HW01.pdf - Math 104A Homework#1 Instructor Xu Yang General Instructions Please write your homework papers neatly You need to turn in both your codes and

# HW01.pdf - Math 104A Homework#1 Instructor Xu Yang General...

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Math 104A Homework #1 * Instructor: Xu Yang General Instructions: Please write your homework papers neatly. You need to turn in both your codes and descriptions on the appropriate runs you made by compressing and emailing them to TA with your name and ID number as the file name. 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 thetextbook):(a) The Intermediate Value Theorem.(b) The Mean Value Theorem.(c) Rolles 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 quadratureTh[f] =h12f(x0) +f(x1) +...+f(xN-1) +12f(xN),(1)to approximate the definite integralZbaf(x)dx,(2)using the equally spaced points