exam matlab 2 prep.oo3
Topic functions and files 1 141-162 3.1 elementary mathematical functions lookfor ex. lookfor imaginary to get a list of functions that deal with imaginary numbers exponential and logarithmic functions exponential exp(x) exponential; e^x sqrt(x) square root; x^(1/2) logarithmic log(x) natural logarithm; ln(x) log10(x) common (base 10) logarithm; log x = log[10] x complex abs(x) absolute value; x angle(x) angle of a complex number x conj(x) complex conjugate imag(x) imaginary part of a complex number x real(x) real part of a complex number x numeric ceil(x) round to the nearest integer toward fix(x) round to the nearest integer toward 0 floor(x) round to the nearest integer towards - sign(x) signum function (+1 if x > 0; 0 if x = 0; -1 if x <0) complex number functions numeric functions trigonometric functions trigonometric cos(x) cot(x) csc(x) sec(x) sin(x) tan(x) inverse trigonometric acos(x) acot(x)
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inverse trigonometric acos(x) acot(x) acsc(x) asec(x) asin(x) atan(x) atan2(x,y) four quadrant inverse tangent hyperbolic functions cosh x = (e^x + e^-x) / 2 sinh x = (e^x - e^-x) / 2 sinh^-1 = ln(x + (x^2 + 1)^(1/2)) hyperbolic cosh(x) coth(x) csch(x) sech(x) sinh(x) tanh(x) inverse hyperbolic acosh(x) acoth(x) acsch(x) asech(x) asinh(x) atanh(x) 3.2 user-defined functions function [output variables] = function_name(input variables) function definition line variants function [area_square] = square(side); square.m function area_square = square(side); square.m function [volume_box] = box(height, width, length); box.m function [area_circle, circumf] = circle(radius); circle.m function sqplot(side); sqplot.m variations in function calls function arguments local variables global variables applications finding the zeroes of a function minimizing a function of one variable
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applications finding the zeroes of a function minimizing a function of one variable minimizing a function of several variables design optimization problems 4, 6, 9, 12, 14, 16 (178-180) 4 for several values of x, use matlab to confirm that sinh x = (e^x-e^-x)/2 6 the capacitance of two paralell conductors of length L and radius r, separated by a distance d in the air, is given by C = ((permittivity)L)/ln((d-r)/r) permittivity = 8.854*10^-12 F/m write a script file that accepts user input for d, l, and r, and computes and displays C. test the file with the values L=1m, r=0.001m, and d=0.004m 9 write a function that accepts input in degrees F and computes the corresponding values in degrees C the relation between the two is CT = (5/9)(TF-32) 12 a fence around a field is shaped as shown in figure p12 (p179). it consists of a rectangle of length L and width W, and a right triangle that is symmetrical about the central horizontal axis of the rectangle. suppose the width w is known in meters and the enclosed area a is known in square meters. writre a user-defined function file with W and A as inputs. the outputs are the length L required so the area is A, and the total length of fence required. Test your function for the values W = 6m and A = 80 m^2 14 using estimates of rainfall, evaporation, and water consumption, the town engineer deveoped the following model of the water volume in the resovior as a function of time V(t) = 10^9+10^8(1-e^(-t/100)) -rt where V is the water volume in liters, t is the time in days, and r is the town's consumption rate in liters/ day. write two user defined functions. the first function should define the function V(t) for use with fzero function the second function should use fzero to compute how long it would take for the volume of water o decrease to x percent of its initial value of 10^9 liters the inputs to the second function should be x and r. test your functions with x = 50 percent, and r=10^7 liters/ day 16 a torus is shaped like a donut. if it's inner radius is a and its outer radius is b, the volume and surface area are given by
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16 a torus is shaped like a donut. if it's inner radius is a and its outer radius is b, the volume and surface area are given by V=(1/4)^2(a+b)(b-a)^2 A=^2(b^2-a^2) create a user defined function that computes V and A from the arguments a and b suppose that the outer radius is constrained to be 2 in greater than the inner radius. write a script file that uses your function to plot A and V versus a for 0.25a4 in functions and files 2 163-172 3.3 advanced function programming function handles methods for calling functions types of functions primary anonymous subfunctions nested overloaded private anonymous functions multiple input arguments no input arguments calling one function within another variables and anonymous functions subfunctions nested functions private functions problems 18, 19, 20, 21, 22, 23 (180-181) 18 use the gen_plot function described in section 3.3 to obtain two subplots, one plot of the function 10e^(-2x) over the range 0x2, and the other of a plot of 5sin(2x /3) over the range 0x6 19 create an anonymous function for 10e^(-2x) and use it to plot the function over the range 0x2 20 create an anonymous function for 20x^2-200x+3 and use it a) to plot the function to determine the approximate location of its minimum, and
