homework_1_F17.pdf

# homework_1_F17.pdf - Homework 1 Math 104 A 1 Instructor...

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Homework # 1 , Math 104 A 1 Instructor: Prof. Hector D. Ceniceros General Instructions : Please write your homework papers neatly. You need to upload both full your codes and the runs you made, properly commented. Make sure that all your codes have a preamble which describes the purpose of the code, all the input variables, the expected output, your name, and the date of the last time you modified the code. Write your own code, individually. Do not copy codes! 1. Review and state the following theorems of Calculus (see for example 1.1 and 1.2 in the textbook): (a) The Intermediate Value Theorem, (b) The Mean Value Theorem, (c) Rolle’s Theorem, (d) The Mean Value Theorem for Integrals, (e) The Weighted Mean Value Theorem for Integrals. 2. Write a computer code to implement the Composite Trapezoidal Rule quadrature T h [ f ] = h 1 2 f ( x 0 ) + f ( x 1 ) + . . . + f ( x N - 1 ) + 1 2 f ( x N ) (1) to approximate the definite integral I [ f ] = Z b a f ( x ) dx, (2) using the equally spaced points x 0 = a, x 1 = x 0 + h, x 2 = x 0 + 2 h, . . . , x N = b , where h = ( b - a ) /N .

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