MATH104A_HW1.pdf - MATH 104A Homework 1 General Instructions You have to integrate all the problems that require coding and\/or numerical computation in

MATH104A_HW1.pdf - MATH 104A Homework 1 General...

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MATH 104A Homework 1 General Instructions: You have to integrate all the problems that require coding and/or numerical computation in a single jupyter notebook. Make sure all your codes have a preamble which describes purpose of the code, all the input variables, the expected output, your name, and the date of the last time you modified it. Write your own code, individually. Do not copy codes! The solutions to the problems that do not require coding must be uploaded as a single pdf or as part of the jupyter notebook. 1. Review and state the following theorems of Calculus:(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 Integrals2. 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 integralI[f] =Zbaf(x)dx(2)using the equally spaced pointsx0=a, x1=x0+h, x2=x0+ 2h, . . . xN=x0+Nh=b,whereh=b-aN.

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