Introduction to MATLAB (2.29 Spring 06)

Save this PDF as:
 WORD  PNG  TXT  JPG

Size: px
Start display at page:

Download "Introduction to MATLAB (2.29 Spring 06)"

Transcription

1 Introduction to MATLAB (2.29 Spring 06) 1. Assignment of Variables (i.e. scalars, vectors, matrices) 2. Mathematical Operations 3. Built-in Variables and Functions 4. Input/Output Data Files 5. Basic Graphics 6. Functions 7. Decisions 8. Loops (for loops and while loops) 1

2 Built-in Variables and Functions Built-in variables: Variable Meaning ans value of an expression when that expression is not assigned to a variable eps floating-point precision i, j unit imaginary numbers, i=j=sqrt(-1) pi π, realmax largest positive floating-point number realmin smallest positive floating-point number Inf, the result of evaluation 1/0 NaN not a number (i.e. the result of evaluating 0/0) * Although you can assign the values of these built-in variables, it is not a good idea to do so, because they are used by the built-in functions. Built-in functions: Trigonometric: sin - Sine. sind - Sine of argument in degrees. sinh - Hyperbolic sine. asin - Inverse sine. asind - Inverse sine, result in degrees. asinh - Inverse hyperbolic sine. cos - Cosine. cosd - Cosine of argument in degrees. cosh - Hyperbolic cosine. acos - Inverse cosine. acosd - Inverse cosine, result in degrees. acosh - Inverse hyperbolic cosine. tan - Tangent. tand - Tangent of argument in degrees. tanh - Hyperbolic tangent. atan - Inverse tangent. atand - Inverse tangent, result in degrees. atan2 - Four quadrant inverse tangent. Exponential: exp - Exponential. log - Natural logarithm. log10 - Common (base 10) logarithm. log2 - Base 2 logarithm and dissect floating point number. reallog - Natural logarithm of real number. 2

3 realsqrt sqrt nthroot - Square root of number greater than or equal to zero. - Square root. - Real n-th root of real numbers. Complex: abs - Absolute value. angle - Phase angle. complex - Construct complex data from real and imaginary parts. conj - Complex conjugate. imag - Complex imaginary part. real - Complex real part. * To find more built-in elementary mathematical functions, use the help command: >> help elfun ** To find the meaning of a specific function and how to use it, use the help command: >> help function-name (e.g. help sind) 3

4 Input/Output Data Files Export data to a file using save command: save filename save filename variable1 variable2 save filename variable1 variable2 -ascii >> % for example >> clear >> x=[0:10]; y=10*x; >> save xyfile1 %save all variables in xyfile1.mat file >> save xyfile2 x y %save x and y in xyfile2.mat file >> save xyfile3 x y ascii %save x and y in xyfile3 file in ascii format >> >> xy=[x y ] >> save xyfile4 xy -ascii >> type xyfile4 Equivalently to a function form: save( filename, ariable1, variable2 ) >> % for example >> clear >> x=[0:10]; y=10*x; >> save( xyfile5, x, y ) % xyfile5.mat is identical to xyfile2.mat Import data from a file into Matlab using load command: load filename load filename matrixvariable %filename must be in a binary mat file %filename contains only columns of numbers %corresponding to a matrix The syntax of the function form of load : D=load( filename ) If filename is a mat file, the D variable created by this function is a Matlab structure. >> D=load( xyfile2 ) >> D = x: [ ] y: [ ] If filename is a plain text file, the D variable will be a matrix containing all of the data in filename. >> D=load( xyfile3 ) D =

