# Introduction to Matlab

Save this PDF as:

Size: px
Start display at page:

## Transcription

1 Information Technology Rice University Document UNIX 17 July 11, 2002 Introduction to Matlab Basic Matlab Commands and Syntax This document teaches the user how to create Matlab matrices, learn about Matlab plots and printing, and discover how to use mathematical equations in Matlab, and to acquire rudimentary Matlab skills. Rice University, 2002 All Rights Reserved Document may not be resold to, used by, nor licensed to third parties without written permission from User Services, Rice University.

2 Table of Contents What is Pro-Matlab?... 3 Entering and Leaving Matlab... 3 Variables and the Workspace... 3 Defining Numbers and Characters... 3 Examining Numbers and Characters... 4 Workspace Commands... 4 Mathematical Functions... 4 Basic Math... 4 A Little Higher Math... 5 Polynomials... 5 Linear Equation Solving... 5 If you have any comments or suggestions about this document, send them to via electronic mail. Graphing... 5 Creating the Graph... 5 Printing the Graph... 6 M-files... 6 Scripts and Functions... 6 Control Flow... 7 For Loops... 7 While... 7 If Then... 7 Function Functions... 7 Numerical Integration... 7 Finding Zeros... 8 Differential Equation Solving... 8 Problems or Questions... 8 Faculty, Staff, and Graduate Students:... 8 Undergraduates:

3 What is Pro-Matlab? What is Pro-Matlab? Pro-Matlab (Matlab) is an interactive software package from the Math Works Inc. Matlab stands for Matrix Laboratory. It will define and perform operations on both numbers and characters. There are a number of higher math functions, such as filtering and numeric integration, built into the package. Matlab also has a graphics interface, and the capablility for programming through M-files. Entering and Leaving Matlab There are two ways to start Matlab on the Rice Unix Facility. (These methods will also work for Information Systems and Owlnet.) One is to type % matlab in an xterm. Another is to use the right button menu option for Matlab. The test accounts used for this course have this option. If you have a personal Unix account on RUF, IS, or Owlnet and you do not have Matlab as a menu option, you can add the following line to your.twmrc file. Matlab! "xterm -n Matlab -e sh -c /usr/local/gomatlab & To exit Matlab. you simply type: quit in the Matlab window. Try one of these methods to start Matlab. Exit, and try the other. Please do not run more than one copy of Matlab at any given time on this system, as we only have a limited number of licenses, and if you run two another user may not be able to run any. Variables and the Workspace Defining Numbers and Characters To define a scalar we may simply use the equal sign. a=3 To define a vector we use the equal sign and square brackets. v=[3 5 7] Matrix definition follows the same form as vector definition. The matrix rows are separated by semicolons, or by returns. or ml=[1 2 3; 4 5 6] m2=[ ] To define character variables we use the equal sign and single quotes. c= abc 3

4 Mathematical Functions Examining Numbers and Characters who size clear This command lists the names of all currently defined variables. Size (name) returns the size of the variable (name). Erases the values of all defined variables. Workspace Commands save save (name) load load (name) diary help help (cmd) Saves all of the defined variables into a workspace called matlab.mat. Saves variables to a workspace called name.mat. Loads the workspace matlab.mat. Loads the workspace name.mat. Saves everything you see in the Matlab window into a text file. Lists all of the available operators and functions. Lists the help file for (cmd). Mathematical Functions Basic Math + Is the addition operator. - Is the subtraction operator. * Performs multiplication. / Performs right division. (b/a = b*inv(a)) \ Performs left division. (b\a= Inv(a)*b) ^ Performs exponentiation. For scalar-scalar or scalar-matrix operations these perform as we expect them to. For matrix-matrix operations Matlab assumes it is attempting to perform matrix math operations. To perform element to element operations you must place a. before the operator. Note: if the left hand argument is an integer, there should be a space between the integer and the. operator, or else two.. S. 4

