3) • The previous example shows a type of built-in function in MATLAB (i.e. the sin function) • You can create your own function in MATLAB and use it anytime. • Suppose we want to create a function that is called “vol_cylinder.m”. • This function will calculate the volume of a cylinder based on two input parameters: radius, height. 24

  25. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – MATLAB (Example 3) 25

  26. EECS 1541 -- Introduction to Computing for the Physical Sciences Introduction – Matlab (Example 3) 26

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