5 Graphics Line plots: Single line: plot(xdata,ydata,symbol) Two lines: plot(xdata1,ydata1,symbol1,xdata2,ydata2,symbol2) Multiple lines: plot(xdata1,ydata1,symbol1,xdata2,ydata2,symbol2, ) symbol is a string constructed from the characters of color and symbol (or line) type. >> clear >> x=[0:20]; y=x.^2; >> plot(x,y) % solid line of x-y curve >> plot(x,y, o ) % x-y curve with open circle at each data point >> plot(x,y, yo ) % x-y curve with yellow open circle at each data point >> plot(x,y, r-- ) % x-y curve with data points connected by red dash line >> plot(x,y, r--,x,-y, yo ) % two curves in one figure >> plot(x,y, r--,x,-y, yo,x,2*y, r*,-x,-3*y, - ) %four curves >> xlabel( time (seconds) ) >> ylable( position (meters) ) >> title( position vs. time ) >> legend( curve1, curve2, curve3, curve4 ) Surface plots Contour plots 5

6 Functions User-defined Matlab functions work just like the built-in functions. The syntax of a userdefined Matlab function is: function [outputparameterlist] = functionname (inputparameterlist) % helpcomments statements outputparameter = value; return where inputparameterlist and outputparameterlist are comma-separated list of variables used to pass data into and out of the function, statements are Matlab statements that compute the value that is assigned to outputparamter. The function M-file should be saved as functionname.m. functionname must also be the same as the name of the file (without the.m ). % for example % sumprod.m function [s,p]=sumprod(x,y) % sumpord computes the sum and element-wise product of x and y s=x+y; p=x.* y; return Primary function vs. subfunctions % for example --- use of subfunctions % sumprod2.m function [s,p]=sumprod2(x,y) % sumpord2 computes the sum and element-wise product of x and y s=sum2(x,y) p=prod2(x,y) return function s2=sum2(x,y) s2=x+y function p2=prod2(x,y) p2=x.* y 6

MATLAB Basics MATLAB numbers and numeric formats

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

More information

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

More information

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

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

More information

Introductory Course to Matlab with Financial Case Studies

Introductory Course to Matlab with Financial Case Studies University of Cyprus Public Business Administration Department Introductory Course to Matlab with Financial Case Studies Prepared by: Panayiotis Andreou PhD Candidate PBA UCY Lefkosia, September 003 Table

More information

MAT 275 Laboratory 1 Introduction to MATLAB

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

More information

Expense Management. Configuration and Use of the Expense Management Module of Xpert.NET

Expense Management. Configuration and Use of the Expense Management Module of Xpert.NET Expense Management Configuration and Use of the Expense Management Module of Xpert.NET Table of Contents 1 Introduction 3 1.1 Purpose of the Document.............................. 3 1.2 Addressees of the

More information

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

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

More information

AIMMS Function Reference - Arithmetic Functions

AIMMS Function Reference - Arithmetic Functions AIMMS Function Reference - Arithmetic Functions This file contains only one chapter of the book. For a free download of the complete book in pdf format, please visit www.aimms.com Aimms 3.13 Part I Function

More information

Lecture 4 Representing Data on the Computer. Ramani Duraiswami AMSC/CMSC 662 Fall 2009

Lecture 4 Representing Data on the Computer. Ramani Duraiswami AMSC/CMSC 662 Fall 2009 Lecture 4 Representing Data on the Computer Ramani Duraiswami AMSC/CMSC 662 Fall 2009 x = ±(1+f) 2 e 0 f < 1 f = (integer < 2 52 )/ 2 52-1022 e 1023 e = integer Effects of floating point Effects of floating

More information

ERDAS Spatial Modeler Language Reference Manual

ERDAS Spatial Modeler Language Reference Manual ERDAS Spatial Modeler Language Reference Manual ERDAS IMAGINE V8.5 ERDAS, Inc. Atlanta, Georgia Copyright 2000 by ERDAS, Inc. All Rights Reserved. Printed in the United States of America. ERDAS Proprietary

More information

A Quick Tutorial on MATLAB. Gowtham Bellala

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

More information

SMART Notebook Math Tools. User s Guide

SMART Notebook Math Tools. User s Guide SMART Notebook Math Tools User s Guide The content of this guide is provided for informational purposes only and is subject to change without notice. Trademark Notice SMART Board, SMART Notebook, the SMART