5 Graphing A Little Higher Math Matlab has a wide variety of built in higher math functions. We won't be able to cover all of them here, but for further information you can consult the on-line demo, and the tutorial and reference sections of the Math-Works Pro-MAT- LAB manual. Polynomials There are a number of operations we may perform involving polynomials. One of these is root finding. Matlab will automatically find the roots of a polynomial with the roots function. The syntax is: roots(coeff) where coeff is a vector of the polynomial's coefficients ordered by descending powers of x. Polynomials are also useful in data fitting. Given two vectors of experimental points we can fit different orders of polynomial to them using polyfit, and polyval. polyfit(x,y,n) returns the coefficients of a polynomial of order n that fits x to y. polyval(c,x) returns the value of a polynomial in x with coefficients c. Try out polyfit and polyval on the vectors xdata and ydata in the workspace test1. Compare the ydata values and the yexpected values for several orders of polynomial. Linear Equation Solving Matlab is very handy to solve series of linear equations. We define the equation coefficients as a matrix, and the scalar answers as a transposed vector. For instance, if we wanted to solve the following equations: 3x1 +5x2=6 4x1-8x2=1 we would define mat=[3 5; 4-8] vec=[6 1] To solve we need to divide. However, the matrix inner dimensions do not agree, so we can't. We need to transpose the vector, using a single quote. vec=vec Then we can divide mat \vec and solve the equations. Graphing Creating the Graph The basic graphics command in Matlab is plot. Plot will take multiple arguments, always in x,y pairs. For instance: plot(x,y,x,z,w,d) 5

7 Function Functions before the first line of actual code in the m-file. Control Flow Matlab does have flow control statements. Although these may be used in an interactive fashion, they are frequently less confusing and generally more useful in conjuntion with m-file programming. There are three main constructions. For Loops To iterate in Matlab we may employ a for loop. The syntax is: for i = 1:n, v(i)=i+2 end While While statements employ the logical operators. For instance: while n ~ =1 n=n/2 end If Then Matlab also has the conditional if, elseif, then statements. For example, if i ==j, a(i,j) = 2; elseif (i-j) == 1, a(i,j) = -1; else a(i,j) = 0; end Function Functions There is a class of Matlab routines which require you to define a function to use them. Several of them are worth examining. Numerical Integration There are two numerical integration functions built into Matlab. These are quad and quad 8. The syntax for both of them is: quad ( f,a,b) Where a and b define the range to integrate the function over, and 'f comes from an m-file called f.m which returns the value of f(x). 7

### AMATH 352 Lecture 3 MATLAB Tutorial Starting MATLAB Entering Variables

AMATH 352 Lecture 3 MATLAB Tutorial MATLAB (short for MATrix LABoratory) is a very useful piece of software for numerical analysis. It provides an environment for computation and the visualization. Learning

### Beginner s Matlab Tutorial

Christopher Lum lum@u.washington.edu Introduction Beginner s Matlab Tutorial This document is designed to act as a tutorial for an individual who has had no prior experience with Matlab. For any questions

Operators Lecture 2 Mathcad Basics + Addition, - Subtraction, * Multiplication, / Division, ^ Power ( ) Specify evaluation order Order of Operations ( ) ^ highest level, first priority * / next priority

### CD-ROM Appendix E: Matlab

CD-ROM Appendix E: Matlab Susan A. Fugett Matlab version 7 or 6.5 is a very powerful tool useful for many kinds of mathematical tasks. For the purposes of this text, however, Matlab 7 or 6.5 will be used

### Introduction to Matlab

Introduction to Matlab Social Science Research Lab American University, Washington, D.C. Web. www.american.edu/provost/ctrl/pclabs.cfm Tel. x3862 Email. SSRL@American.edu Course Objective This course provides

### How long is the vector? >> length(x) >> d=size(x) % What are the entries in the matrix d?

MATLAB : A TUTORIAL 1. Creating vectors..................................... 2 2. Evaluating functions y = f(x), manipulating vectors. 4 3. Plotting............................................ 5 4. Miscellaneous

### MAT 275 Laboratory 1 Introduction to MATLAB

MAT 275 Laboratory 1 Introduction to MATLAB MATLAB is a computer software commonly used in both education and industry to solve a wide range of problems. This Laboratory provides a brief introduction to

