{ "cells": [ { "cell_type": "markdown", "id": "adafc981-15f1-42e0-a75f-96d981728b48", "metadata": {}, "source": [ "# 3. Numerical Methods in MATLAB" ] }, { "cell_type": "markdown", "id": "a1797ce2-ed6e-44e7-8503-5643a334d875", "metadata": {}, "source": [ "DING Minjie, Spring 2025" ] }, { "cell_type": "markdown", "id": "b2bcd357-6b75-476c-a940-00c9f4f9b58e", "metadata": {}, "source": [ "___________________________________________________________________________________________________________________________________________\n", "\n" ] }, { "attachments": {}, "cell_type": "markdown", "id": "58b996bb-2639-45fd-a4c4-c7cd88415d59", "metadata": {}, "source": [ "In this tutorial, we will discuss basics and numerical methods in MATLAB, including:\n", "\n", "* 1. Preparation for MATLAB\n", " * Set Working Directory\n", " * Clear Work\n", "* 2. Basic of MATLAB\n", " * Data Type\n", " * Logical Operations\n", " * Define Functions\n", "* 3. Graph\n", "* 4. Matrix Manipulation and Calculation\n", "* 5. Solve Nonlinear Equations/Root Finding\n", "* 6. Numerical Optimization\n", "* 7. Function Approximation with Interpolation\n", "* 8. Discretization\n", "* 9. Simulation" ] }, { "cell_type": "markdown", "id": "5248b545-4889-4cee-b3bf-b7ff15c4b039", "metadata": {}, "source": [ "___________________________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "7197d430-db6f-40ac-ba56-d2dbfd97f183", "metadata": {}, "source": [ "# 1.1 Set Working Directory" ] }, { "cell_type": "markdown", "id": "e021186b-f6f0-43fb-8787-57c208283595", "metadata": {}, "source": [ "We use \"pwd\" to get current working directory, and use \"cd\" to change working directory. \n", "\n", "When we work on MATLAB, we can also select working directory by right click with the mouse.\n", "\n", "If we use MATLAB as kernel on other platform, these two code instructions are indispensable.\n" ] }, { "cell_type": "code", "execution_count": 1, "id": "76375d7e-ba1d-4202-835c-6f4cc304c43e", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

ans = 'C:\\Users\\ading\\A_TA_Notes'

" ], "text/plain": [ "ans = 'C:\\Users\\ading\\A_TA_Notes'" ] }, "execution_count": 1, "metadata": {}, "output_type": "execute_result" } ], "source": [ "cd\"C:\\Users\\ading\\A_TA_Notes\"\n", "pwd" ] }, { "cell_type": "markdown", "id": "90f0b8a2-123d-49c8-a72a-b46c5f8587a0", "metadata": {}, "source": [ "# 1.2 Clear Work" ] }, { "cell_type": "markdown", "id": "4adaebc8-91eb-4fb9-9afb-96f3debcf95f", "metadata": {}, "source": [ "Before starting the work, we need to clean up the previous work." ] }, { "cell_type": "code", "execution_count": 2, "id": "d7a546f0-925d-4f70-8364-c2ed2d5e3daa", "metadata": {}, "outputs": [], "source": [ "clear all; % Clears all variables from the workspace\n", "close all; % Closes all open figure windows\n", "clc; % Clears the Command Window" ] }, { "cell_type": "markdown", "id": "e0a857ec-89f1-4751-a2e5-6eded7dac5aa", "metadata": {}, "source": [ "___________________________________________________________________________________________________________________________________________" ] }, { "cell_type": "markdown", "id": "31c10c52-e98e-4dd0-a3d6-55c6d3f840ec", "metadata": {}, "source": [ "# 2.1 Data Type" ] }, { "cell_type": "markdown", "id": "fb5120c2-a88a-42c1-a14f-b237752dd6c6", "metadata": {}, "source": [ "Here are three concepts used to store and manipulate data: Variable, Matrix, and Structure." ] }, { "cell_type": "code", "execution_count": 3, "id": "6cda03a5-37ea-4c13-93f6-737739d05eca", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

name = 'Alice'