More information

South Carolina College- and Career-Ready (SCCCR) Pre-Calculus

South Carolina College- and Career-Ready (SCCCR) Pre-Calculus South Carolina College- and Career-Ready (SCCCR) Pre-Calculus Key Concepts Arithmetic with Polynomials and Rational Expressions PC.AAPR.2 PC.AAPR.3 PC.AAPR.4 PC.AAPR.5 PC.AAPR.6 PC.AAPR.7 Standards Know

More information

CD-ROM Appendix E: Matlab

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

More information

Scripting with TCL, Part 1

Scripting with TCL, Part 1 Scripting with TCL, Part 1 Axel Kohlmeyer Center for Molecular Modeling University of Pennsylvania SBS 2007 @ JNCASR, Bangalore The VMD Execution Model GUI (FLTK) Internal State Visualization Python Interpreter

More information

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

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

More information

Graphing Calculator by Mathlab: User Manual

Graphing Calculator by Mathlab: User Manual Graphing Calculator by Mathlab: User Manual INTRODUCTION 4 FEATURES 5 CHAPTER 1: BASICS 6 1.1 Navigation 6 1.2 UI Elements 7 1.3 Keyboard 8 1.4 Input 13 1.5 Workspace Area 16 1.6 Graph Mode 18 1.7 Table

More information

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

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

More information

Precalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES

Precalculus REVERSE CORRELATION. Content Expectations for. Precalculus. Michigan CONTENT EXPECTATIONS FOR PRECALCULUS CHAPTER/LESSON TITLES Content Expectations for Precalculus Michigan Precalculus 2011 REVERSE CORRELATION CHAPTER/LESSON TITLES Chapter 0 Preparing for Precalculus 0-1 Sets There are no state-mandated Precalculus 0-2 Operations

More information

Introduction to MATLAB

Introduction to MATLAB Introduction to MATLAB What is MATLAB? MATLAB ( MATrix LABoratory ) is a tool for numerical computation and visualization. The basic data element is a matrix, so if you need a program that manipulates

More information

Georgia Department of Education Kathy Cox, State Superintendent of Schools 7/19/2005 All Rights Reserved 1

Georgia Department of Education Kathy Cox, State Superintendent of Schools 7/19/2005 All Rights Reserved 1 Accelerated Mathematics 3 This is a course in precalculus and statistics, designed to prepare students to take AB or BC Advanced Placement Calculus. It includes rational, circular trigonometric, and inverse

More information

Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum

Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum Calculus C/Multivariate Calculus Advanced Placement G/T Essential Curriculum UNIT I: The Hyperbolic Functions basic calculus concepts, including techniques for curve sketching, exponential and logarithmic

More information

Version default Titre : Opérateur FORMULE Date : 18/10/2011 Page : 1/5 Responsable : Mathieu COURTOIS Clé : U4.31.

Version default Titre : Opérateur FORMULE Date : 18/10/2011 Page : 1/5 Responsable : Mathieu COURTOIS Clé : U4.31. Titre : Opérateur FORMULE Date : 18/10/2011 Page : 1/5 Operator FORMULATES 1 Goal Defining a formula in actual value or complex from his mathematical statement. The formula will be usable in a further

More information

MATLAB Tutorial. to accompany Partial Differential Equations: Analytical and Numerical Methods, 2 nd edition by Mark S. Gockenbach (SIAM, 2010)

MATLAB Tutorial. to accompany Partial Differential Equations: Analytical and Numerical Methods, 2 nd edition by Mark S. Gockenbach (SIAM, 2010) MATLAB Tutorial to accompany Partial Differential Equations: Analytical and Numerical Methods, 2 nd edition by Mark S. Gockenbach (SIAM, 2) MATLAB Tutorial... Introduction... 3 About this tutorial... 3