### Introduction. Chapter 1

Chapter 1 Introduction MATLAB (Matrix laboratory) is an interactive software system for numerical computations and graphics. As the name suggests, MATLAB is especially designed for matrix computations:

### MATLAB Functions. function [Out_1,Out_2,,Out_N] = function_name(in_1,in_2,,in_m)

MATLAB Functions What is a MATLAB function? A MATLAB function is a MATLAB program that performs a sequence of operations specified in a text file (called an m-file because it must be saved with a file

### u = [ 2 4 5] has one row with three components (a 3 v = [2 4 5] has three rows separated by semicolons (a 3 w = 2:5 generates the row vector w = [ 2 3

MATLAB Tutorial You need a small numb e r of basic commands to start using MATLAB. This short tutorial describes those fundamental commands. You need to create vectors and matrices, to change them, and

### A Quick Tutorial on MATLAB. Gowtham Bellala

A Quick Tutorial on MATLAB Gowtham Bellala MATLAB MATLAB is a software package for doing numerical computation. It was originally designed for solving linear algebra type problems using matrices. It s

### Differential Equations (Aggregate) Models with MATLAB and Octave A Predator-Prey Example

Differential Equations (Aggregate) Models with MATLAB and Octave A Predator-Prey Example Differential equations in biology are most commonly associated with aggregate models. Aggregate models consider

### a) x 2 8x = 25 x 2 8x + 16 = (x 4) 2 = 41 x = 4 ± 41 x + 1 = ± 6 e) x 2 = 5 c) 2x 2 + 2x 7 = 0 2x 2 + 2x = 7 x 2 + x = 7 2

Solving Quadratic Equations By Square Root Method Solving Quadratic Equations By Completing The Square Consider the equation x = a, which we now solve: x = a x a = 0 (x a)(x + a) = 0 x a = 0 x + a = 0

### Curve Fitting, Loglog Plots, and Semilog Plots 1

Curve Fitting, Loglog Plots, and Semilog Plots 1 In this MATLAB exercise, you will learn how to plot data and how to fit lines to your data. Suppose you are measuring the height h of a seedling as it grows.

### Appendix: Tutorial Introduction to MATLAB

Resampling Stats in MATLAB 1 This document is an excerpt from Resampling Stats in MATLAB Daniel T. Kaplan Copyright (c) 1999 by Daniel T. Kaplan, All Rights Reserved This document differs from the published

### b) lower case always use lower case for all matlab commands. This is what matlab recognizes.

1 Matlab 1) Fundamentals a) Getting Help for more detailed help on any topic, typing help, then a space, and then the matlab command brings up a detailed page on the command or topic. For really difficult

### Using MATLAB to Solve Differential Equations

ECE 350 Linear Systems I MATLAB Tutorial #3 Using MATLAB to Solve Differential Equations This tutorial describes the use of MATLAB to solve differential equations. Two methods are described. The first

### Computational Mathematics with Python

Boolean Arrays Classes Computational Mathematics with Python Basics Olivier Verdier and Claus Führer 2009-03-24 Olivier Verdier and Claus Führer Computational Mathematics with Python 2009-03-24 1 / 40

### Computational Mathematics with Python

Computational Mathematics with Python Basics Claus Führer, Jan Erik Solem, Olivier Verdier Spring 2010 Claus Führer, Jan Erik Solem, Olivier Verdier Computational Mathematics with Python Spring 2010 1

### MATLAB Basics MATLAB numbers and numeric formats

MATLAB Basics MATLAB numbers and numeric formats All numerical variables are stored in MATLAB in double precision floating-point form. (In fact it is possible to force some variables to be of other types

### 3.2. Solving quadratic equations. Introduction. Prerequisites. Learning Outcomes. Learning Style

Solving quadratic equations 3.2 Introduction A quadratic equation is one which can be written in the form ax 2 + bx + c = 0 where a, b and c are numbers and x is the unknown whose value(s) we wish to find.

