CPET 190 Problem Solving with MATLAB. Lecture 2

Transcription

1 CPET 190 Problem Solving with MATLAB Lecture 2 Introduction to MATLAB August 30, 2005 Lecture 2 - By P. Lin 1

2 Lecture 2: Math Problem Solving with MATLAB Part I 2-1 Constants and Variables Sum of two Resistances MATLAB Variables and Assignments Natural Numbers Whole Numbers Integers Predefined MATLAB Variables Some Prefixes for SI Units (International Standard) August 30, 2005 Lecture 2 - By P. Lin 2

3 Lecture 2: Math Problem Solving with MATLAB Part I (continue) 2-2 MATLAB Math Operators Addition, subtraction, multiplication, division, power Example 2-1: Mr. A rides a bike 140 meters in 20 second. What is the average speed of bike riding? Example 2-2: Neglecting friction and air resistance, what force is required to accelerate an automobile weighting 2000 lbs from 30.0 miles/hr to 55.0 miles/hr in 10.0 second? Example 2-3: Electric Power Calculation, for R = 15 ohms, voltage = 120 volts: P = V^2 /R (watts) August 30, 2005 Lecture 2 - By P. Lin 3

4 Lecture 2: Math Problem Solving with MATLAB Part I (continue) 2-3 Writing and Evaluating Math Equations Example 2-4: The sum of three consecutive numbers is 93. Find the numbers. Example 2-5: There are two ICs on a circuit board, one called IC1 and another called IC2. There is an average operating temperature of 65ºC. What is the operating temperature of each IC if the IC2 has a 10ºC lower operating temperature than IC1? Example 2-6: Graph the line y = a x + b, where b is called the offset (b = 0), a is called the slope (m = 3), and x is in the following range: -20 x 20. August 30, 2005 Lecture 2 - By P. Lin 4

5 2.1 Constants and Variables Constants: sum of resistance (ohms) Variables: sum of resistance R1 + R August 30, 2005 Lecture 2 - By P. Lin 5

6 2.1 Constants and Variables (cont.) MATLAB Sum Calculator: enter the following lines at the MATLAB command window: >> ans = 220 >> Rt = Rt = 220 >> R1 = 100; >> R2 = 120; >> R1 + R ans = August 30, 2005 Lecture 2 - By P. Lin 6

7 2.1 Constants and Variables (cont.) MATLAB Variables and Assignments No need to declare MATLAB variables Variable names must begin with a letter, which may be followed by any combination of letters, digits, and underscores. Case Sensitive, so A and a are not the same variable. Assigns a value to a variable creates the variable. The variable on the right-hand side of the assignment must has a value A variable s value is over written if it already exists. August 30, 2005 Lecture 2 - By P. Lin 7

8 2.1 Constants and Variables (cont.) Natural Numbers: counting numbers) = {1, 2, 3, 4, 5, 6, } MATLAB row vector commands >> x = 1: 1: 10 or >> x = 1:10 August 30, 2005 Lecture 2 - By P. Lin 8

9 2.1 Constants and Variables (cont.) Whole Numbers: {0, 1, 2, 3, 4, 5, 6, } Add 0 to the whole numbers MATLAB Commands >> x = [0, x] or >> clear x >> x = 0:1:10 August 30, 2005 Lecture 2 - By P. Lin 9

10 2.1 Constants and Variables (cont.) Integers: {, -3, -2, -1, 0, 1, 2, 3, } Combining whole numbers and negatives of the whole numbers MATLAB Commands >> y = -3:3 y = August 30, 2005 Lecture 2 - By P. Lin 10

11 2.1 Constants and Variables (cont.) Some Predefined MATLAB Variables ans holds the value of the most recent calculation result pi π (Circumference/Diameter), ratio of the circumference of a circle to its diameter; pi = eps - Smallest number such that when added to 1 create a floating-point number greater than 1; eps = e-016. inf - Positive infinity, generated through divided by zero, such as 1/0 August 30, 2005 Lecture 2 - By P. Lin 11

12 2.1 Constants and Variables (cont.) Some Predefined MATLAB Variables NaN - Not a number, obtained from invalid operations such as 0/0, inf/inf, and so on. realmax - Largest positive floating point number; realmax = e308. realmin - Smallest positive floating point number; realmin = e-308. August 30, 2005 Lecture 2 - By P. Lin 12

13 2.1 Constants and Variables (cont.) Some Prefixes for SI Units (International Standard) Power Prefix Abbrevi ation yocto y zepto z atto a femto f pico p 10-9 nano n 10-6 micro μ August 30, 2005 Lecture 2 - By P. Lin 13

14 2.1 Constants and Variables Some Prefixes for SI Units (International Standard) Power Prefix Abbrevi ation 10-3 milli m 10-2 centi c 10-1 deci d 10 1 deka da 10 3 kilo k 10 6 mega M 10 9 giga G Source: August 30, 2005 Lecture 2 - By P. Lin 14