More information

Chapter 7 Outline Math 236 Spring 2001

Chapter 7 Outline Math 236 Spring 2001 Chapter 7 Outline Math 236 Spring 2001 Note 1: Be sure to read the Disclaimer on Chapter Outlines! I cannot be responsible for misfortunes that may happen to you if you do not. Note 2: Section 7.9 will

More information

Inverse Circular Function and Trigonometric Equation

Inverse Circular Function and Trigonometric Equation Inverse Circular Function and Trigonometric Equation 1 2 Caution The 1 in f 1 is not an exponent. 3 Inverse Sine Function 4 Inverse Cosine Function 5 Inverse Tangent Function 6 Domain and Range of Inverse

More information

SOME EXCEL FORMULAS AND FUNCTIONS

SOME EXCEL FORMULAS AND FUNCTIONS SOME EXCEL FORMULAS AND FUNCTIONS About calculation operators Operators specify the type of calculation that you want to perform on the elements of a formula. Microsoft Excel includes four different types

More information

Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary)

Prentice Hall Mathematics: Algebra 2 2007 Correlated to: Utah Core Curriculum for Math, Intermediate Algebra (Secondary) Core Standards of the Course Standard 1 Students will acquire number sense and perform operations with real and complex numbers. Objective 1.1 Compute fluently and make reasonable estimates. 1. Simplify

More information

DRAFT. Further mathematics. GCE AS and A level subject content

DRAFT. Further mathematics. GCE AS and A level subject content Further mathematics GCE AS and A level subject content July 2014 s Introduction Purpose Aims and objectives Subject content Structure Background knowledge Overarching themes Use of technology Detailed

More information

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

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

More information

Beginner s Matlab Tutorial

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

More information

WASSCE / WAEC ELECTIVE / FURTHER MATHEMATICS SYLLABUS

WASSCE / WAEC ELECTIVE / FURTHER MATHEMATICS SYLLABUS Visit this link to read the introductory text for this syllabus. 1. Circular Measure Lengths of Arcs of circles and Radians Perimeters of Sectors and Segments measure in radians 2. Trigonometry (i) Sine,

More information

MATHEMATICS CLASS - XII BLUE PRINT - II. (1 Mark) (4 Marks) (6 Marks)

MATHEMATICS CLASS - XII BLUE PRINT - II. (1 Mark) (4 Marks) (6 Marks) BLUE PRINT - II MATHEMATICS CLASS - XII S.No. Topic VSA SA LA TOTAL ( Mark) (4 Marks) (6 Marks). (a) Relations and Functions 4 () 6 () 0 () (b) Inverse trigonometric Functions. (a) Matrices Determinants

More information

Trigonometry Lesson Objectives

Trigonometry Lesson Objectives Trigonometry Lesson Unit 1: RIGHT TRIANGLE TRIGONOMETRY Lengths of Sides Evaluate trigonometric expressions. Express trigonometric functions as ratios in terms of the sides of a right triangle. Use the

More information

Function Name Algebra. Parent Function. Characteristics. Harold s Parent Functions Cheat Sheet 28 December 2015

Function Name Algebra. Parent Function. Characteristics. Harold s Parent Functions Cheat Sheet 28 December 2015 Harold s s Cheat Sheet 8 December 05 Algebra Constant Linear Identity f(x) c f(x) x Range: [c, c] Undefined (asymptote) Restrictions: c is a real number Ay + B 0 g(x) x Restrictions: m 0 General Fms: Ax

More information

MATHEMATICS (CLASSES XI XII)

MATHEMATICS (CLASSES XI XII) MATHEMATICS (CLASSES XI XII) General Guidelines (i) All concepts/identities must be illustrated by situational examples. (ii) The language of word problems must be clear, simple and unambiguous. (iii)

More information

Roots and Coefficients of a Quadratic Equation Summary

Roots and Coefficients of a Quadratic Equation Summary Roots and Coefficients of a Quadratic Equation Summary For a quadratic equation with roots α and β: Sum of roots = α + β = and Product of roots = αβ = Symmetrical functions of α and β include: x = and

More information

SCILAB - Kommandos und Keywords (Auswahl)