### Factoring Trinomials: The ac Method

6.7 Factoring Trinomials: The ac Method 6.7 OBJECTIVES 1. Use the ac test to determine whether a trinomial is factorable over the integers 2. Use the results of the ac test to factor a trinomial 3. For

### MATLAB Programming. Problem 1: Sequential

Division of Engineering Fundamentals, Copyright 1999 by J.C. Malzahn Kampe 1 / 21 MATLAB Programming When we use the phrase computer solution, it should be understood that a computer will only follow directions;

### EXCEL SOLVER TUTORIAL

ENGR62/MS&E111 Autumn 2003 2004 Prof. Ben Van Roy October 1, 2003 EXCEL SOLVER TUTORIAL This tutorial will introduce you to some essential features of Excel and its plug-in, Solver, that we will be using

### G563 Quantitative Paleontology. SQL databases. An introduction. Department of Geological Sciences Indiana University. (c) 2012, P.

SQL databases An introduction AMP: Apache, mysql, PHP This installations installs the Apache webserver, the PHP scripting language, and the mysql database on your computer: Apache: runs in the background

### An Introduction to Using Simulink

An Introduction to Using Simulink Eric Peasley, Department of Engineering Science, University of Oxford version 4.0, 2013 An Introduction To Using Simulink. Eric Peasley, Department of Engineering Science,

### Method To Solve Linear, Polynomial, or Absolute Value Inequalities:

Solving Inequalities An inequality is the result of replacing the = sign in an equation with ,, or. For example, 3x 2 < 7 is a linear inequality. We call it linear because if the < were replaced with

This assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the

### MATLAB Workshop 14 - Plotting Data in MATLAB

MATLAB: Workshop 14 - Plotting Data in MATLAB page 1 MATLAB Workshop 14 - Plotting Data in MATLAB Objectives: Learn the basics of displaying a data plot in MATLAB. MATLAB Features: graphics commands Command

### Linear Algebra and TI 89

Linear Algebra and TI 89 Abdul Hassen and Jay Schiffman This short manual is a quick guide to the use of TI89 for Linear Algebra. We do this in two sections. In the first section, we will go over the editing

### Spline Toolbox Release Notes

Spline Toolbox Release Notes Note The Spline Toolbox 3.1 was released in Web-downloadable form after Release 12.1 was released, but before Release 13. The Spline Toolbox 3.1.1 that is part of Release 13

### Functions and Equations

Centre for Education in Mathematics and Computing Euclid eworkshop # Functions and Equations c 014 UNIVERSITY OF WATERLOO Euclid eworkshop # TOOLKIT Parabolas The quadratic f(x) = ax + bx + c (with a,b,c

### Computational Mathematics with Python

Numerical Analysis, Lund University, 2011 1 Computational Mathematics with Python Chapter 1: Basics Numerical Analysis, Lund University Claus Führer, Jan Erik Solem, Olivier Verdier, Tony Stillfjord Spring

### Linear Algebra Notes for Marsden and Tromba Vector Calculus

Linear Algebra Notes for Marsden and Tromba Vector Calculus n-dimensional Euclidean Space and Matrices Definition of n space As was learned in Math b, a point in Euclidean three space can be thought of

### by the matrix A results in a vector which is a reflection of the given

Eigenvalues & Eigenvectors Example Suppose Then So, geometrically, multiplying a vector in by the matrix A results in a vector which is a reflection of the given vector about the y-axis We observe that

### Mth 95 Module 2 Spring 2014

Mth 95 Module Spring 014 Section 5.3 Polynomials and Polynomial Functions Vocabulary of Polynomials A term is a number, a variable, or a product of numbers and variables raised to powers. Terms in an expression

### Visual basic tutorial problems, developed by Dr. Clement,

EXCEL Visual Basic Tutorial Problems (Version January, 2011) Dr. Prabhakar Clement Arthur H. Feagin Distinguished Chair Professor Department of Civil Engineering, Auburn University Home page: http://www.eng.auburn.edu/users/clemept/