20 Topic create an anonymous function for 20x^2-200x+3 and use it a) to plot the function to determine the approximate location of its minimum, and b) with the fminbnd function to precisely determine the location of the minimum 21 four create anonymous functions to represent the function 6e^(3cos(x^2))), which is composed of the functions h(z)=6e^z, g(y)=3cos(y), and f(x)=x^2. use the anonymous functions to plot 6e^(3cos(x^2)) over the range 0x4 22 use a primary function with a subfunction to compute the zeroes of the function 3x^3 - 12x^2 -33x +90 over the range -10x10 23 create a primary function that used a function handle with a nested function to compute the minimum of the function 20x^2-200x+3 over the range 0x10 functions and files 3 172-181 3.4 working with data files importing data from externally generated files importing spreadsheet files the import wizard importing ASCII data files with text headers importing binary data files exporting delimited ASCII data files 3.5 summary problems 24, 25 (181) 24 use a text editor to create a file containing the following data. then use the load function to load the file into Matlab, and use the mean function to compute the mean value of each column 55 42 98 51 39 95 63 43 94 58 45 90 25 enter and save the data given in problem 24 in a spreadsheet. then import the spreadsheet file into the matlab variable A. Use matlab to compute the sum of each column. programming with matlab 1 183-200
Topic programming with matlab 1 183-200 4.1 program design and development algorithms and control structures structured programming top-down design and program documentation pseudocode example 1 sequential operations example 2 conditional operations example 3 iterative operations finding bugs development of large programs 4.2 relational operators and logical variables the logical class the logical function accessing arrays using logical arrays 4.3 logical operators and functions table 4.3-1 p 194 Logical Operators table 4.3-2 p 195 Order of prescedence for operator types table 4.3-3 p 196 truth table short-circuit operators table 4.3-4 logical functions logical operators and the find function problems 2, 9, 12, 14 (244-254) 2 the roots of the quadratic equation ax^2+bx+c=0 are given by x=(-bsqrt(b^2-4ac))/(2a) a) develop a pseudocode description of a program to compute both roots given the values of a, b, and c. Be sure to identify the real and imaginary parts. b) write the program described in part a and test it for the following cases: 1. a=2, b=10, c=12 2. a=3, b=24, c=48 3. a=4, b=24, c=100 9 the arrays price_A and price_B given below contain the price in dollars of two stocks over 10 days. Use Matlab to determine how many days the price of stock A was above the price of stock B price_A = [19, 18, 22, 21, 25, 19, 17, 21, 27, 29] price_B = [22, 17, 20, 19, 24, 18, 16, 25, 28, 27] 12
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price_A = [19, 18, 22, 21, 25, 19, 17, 21, 27, 29] price_B = [22, 17, 20, 19, 24, 18, 16, 25, 28, 27] the height and speed of a projectile (such as a thrown ball) launched with a speed of v0 at an angle A to the horizontal are given by h(t) = v0*t*sin(A)-0.5*g*t^2 v(t) = sqrt(v0^2-2*v0*g*t*sin(A)+g^2*t^2) 14 Let e1 and e2 be logical expressions. DeMorgan's laws for logical expressions state that NOT(e1 AND e2) implies that (NOT e1) OR (NOT e2) and NOT(e1 OR e2) implies that (NOT e1) AND (NOT e2) use these laws o find an equivalent expression for each of the following expressions and use Matlab to verify the equivalence a. ~ ( ( x < 10 ) & ( x >= 6 ) ) b. ~ ( ( x == 2 ) | ( x > 5 ) ) programming with matlab 2 200-225 4.4 conditional statements the if statement the else statement the ifelse statement checking the number of input and output arguments strings and conditional statements 4.5 loops for loops the break and continue statements using an array as a loop index implied loops use of logical arrays as masks while loops problems 18, 20, 23, 27, 31, 33 (244-254) 18 write a program that accepts a year and determines whether or not the year is a leap year. use the mod function. The output should be the variable extra_day, which should be 1 if the year is a leap year and 0 otherwise. The rules for determining leap years in the Gregorian calendar are: 1. all years evenly divisible by 400 are leap years 2. years evenly divisible by 100 but not 400 are not leap years 3.years divisible by 4 but not 100 are leap years 4.all other years are not leap years
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1. all years evenly divisible by 400 are leap years 2. years evenly divisible by 100 but not 400 are not leap years 3.years divisible by 4 but not 100 are leap years 4.all other years are not leap years for example, the years 1800, 1900, 2100, 2300, and 2500 are not leap years, but 2400 is a leap year 20 the (x,y) coordinates of a certain object as a function of time t are given by x(t) = 5t-10 y(t) = 25t^2-120t+144 for 0x4. Write a program to determine the time at which the object is the closest to the origin at (0, 0). Determine also the minimum distance. do this two ways: a. By using a for loop b. By not using a for loop 23 electrical resistors are said to be connected "in series" if the same current passes through each and "in parallel" if the same voltage is applied across each. If in a series, they are equivalent to a single resistor whose resistance is given by R = R1 + R2 + R3 + ... + Rn If in parallel, their equivalent resistance is given by 1/R = 1/R1 + 1/R2 + 1/R3 + ... + 1/Rn write an M-file that prompts the user for the type of connection (series or parallel) and the number of resistors n and then computes the equivalent resistance 27 31 33