SCILAB - Kommandos und Keywords (Auswahl) Download der Freeware http://www.scilab.org/products/scilab/download Einführungen www.fh-htwchur.ch/uploads/media/arbeiten_mit und_scicos_v1_01.pdf www.scilab.org/support/documentation/tutorials Dort:

More information

PTC Mathcad Prime 3.0 Keyboard Shortcuts

PTC Mathcad Prime 3.0 Keyboard Shortcuts PTC Mathcad Prime 3.0 Shortcuts Swedish s Regions Inserting Regions Operator/Command Description Shortcut Swedish Area Inserts a collapsible area you can collapse or expand to toggle the display of your

More information

Algebra and Geometry Review (61 topics, no due date)

Algebra and Geometry Review (61 topics, no due date) Course Name: Math 112 Credit Exam LA Tech University Course Code: ALEKS Course: Trigonometry Instructor: Course Dates: Course Content: 159 topics Algebra and Geometry Review (61 topics, no due date) Properties

More information

Beginning Matlab Exercises

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

More information

Numerical Matrix Analysis

Numerical Matrix Analysis Numerical Matrix Analysis Lecture Notes #10 Conditioning and / Peter Blomgren, blomgren.peter@gmail.com Department of Mathematics and Statistics Dynamical Systems Group Computational Sciences Research

More information

1. Objective. 2. MATLAB Scripting: Input, Process, Output. 3. Analysis and Assistance

1. Objective. 2. MATLAB Scripting: Input, Process, Output. 3. Analysis and Assistance 1. Objective University of Cincinnati Department of Electrical & Computer Engineering and Computer Science 20 ENFD 112 Fundamentals of Programming Laboratory 2: Modeling, Scripting, Visualization Spring

More information

Algebra 2 with Trigonometry. Sample Test #1

Algebra 2 with Trigonometry. Sample Test #1 Algebra with Trigonometry Sample Test # Answer all 9 questions in this eamination. Write your answers to the Part I multiple-choice questions on the separate answer sheet. No partial credit will be allowed

More information

MATHEMATICAL INSTITUTE UNIVERSITY OF OXFORD. Exploring Mathematics with MuPAD

MATHEMATICAL INSTITUTE UNIVERSITY OF OXFORD. Exploring Mathematics with MuPAD MATHEMATICAL INSTITUTE UNIVERSITY OF OXFORD Exploring Mathematics with MuPAD Students Guide Michaelmas Term 2011 by Colin MacDonald y 1 0 0.2 0.3 0.4 0.5 0.6 0.7 x 1 2 3 Version 1.0, October 2010, written

More information

Trigonometric Functions and Equations

Trigonometric Functions and Equations Contents Trigonometric Functions and Equations Lesson 1 Reasoning with Trigonometric Functions Investigations 1 Proving Trigonometric Identities... 271 2 Sum and Difference Identities... 276 3 Extending

More information

Introduction to Matlab

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

More information

SCIENTIFIC CALCULATOR OPERATION GUIDE. <V/R Series>

SCIENTIFIC CALCULATOR OPERATION GUIDE. <V/R Series> SCIENTIFIC CALCULATOR OPERATION GUIDE C O N T EN T S HOW TO OPERATE Read Before Using Key layout/reset switch 2 Display pattern 3 Display format 3 Exponent display 4 Angular unit 5 Function

More information

Estimated Pre Calculus Pacing Timeline

Estimated Pre Calculus Pacing Timeline Estimated Pre Calculus Pacing Timeline 2010-2011 School Year The timeframes listed on this calendar are estimates based on a fifty-minute class period. You may need to adjust some of them from time to

More information

Complex Numbers Basic Concepts of Complex Numbers Complex Solutions of Equations Operations on Complex Numbers

Complex Numbers Basic Concepts of Complex Numbers Complex Solutions of Equations Operations on Complex Numbers Complex Numbers Basic Concepts of Complex Numbers Complex Solutions of Equations Operations on Complex Numbers Identify the number as real, complex, or pure imaginary. 2i The complex numbers are an extension

More information

TI-92 GRAPHING CALCULATOR BASIC OPERATIONS

TI-92 GRAPHING CALCULATOR BASIC OPERATIONS TI-92 GRAPHING CALCULATOR BASIC OPERATIONS by Carolyn Meitler Concordia University Wisconsin B-1 Getting Started Press ON to turn on the calculator. Press 2nd 6 to get the MEMORY screen (shown at the right).