### LAYOUT OF THE KEYBOARD

Dr. Charles Hofmann, LaSalle hofmann@lasalle.edu Dr. Roseanne Hofmann, MCCC rhofman@mc3.edu ------------------------------------------------------------------------------------------------- DISPLAY CONTRAST

### WESTMORELAND COUNTY PUBLIC SCHOOLS 2011 2012 Integrated Instructional Pacing Guide and Checklist Computer Math

Textbook Correlation WESTMORELAND COUNTY PUBLIC SCHOOLS 2011 2012 Integrated Instructional Pacing Guide and Checklist Computer Math Following Directions Unit FIRST QUARTER AND SECOND QUARTER Logic Unit

### PGR Computing Programming Skills

PGR Computing Programming Skills Dr. I. Hawke 2008 1 Introduction The purpose of computing is to do something faster, more efficiently and more reliably than you could as a human do it. One obvious point

### MATLAB Tutorial. Chapter 6. Writing and calling functions

MATLAB Tutorial Chapter 6. Writing and calling functions In this chapter we discuss how to structure a program with multiple source code files. First, an explanation of how code files work in MATLAB is

### Course Outline. Mechanical Engineering 309 Numerical Analysis of Engineering Systems

College of Engineering and Computer Science Mechanical Engineering Department Mechanical Engineering 309 Numerical Analysis of Engineering Systems Spring 2014 Number: 15237 Instructor: Larry Caretto Catalog

### MatLab - Systems of Differential Equations

Fall 2015 Math 337 MatLab - Systems of Differential Equations This section examines systems of differential equations. It goes through the key steps of solving systems of differential equations through

### (!' ) "' # "*# "!(!' +,

Normally, when single line commands are entered, MATLAB processes the commands immediately and displays the results. MATLAB is also capable of processing a sequence of commands that are stored in files

### Algebra Unpacked Content For the new Common Core standards that will be effective in all North Carolina schools in the 2012-13 school year.

This document is designed to help North Carolina educators teach the Common Core (Standard Course of Study). NCDPI staff are continually updating and improving these tools to better serve teachers. Algebra

### Introduction to Matrix Algebra I

Appendix A Introduction to Matrix Algebra I Today we will begin the course with a discussion of matrix algebra. Why are we studying this? We will use matrix algebra to derive the linear regression model

### Introduction to Modern Data Acquisition with LabVIEW and MATLAB. By Matt Hollingsworth

Introduction to Modern Data Acquisition with LabVIEW and MATLAB By Matt Hollingsworth Introduction to Modern Data Acquisition Overview... 1 LabVIEW Section 1.1: Introduction to LabVIEW... 3 Section 1.2:

### 0 Introduction to Data Analysis Using an Excel Spreadsheet

Experiment 0 Introduction to Data Analysis Using an Excel Spreadsheet I. Purpose The purpose of this introductory lab is to teach you a few basic things about how to use an EXCEL 2010 spreadsheet to do

### (!' ) "' # "*# "!(!' +,

MATLAB is a numeric computation software for engineering and scientific calculations. The name MATLAB stands for MATRIX LABORATORY. MATLAB is primarily a tool for matrix computations. It was developed

### Introduction to Matrix Algebra

Psychology 7291: Multivariate Statistics (Carey) 8/27/98 Matrix Algebra - 1 Introduction to Matrix Algebra Definitions: A matrix is a collection of numbers ordered by rows and columns. It is customary

### Texas Instruments TI-83, TI-83 Plus Graphics Calculator I.1 Systems of Linear Equations

Part I: Texas Instruments TI-83, TI-83 Plus Graphics Calculator I.1 Systems of Linear Equations I.1.1 Basics: Press the ON key to begin using your TI-83 calculator. If you need to adjust the display contrast,

### Simulation Tools. Python for MATLAB Users I. Claus Führer. Automn 2009. Claus Führer Simulation Tools Automn 2009 1 / 65

Simulation Tools Python for MATLAB Users I Claus Führer Automn 2009 Claus Führer Simulation Tools Automn 2009 1 / 65 1 Preface 2 Python vs Other Languages 3 Examples and Demo 4 Python Basics Basic Operations

