جزوه کلاسی آموزش نرم افزار مطلب و کاربرد آن در محاسبات عددی

جزوه کلاسی آموزش مطلب و کاربرد آن در محاسبات عددی

لینکهای زیر شامل آموزش کلاسی مطلب دانشگاه یوتا و روش حل معادلات دیفرانسیلی با استفاده از نرم افزار مطلب است. این جزوه برای دانشجویان رشته مهندسی که با روشهای عددی و حل آنها سرو کار دارند بسیار مفید است. امید است مورد استفاده قرار بگیرد.

منبع: سایت دانشگاه یوتا

Class Notes on Matlab

The following links allow you to download documents related to Matlab operation, programming, functions, etc.

Getting started with Matlab

  1. Introduction to Matlab with the Help menu - a brief introduction to the Matlab interface and its use, then uses Matlab Help Desk to guide you in learning Matlab (optional reading)
  2. Introduction to Matlab - specific exercises introducing Matlab
  3. Programming, I/O, Strings - logical operations, programming structures, scripts and functions, input and output, and string manipulation - basic components for developing programs in Matlab
  4. Elementary Matlab Graphics - two- and three-dimensional plots with Matlab:
  5. Matlab for SCILAB users - although originally developed to show the differences between Matlab and Scilab, it is also useful to understand many Matlab concepts.
  6. Elementary mathematical functions with Matlab - description and graphics of elementary mathematical functions using Matlab
  7. Using logical vectors in Matlab - exercises on graphics and other manipulations of logical vectors
  8. Moler's book Ch. 1 - Introduction to Matlab (intro.pdf) - highly mathematical introduction (optional reading)
  9. Symbolic functions in Matlab -- download this script and run it in Matlab to see examples of symbolic functions

Computer programming with Matlab

  1. Introduction to computer programming - principles of computer programming: programming structures, flow charts, pseudo-code
  2. Programming with Matlab - specific examples of Matlab functions including all programming structures introduced earlier.
  3. Notes on Functions in Matlab - discusses issues related to m-file and inline user-defined functions in Matlab.
  4. Passing functions as arguments in Matlab - shows examples of functions used as arguments of other functions
  5. Gradually Varied Flow solution through the direct step - an example of Matlab programming with functions and sub-functions

Elementary numerical methods with Matlab

NOTE: See the Using Matlab guide corresponding to these subjects. Also, see the chapters in the SIAM book referred to below. For items 1 through 3, you may want to download this free book on Matrix Algebra by Autar K Kaw, University of Florida

  1. Matrix operations in Matlab (transpose, addition and subtraction, multiplication, term-by-term multiplication, creating matrices, manipulating matrix elements)
    • Read the chapter on Matrices and linear algebra from the Using Matlab guide
  2. Linear algebra operations in Matlab (solution to systems of linear equations, LU factorization, sparse matrices)
  3. Eigenvalues in Matlab (eigenvalues, eigenvectors, and singular value decomposition)
  4. Solution to single equations and multiple non-linear equations in Matlab (single equation solution: bisection, Newton-Raphson, secant; systems of non-linear equations: Newton-Raphson, "secant" methods:
    • Solution to non-linear equations - a pdf document with examples of single and multiple non-linear equations
    • Read the chapter on Functions: zeros, maxima and minima, integration from the Using Matlab guide
    • Read Moler's book Ch. 3 - Zeroes and Roots
    • Examples from hydraulics - click here to download zip file with documentation and scripts - Examples included:
      • pipe flow
      • Manning's equation
      • pipe-pump system
      • entrance from a reservoir into a channel.
  5. Numerical integration in Matlab (rectangular elements, trapezoidal rule, Simpson's rule, Gaussian quadrature, multiple integrals) --
    • Read the chapter on Functions: zeros, maxima and minima, integration from the Using Matlab guide
    • Read Moler's book Ch. 6 - Quadrature
  6. Data fitting in Matlab (interpolating polynomials, cubic splines, cubic Hermite polynomials)
    • Read the chapter on Polynomials and interpolation from the Using Matlab guide
    • Read the chapter on Statistics, difference equations, Fourier analysis from the Using Matlab guide (read only parts related to least-square fitting)
    • Read Moler's book Ch. 5 - Data Fitting (leastsquares.pdf)
  7. Solution to Ordinary Differential Equations in Matlab (Euler method, Runge-Kutta methods, etc)


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جزوه کلاسی آموزش نرم افزار مطلب و کاربرد آن در محاسبات عددی

این جزوه برای دانشجویان رشته مهندسی که با روشهای عددی و حل آنها سرو کار دارند بسیار مفید است.



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