15 2.1 Constants and Variables Some Prefixes for SI Units (International Standard) Power Prefix Abbreviation tera T peta P exa E Zetta Z Yotta Y August 30, 2005 Lecture 2 - By P. Lin 15

16 2.2 MATLAB Math. Operators Operators + op1 + op2 Adds op1 and op2 - op1 op2 Subtract op2 from op1 * op1 * op2 Multiplies op1 by op2 / op1 / op2 Divide op1 by op2 ^ op1 ^ op2 Computes the power op1 goes to the power of op2 August 30, 2005 Lecture 2 - By P. Lin 16

17 2.2 MATLAB Math. Operators (cont.) Arithmetic Expressions velocity = distance / time; force = mass * acceleration; count = count + 1; power = V^2/R; August 30, 2005 Lecture 2 - By P. Lin 17

18 2.2 MATLAB Math. Operators Example 2-1: Mr. A rides a bike 140 meters in 20 second. What is the average speed of bike riding? MATLAB Solution >> v = 140/20 v = 7 August 30, 2005 Lecture 2 - By P. Lin 18

19 2.2 MATLAB Math. Operators (cont.) Example 2-2: Neglecting friction and air resistance, what force is required to accelerate an automobile weighting 2000 lbs from 30.0 miles/hr to 55.0 miles/hr in 10.0 second. MATLAB Solution >>% acceleration a = vf v1/ dt % force = ma >> m = 2000; >> a = ( )/(10/3600); >> f = m*a f = August 30, 2005 Lecture 2 - By P. Lin 19

20 2.2 MATLAB Math. Operators (cont.) Example 2-3: Electric Power Calculation, for R = 15 ohms, voltage = 120 volts: P = V^2 /R (watts). MATLAB Solution: >>R = 15.0; >>V = 120; >>P = V^2 / R P = 960 August 30, 2005 Lecture 2 - By P. Lin 20

21 2.3 Writing and Evaluating Math. Equations in MATLAB Operators (cont.) Example 2-4: The sum of three consecutive numbers is 93. Find the numbers. Solution: Step 1: Represent unknown quantities as variables Let x be the consecutive number Let x + 1 be the second consecutive number Let x + 2 be the third consecutive number Step 2: Write the equation x + (x + 1) + (x + 2) = 93 Step 3: Solve x 3x + 3 = 93 3x = 90 x = 30 August 30, 2005 Lecture 2 - By P. Lin 21

22 2.3 Writing and Evaluating Math. Equations in MATLAB Operators (cont.) Example 2-4: The sum of three consecutive numbers is 93. Find the numbers. Solution: Step 4; Using the equation in Step 2 and MATLAB command to verify the answer. >> x = 30; >> x + (x +1) + (x +2) >> ans = 93 August 30, 2005 Lecture 2 - By P. Lin 22

23 2.3 Writing and Evaluating Math. Equations in MATLAB Operators (cont.) Example 2-5: There are two ICs on a circuit board, one called IC1 and another called IC2. There is an average operating temperature of 65ºC. What is the operating temperature of each IC if the IC2 has a 10ºC lower operating temperature than IC1? Solution: Step 1: Write the equations: (1) --- Taveg = (T1 + T2)/2 = 65; (2) --- T1 T2 = 10; Step 2: Solve the equations Rewrite equation (2) as equation (3) T1 = 10 + T2 Substitute (3) into (1) Taveg = (10+T2+T2)/2 = T2 = 130 2T2 = 120 T2 = 60ºC Now, we substitute T2 into (2) to solve T1 = 10 + T2 = 70ºC August 30, 2005 Lecture 2 - By P. Lin 23

24 2.3 Writing and Evaluating Math. Equations in MATLAB Operators (cont.) Example 2-5: Step 3: Verify the solution using MATLAB >> T1 = 70; >> T2 = 60; >> (T1 + T2)/2 ans = 65 >> T1 T2 ans = 10 August 30, 2005 Lecture 2 - By P. Lin 24

25 2.3 Writing and Evaluating Math. Equations in MATLAB Operators (cont.) Example 2-6: Graph the line y = a x + b, where b is called the offset (b = 0), a is called the slope (a = 3), and x is in the following range: -20 x 20. Solution: We click on File -> New -> M file to edit the following MATLAB m file. And save it as line.m. August 30, 2005 Lecture 2 - By P. Lin 25

26 2.3 Writing and Evaluating Math. Equations in MATLAB Operators (cont.) August 30, 2005 Lecture 2 - By P. Lin 26

27 Summary Constants and Variables MATLAB Math. Operators Writing and Evaluating Math. Equations in MATLAB August 30, 2005 Lecture 2 - By P. Lin 27

28 Question? Answers August 30, 2005 Lecture 2 - By P. Lin 28