### Beginning Matlab Exercises

Beginning Matlab Exercises R. J. Braun Department of Mathematical Sciences University of Delaware 1 Introduction This collection of exercises is inted to help you start learning Matlab. Matlab is a huge

### http://school-maths.com Gerrit Stols

For more info and downloads go to: http://school-maths.com Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It

### Quick Tour of Mathcad and Examples

Fall 6 Quick Tour of Mathcad and Examples Mathcad provides a unique and powerful way to work with equations, numbers, tests and graphs. Features Arithmetic Functions Plot functions Define you own variables

### Introduction to Matlab (Code)

Introduction to Matlab (Code) intro.m Introduction to Matlab (1) Basics The symbol "" is used to indicate a comment (for the remainder of the line). When writing a long Matlab statement that becomes to

### Curve Fitting and Parameter Estimation

Curve Fitting and Parameter Estimation Glenn Lahodny Jr. Spring 2015 1 Least Squares Regression The first step of the modeling process often consists of simply looking at data graphically and trying to

Chapter 7: Additional Topics In this chapter we ll briefly cover selected advanced topics in fortran programming. All the topics come in handy to add extra functionality to programs, but the feature you

### Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704.

Basic Math Refresher A tutorial and assessment of basic math skills for students in PUBP704. The purpose of this Basic Math Refresher is to review basic math concepts so that students enrolled in PUBP704:

### GeoGebra. 10 lessons. Gerrit Stols

GeoGebra in 10 lessons Gerrit Stols Acknowledgements GeoGebra is dynamic mathematics open source (free) software for learning and teaching mathematics in schools. It was developed by Markus Hohenwarter

### MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS. + + x 2. x n. a 11 a 12 a 1n b 1 a 21 a 22 a 2n b 2 a 31 a 32 a 3n b 3. a m1 a m2 a mn b m

MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS 1. SYSTEMS OF EQUATIONS AND MATRICES 1.1. Representation of a linear system. The general system of m equations in n unknowns can be written a 11 x 1 + a 12 x 2 +

### 4. Matrix inverses. left and right inverse. linear independence. nonsingular matrices. matrices with linearly independent columns

L. Vandenberghe EE133A (Spring 2016) 4. Matrix inverses left and right inverse linear independence nonsingular matrices matrices with linearly independent columns matrices with linearly independent rows

### A linear combination is a sum of scalars times quantities. Such expressions arise quite frequently and have the form

Section 1.3 Matrix Products A linear combination is a sum of scalars times quantities. Such expressions arise quite frequently and have the form (scalar #1)(quantity #1) + (scalar #2)(quantity #2) +...

### MATLAB LECTURE NOTES. Dr. ADİL YÜCEL. Istanbul Technical University Department of Mechanical Engineering

MATLAB LECTURE NOTES Dr. ADİL YÜCEL Istanbul Technical University Department of Mechanical Engineering MATLAB LECTURE NOTES Student Name Student ID Dr. ADİL YÜCEL Istanbul Technical University Department

### 2+2 Just type and press enter and the answer comes up ans = 4

Demonstration Red text = commands entered in the command window Black text = Matlab responses Blue text = comments 2+2 Just type and press enter and the answer comes up 4 sin(4)^2.5728 The elementary functions

### Financial Econometrics MFE MATLAB Introduction. Kevin Sheppard University of Oxford

Financial Econometrics MFE MATLAB Introduction Kevin Sheppard University of Oxford October 21, 2013 2007-2013 Kevin Sheppard 2 Contents Introduction i 1 Getting Started 1 2 Basic Input and Operators 5

### 2.1: MATRIX OPERATIONS

.: MATRIX OPERATIONS What are diagonal entries and the main diagonal of a matrix? What is a diagonal matrix? When are matrices equal? Scalar Multiplication 45 Matrix Addition Theorem (pg 0) Let A, B, and

### Linear Programming. March 14, 2014

Linear Programming March 1, 01 Parts of this introduction to linear programming were adapted from Chapter 9 of Introduction to Algorithms, Second Edition, by Cormen, Leiserson, Rivest and Stein [1]. 1

