课程名称︰数值方法 课程性质︰必修 课程教师︰张恒华 开课学院：工学院 开课系所︰工科海洋系 考试日期（年月日）︰2011/3/30 (三) 考试时限（分钟）：3小时 (9:10am ~ 12:10pm) 是否需发放奖励金：是 （如未明确表示，则不予发放） Numerical Methods: 505 29120/ESOE 2024 This is an open book, open notes exam. Electronic devices are forbidden on your person, including cell phones,iPods, iPads, headphones, PDAs, calculators, and computers. Turn your cell phone off and leave all electronics in your backpack or bag, or risk getting a zero on the exam. 试题 : 1. Conversion. (10 pts) (a) Convert the binary number 1011101 to decimal format. (b) Convert the binary number 11000101.101 to decimal format. 2. Express the following quantities in the form 0.xxx...xEyy. (10 pts) (a) 0.00001325 (b) 123456789 (c) 0.0000002 3. Write a user-defined MATLAB function that carries out multiplication of two matrices [c] = [a][b]. For function name and arguments use C = MatrixMult(A,B). The input arguments A and B are the matrices that are multiplied. The output argument C is the result. DO NOT use the matrix multiplication of MATLAB. The function MatrixMult should first check if the two matrices can be multiplied, and if not the output C should be the message "The matrices cannot be multiplied since the number of rows in [b] is not equal to the number of columns in [a]". (15 pts) 4. Use three-digit rounding arithmetic to perform the following calculations. (a) 133 + 0.921 (b) (121 - 0.327) - 119 (c) (121 - 119) - 0.327 (10 pts) 5. Repeat Problem 4 using four-digit rounding arithmetic. (10 pts) 6. Use colon notation to create vectors identical to the following created with the linspace function: (10 pts) (a) v = linspace(-3,1,9). (b) r = linspace(8,0,17). 7. Exactly what will be displayed after the following MATLAB commands are typed? (10 pts) (a) >> x = 2; >> x ^ 3; >> y = 8 - x (b) >> q = 4:2:10; >> r = [7 8 4; 3 6 -2]; >> sum(q) * r(2,3) 8. Develop a vectorized version of the following code: (10 pts) tstart = 0; tend = 20; ni = 5; t(1) = tstart; y(1) = 10 + 5 * cos(2 * pi * t(1) / (tend - tstart)); for i = 2:ni+1 t(i) = t(i-1) + (tend - tstart) / ni; y(i) = 10 + 5 * cos(2 * pi * t(i) / (tend - tstart)); end 9. The "divide and average" method, an old-time method for approximate the square root of any positive number a, can be formulated as x + a/x x = —————— 2 Write a well-structured M-file function based on a while...break loop structure to implement this algorithm. Use proper indentation so that the structure is clear. At each step estimate the error in your approximation as ∣ x - x ∣ ∣ new old ∣ ε = ∣————————∣ a ∣ x ∣ ∣ new ∣ Repeat the loop until ε is less than or equal to a specified value. A good a initial guess of x is a/2. Make sure that it can evaluate the square root of numbers that are equal to and less than zero. For the latter case, display the result as an imaginary number. For function name and arguments use s = SquareRoot(a,eps). The input arguments a and eps are the number to be computed and the specified tolerance value, respectively. The output argument s is the result. (15 pts) --

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