" ], "text/plain": [ "name = 'Alice'" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%% Variable\n", "x = 10; % Numeric variable\n", "name = 'Alice'; % String variable\n", "name" ] }, { "cell_type": "code", "execution_count": 4, "id": "5a735a03-f233-4320-b326-9496374c0bb9", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

matrix_y = 2×3 double\n",
       "     1     2     3\n",
       "     4     5     6\n",
       "

" ], "text/plain": [ "matrix_y = 2×3 double\n", " 1 2 3\n", " 4 5 6\n" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/html": [ "

ans = 6

" ], "text/plain": [ "ans = 6" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/html": [ "

ans = 2×1 double\n",
       "     3\n",
       "     6\n",
       "

" ], "text/plain": [ "ans = 2×1 double\n", " 3\n", " 6\n" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/html": [ "

ans = 1×3 double\n",
       "     4     5     6\n",
       "

" ], "text/plain": [ "ans = 1×3 double\n", " 4 5 6\n" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/html": [ "

ans = 4×1 double\n",
       "     4\n",
       "     5\n",
       "     3\n",
       "     6\n",
       "

" ], "text/plain": [ "ans = 4×1 double\n", " 4\n", " 5\n", " 3\n", " 6\n" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/html": [ "

matrix_y = 2×3 double\n",
       "     1     2     0\n",
       "     0     0     0\n",
       "

" ], "text/plain": [ "matrix_y = 2×3 double\n", " 1 2 0\n", " 0 0 0\n" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/html": [ "

matrix_y = 3×2 double\n",
       "     0     0\n",
       "     0     0\n",
       "     0     0\n",
       "

" ], "text/plain": [ "matrix_y = 3×2 double\n", " 0 0\n", " 0 0\n", " 0 0\n" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/html": [ "

matrix_y = 3×2 double\n",
       "     1     1\n",
       "     1     1\n",
       "     1     1\n",
       "

" ], "text/plain": [ "matrix_y = 3×2 double\n", " 1 1\n", " 1 1\n", " 1 1\n" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" }, { "data": { "text/html": [ "

matrix_y = 3×2 double\n",
       "   NaN   NaN\n",
       "   NaN   NaN\n",
       "   NaN   NaN\n",
       "

" ], "text/plain": [ "matrix_y = 3×2 double\n", " NaN NaN\n", " NaN NaN\n", " NaN NaN\n" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%% Matrix(Vector)\n", "matrix_y=[1,2,3; 4,5,6] % Create a 2x3 matrix\n", "\n", "matrix_y(2,3) % Access the element in the 2nd row, 3rd column\n", "matrix_y(:,3) % Access all elements in the 3rd column\n", "matrix_y(2,:) % Access all elements in the 2nd row\n", "\n", "matrix_y(matrix_y>=3) % Retrieve elements greater than or equal to 3\n", "matrix_y(matrix_y>=3)=0 % Set elements greater than or equal to 3 to 0\n", "\n", "matrix_y=zeros(3,2) % Create a 3x2 matrix filled with zeros\n", "matrix_y=ones(3,2) % Create a 3x2 matrix filled with ones\n", "matrix_y=NaN(3,2) % Create a 3x2 matrix filled with NaN (Not a Number)" ] }, { "cell_type": "code", "execution_count": 5, "id": "0ddfafdc-4d8d-4e74-869c-cc12b9892128", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

person = 包含以下字段的 struct:\n",
       "      name: 'Alice'\n",
       "       age: 30\n",
       "    height: 5.5000\n",
       "

" ], "text/plain": [ "person = 包含以下字段的 struct:\n", " name: 'Alice'\n", " age: 30\n", " height: 5.5000\n" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%% Structure\n", "person.name = 'Alice'; % Field 'name'\n", "person.age = 30; % Field 'age'\n", "person.height = 5.5; % Field 'height'\n", "person" ] }, { "cell_type": "markdown", "id": "91405655-af36-4123-8e93-2370755e51bd", "metadata": {}, "source": [ "# 2.2 Logical Operations" ] }, { "cell_type": "markdown", "id": "c40ef0f1-b25b-48a0-8914-0922917c71de", "metadata": {}, "source": [ "The following code demonstrates various logical and relational operations in MATLAB." ] }, { "cell_type": "code", "execution_count": 6, "id": "60e59bf8-0138-4c54-bc5e-370515756ef9", "metadata": {}, "outputs": [ { "data": { "text/html": [ "

ans = logical\n",
       "   1\n",
       "