### High School Algebra Reasoning with Equations and Inequalities Solve systems of equations.

Performance Assessment Task Graphs (2006) Grade 9 This task challenges a student to use knowledge of graphs and their significant features to identify the linear equations for various lines. A student

### Simple Programming in MATLAB. Plotting a graph using MATLAB involves three steps:

Simple Programming in MATLAB Plotting Graphs: We will plot the graph of the function y = f(x) = e 1.5x sin(8πx), 0 x 1 Plotting a graph using MATLAB involves three steps: Create points 0 = x 1 < x 2

### Contents. Introduction and Notes pages 2-3 (These are important and it s only 2 pages ~ please take the time to read them!)

Page Contents Introduction and Notes pages 2-3 (These are important and it s only 2 pages ~ please take the time to read them!) Systematic Search for a Change of Sign (Decimal Search) Method Explanation

CHAPTER 1 Introduction to Mathcad Mathcad is a product of MathSoft inc. The Mathcad can help us to calculate, graph, and communicate technical ideas. It lets us work with mathematical expressions using

### Typical Linear Equation Set and Corresponding Matrices

EWE: Engineering With Excel Larsen Page 1 4. Matrix Operations in Excel. Matrix Manipulations: Vectors, Matrices, and Arrays. How Excel Handles Matrix Math. Basic Matrix Operations. Solving Systems of

### Programming in MATLAB

University of Southern Denmark An introductory set of notes Programming in MATLAB Authors: Nicky C. Mattsson Christian D. Jørgensen Web pages: imada.sdu.dk/ nmatt11 imada.sdu.dk/ chjoe11 November 10, 2014

### Running the shell. Tcl/Tk demo. Tcl stuff. Starting Tcl/Tk. If-then-else

Running the shell Tcl/Tk demo Brian Toby Tcl shell = /usr/bin/tclsh (tclsh.exe) Tcl/Tk shell = /usr/bin/wish (wish.exe) As usually distributed requires many extra files Here: combined distribution as one

### USING CASIO CLASSPAD TO ADDRESS SKILLS FOR STAGE 2 MATHS UNITS:

BEFORE BEGINNING: USING CASIO CLASSPAD TO ADDRESS SKILLS FOR STAGE 2 MATHS UNITS: Check Operating Software (OS) version should be 3.03.3000 (or at least 3.02.3000) (Menu, System, System (at top of screen),

### Introduction to Matlab: Application to Electrical Engineering

Introduction to Matlab: Application to Electrical Engineering Houssem Rafik El Hana Bouchekara Umm El Qura University (version 1, Februray 2011) 1 Contents 1 CHAPTER 1... 7 1.1 TUTORIAL LESSONS 1... 7

### 5: Magnitude 6: Convert to Polar 7: Convert to Rectangular

TI-NSPIRE CALCULATOR MENUS 1: Tools > 1: Define 2: Recall Definition --------------- 3: Delete Variable 4: Clear a-z 5: Clear History --------------- 6: Insert Comment 2: Number > 1: Convert to Decimal

### MATH 423 Linear Algebra II Lecture 38: Generalized eigenvectors. Jordan canonical form (continued).

MATH 423 Linear Algebra II Lecture 38: Generalized eigenvectors Jordan canonical form (continued) Jordan canonical form A Jordan block is a square matrix of the form λ 1 0 0 0 0 λ 1 0 0 0 0 λ 0 0 J = 0

### MATH 304 Linear Algebra Lecture 18: Rank and nullity of a matrix.

MATH 304 Linear Algebra Lecture 18: Rank and nullity of a matrix. Nullspace Let A = (a ij ) be an m n matrix. Definition. The nullspace of the matrix A, denoted N(A), is the set of all n-dimensional column

### Math 1050 Khan Academy Extra Credit Algebra Assignment

Math 1050 Khan Academy Extra Credit Algebra Assignment KhanAcademy.org offers over 2,700 instructional videos, including hundreds of videos teaching algebra concepts, and corresponding problem sets. In

### MATHEMATICS FOR ENGINEERING BASIC ALGEBRA

MATHEMATICS FOR ENGINEERING BASIC ALGEBRA TUTORIAL 3 EQUATIONS This is the one of a series of basic tutorials in mathematics aimed at beginners or anyone wanting to refresh themselves on fundamentals.

