Nothing Special   »   [go: up one dir, main page]
Scribd Logo
Upload

Welcome to Scribd!

  • 25 views

    Mum Me Pro 221

    Uploaded by

    TÂM NGUYỄN NGỌC MINH
    Students are assigned three numerical method projects to complete for their semester one course. Each project contains three problems involving solving differential equations, integrals, and regression. Students must write a report for each project with the theory, code, results, and conclusion. Problems involve estimating parameters, solving integrals analytically and numerically, and determining temperature distributions.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd

    Mum Me Pro 221

    Uploaded by

    TÂM NGUYỄN NGỌC MINH
    25 views4 pages
    Students are assigned three numerical method projects to complete for their semester one course. Each project contains three problems involving solving differential equations, integrals, and regression. Students must write a report for each project with the theory, code, results, and conclusion. Problems involve estimating parameters, solving integrals analytically and numerically, and determining temperature distributions.

    Original Description:

    Original Title

    MumMePro221

    Copyright

    © © All Rights Reserved

    Available Formats

    PDF, TXT or read online from Scribd

    Did you find this document useful?

    Is this content inappropriate?

    Students are assigned three numerical method projects to complete for their semester one course. Each project contains three problems involving solving differential equations, integrals, and regression. Students must write a report for each project with the theory, code, results, and conclusion. Problems involve estimating parameters, solving integrals analytically and numerically, and determining temperature distributions.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    25 views4 pages

    Mum Me Pro 221

    Uploaded by

    TÂM NGUYỄN NGỌC MINH
    Students are assigned three numerical method projects to complete for their semester one course. Each project contains three problems involving solving differential equations, integrals, and regression. Students must write a report for each project with the theory, code, results, and conclusion. Problems involve estimating parameters, solving integrals analytically and numerically, and determining temperature distributions.

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 4

    University of Technology - HCMC Numerical Method Project

    Faculty of Applied Mathematics Semester 1 (2022 - 2023)

    Instruction
    Students use Matlab or Python to solve the following problems and write a
    report.
    The report must have 3 parts:

    i) The theory and algorithm;


    ii) The Matlab or Python commands;
    iii) The results and conclusion.

    Project 1
    Problem 1. Three disease carrying organisms decay exponentially in seawater ac-
    cording to the following model:

    p(t) = Ae−1.5t + Be−0.3t + Ce−0.05t

    Use general linear least-squares to estimate the initial concentration


    of each organism (A, B, and C ) given the following measurements:

    t 0.5 1 2 3 4 5 6 7 9
    p(t) 6 4.4 3.2 2.7 2 1.9 1.7 1.4 1.1

    Problem 2. Introduce the following methods and evaluate the following integral:
    Z 4
    (1 − e−x )dx
    0

    (a) analytically,
    (b) single application of the trapezoidal rule,
    (c) composite trapezoidal rule with n = 2 and 4,
    (d) single application of Simpson’s 1/3 rule,
    (e) composite Simpson’s 1/3 rule with n = 4,
    (f) Simpson’s 3/8 rule,
    (g) composite Simpson’s rule, with n = 5. For each of the numerical
    estimates (b) through (g), determine the true percent relative error
    based on (a).
    Problem 3. An insulated heated rod with a uniform heat source can be modeled
    with the Poisson equation:

    d2 T
    = −f (x)
    dx2
    Given a heat source f (x) = 25◦ C/m2 and the boundary conditions
    T (x = 0) = 40◦ C and T (x = 10) = 200◦ C, solve for the temperature
    distribution with (a) the shooting method and (b) the finite-difference
    method (∆x = 2).
    Project 2
    Problem 1. An investigator has reported the data tabulated below. It is known
    that such data can be modeled by the following equation

    x = e(y−b)/a

    where a and b are parameters. Use nonlinear regression to determine


    a and b. Based on your analysis predict y at x = 2.6.

    x 1 2 3 4 5
    y 0.5 2 2.9 3.5 4

    Problem 2. Introduce the following methods and evaluate the following integral:
    Z π/2
    (8 + 4 cos x)dx
    0

    (a) analytically,
    (b) single application of the trapezoidal rule,
    (c) composite trapezoidal rule with n = 2 and 4,
    (d) single application of Simpson’s 1/3 rule,
    (e) composite Simpson’s 1/3 rule with n = 4,
    (f) Simpson’s 3/8 rule,
    (g) composite Simpson’s rule, with n = 5. For each of the numerical
    estimates (b) through (g), determine the true percent relative error
    based on (a).

    Problem 3. Suppose that the position of a falling object is governed by the fol-
    lowing differential equation:

    d2 x c dx
    + −g =0
    dt2 m dt
    where c = a first-order drag coefficient = 12.5 kg /s, m = mass =
    70 kg, and g = gravitational acceleration = 9.81 m/s2 . Use (a) the
    shooting method, (b) the finite-difference method shooting method to
    solve this equation for the boundary conditions: x(0) = 0 x(12) = 500
    Project 3
    Problem 1. The following data represent the bacterial growth in a
    liquid culture over of number of days:

    Day 0 4 8 12 16 20
    6
    Amount x 10 67.38 74.67 82.74 91.69 101.60 112.58

    Introduce the following methods and find a best-fit equa-


    tion to the data trend. Try several possibilities linear,
    quadratic, and exponential. Determine the best equation
    to predict the amount of bacteria after 35 days.
    Problem 2. Introduce the following methods and evaluate the follow-
    ing integral:
    Z 4
    (1 − x − 4x3 + 2x5 )dx
    −2

    (a) analytically,
    (b) single application of the trapezoidal rule,
    (c) composite trapezoidal rule with n = 2 and 4,
    (d) single application of Simpson’s 1/3 rule,
    (e) composite Simpson’s 1/3 rule with n = 4,
    (f) Simpson’s 3/8 rule,
    (g) composite Simpson’s rule, with n = 5. For each of the
    numerical estimates (b) through (g), determine the true
    percent relative error based on (a).
    Problem 3. A heated rod with a uniform heat source can be modeled
    with the Poisson equation,

    d2 T
    = −f (x)
    dx2
    Given a heat source f (x) = 25 and the boundary condi-
    tions, T (0) = 40 and T (10) = 200, solve for the temper-
    ature distribution with (a) the shooting method, (b) the
    finite-difference method

    You might also like