### Lecture 2 Matrix Operations

Lecture 2 Matrix Operations transpose, sum & difference, scalar multiplication matrix multiplication, matrix-vector product matrix inverse 2 1 Matrix transpose transpose of m n matrix A, denoted A T or

### Linear Dependence Tests

Linear Dependence Tests The book omits a few key tests for checking the linear dependence of vectors. These short notes discuss these tests, as well as the reasoning behind them. Our first test checks

### Matrix Algebra and Applications

Matrix Algebra and Applications Dudley Cooke Trinity College Dublin Dudley Cooke (Trinity College Dublin) Matrix Algebra and Applications 1 / 49 EC2040 Topic 2 - Matrices and Matrix Algebra Reading 1 Chapters

### Elementary Statistics. Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination

Scatter Plot, Regression Line, Linear Correlation Coefficient, and Coefficient of Determination What is a Scatter Plot? A Scatter Plot is a plot of ordered pairs (x, y) where the horizontal axis is used

### Overview of Math Standards

Algebra 2 Welcome to math curriculum design maps for Manhattan- Ogden USD 383, striving to produce learners who are: Effective Communicators who clearly express ideas and effectively communicate with diverse

### Quickstart for Web and Tablet App

Quickstart for Web and Tablet App What is GeoGebra? Dynamic Mathematic Software in one easy-to-use package For learning and teaching at all levels of education Joins interactive 2D and 3D geometry, algebra,

### What are the place values to the left of the decimal point and their associated powers of ten?

The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything

### Math 2400 - Numerical Analysis Homework #2 Solutions

Math 24 - Numerical Analysis Homework #2 Solutions 1. Implement a bisection root finding method. Your program should accept two points, a tolerance limit and a function for input. It should then output

### Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information.

Excel Tutorial Below is a very brief tutorial on the basic capabilities of Excel. Refer to the Excel help files for more information. Working with Data Entering and Formatting Data Before entering data

### MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS

MATRIX ALGEBRA AND SYSTEMS OF EQUATIONS Systems of Equations and Matrices Representation of a linear system The general system of m equations in n unknowns can be written a x + a 2 x 2 + + a n x n b a

### Introduction to MATLAB (Basics) Reference from: Azernikov Sergei mesergei@tx.technion.ac.il

Introduction to MATLAB (Basics) Reference from: Azernikov Sergei mesergei@tx.technion.ac.il MATLAB Basics Where to get help? 1) In MATLAB s prompt type: help, lookfor,helpwin, helpdesk, demos. 2) On the

### Zero: If P is a polynomial and if c is a number such that P (c) = 0 then c is a zero of P.

MATH 11011 FINDING REAL ZEROS KSU OF A POLYNOMIAL Definitions: Polynomial: is a function of the form P (x) = a n x n + a n 1 x n 1 + + a x + a 1 x + a 0. The numbers a n, a n 1,..., a 1, a 0 are called

### 3.1. Solving linear equations. Introduction. Prerequisites. Learning Outcomes. Learning Style

Solving linear equations 3.1 Introduction Many problems in engineering reduce to the solution of an equation or a set of equations. An equation is a type of mathematical expression which contains one or

### Command lookfor followed by a key word (which can be anything and not only a command) gives help related to the key word.

1 Using MatLab Help Command help provides a short description of all functions. For example, to get help on the diary command, type help diary. For more information type help -i diary. Command lookfor

### Summary of important mathematical operations and formulas (from first tutorial):

EXCEL Intermediate Tutorial Summary of important mathematical operations and formulas (from first tutorial): Operation Key Addition + Subtraction - Multiplication * Division / Exponential ^ To enter a

Intro to Excel spreadsheets What are the objectives of this document? The objectives of document are: 1. Familiarize you with what a spreadsheet is, how it works, and what its capabilities are; 2. Using