More information

Chapter 5 Polar Coordinates; Vectors 5.1 Polar coordinates 1. Pole and polar axis

Chapter 5 Polar Coordinates; Vectors 5.1 Polar coordinates 1. Pole and polar axis Chapter 5 Polar Coordinates; Vectors 5.1 Polar coordinates 1. Pole and polar axis 2. Polar coordinates A point P in a polar coordinate system is represented by an ordered pair of numbers (r, θ). If r >

More information

Introduction to Numerical Math and Matlab Programming

Introduction to Numerical Math and Matlab Programming Introduction to Numerical Math and Matlab Programming Todd Young and Martin Mohlenkamp Department of Mathematics Ohio University Athens, OH 45701 young@math.ohiou.edu c 2009 - Todd Young and Martin Mohlenkamp.

More information

14.1. Basic Concepts of Integration. Introduction. Prerequisites. Learning Outcomes. Learning Style

14.1. Basic Concepts of Integration. Introduction. Prerequisites. Learning Outcomes. Learning Style Basic Concepts of Integration 14.1 Introduction When a function f(x) is known we can differentiate it to obtain its derivative df. The reverse dx process is to obtain the function f(x) from knowledge of

More information

1 Review of complex numbers

1 Review of complex numbers 1 Review of complex numbers 1.1 Complex numbers: algebra The set C of complex numbers is formed by adding a square root i of 1 to the set of real numbers: i = 1. Every complex number can be written uniquely

More information

Basic Electrical Theory

Basic Electrical Theory Basic Electrical Theory Mathematics Review PJM State & Member Training Dept. Objectives By the end of this presentation the Learner should be able to: Use the basics of trigonometry to calculate the different

More information

With the Tan function, you can calculate the angle of a triangle with one corner of 90 degrees, when the smallest sides of the triangle are given:

With the Tan function, you can calculate the angle of a triangle with one corner of 90 degrees, when the smallest sides of the triangle are given: Page 1 In game development, there are a lot of situations where you need to use the trigonometric functions. The functions are used to calculate an angle of a triangle with one corner of 90 degrees. By

More information

Thinkwell s Homeschool Algebra 2 Course Lesson Plan: 34 weeks

Thinkwell s Homeschool Algebra 2 Course Lesson Plan: 34 weeks Thinkwell s Homeschool Algebra 2 Course Lesson Plan: 34 weeks Welcome to Thinkwell s Homeschool Algebra 2! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson

More information

EXCEL FUNCTIONS MOST COMMON

EXCEL FUNCTIONS MOST COMMON EXCEL FUNCTIONS MOST COMMON This is a list of the most common Functions in Excel with a description. To see the syntax and a more in depth description, the function is a link to the Microsoft Excel site.

More information

Maths Pack. For the University Certificates in Astronomy and Cosmology

Maths Pack. For the University Certificates in Astronomy and Cosmology Maths Pack Distance Learning Mathematics Support Pack For the University Certificates in Astronomy and Cosmology These certificate courses are for your enjoyment. However, a proper study of astronomy or

More information

Quick Tour of Mathcad and Examples

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

More information

General Guide...3. Before Starting Calculation...4

General Guide...3. Before Starting Calculation...4 General Guide...3 Turning on or off...3 Battery replacement...3 Auto power-off function...3 Reset operation...3 Contrast adjustment...3 Display readout...4 Before Starting Calculation...4 Using " MODE

More information

COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015

COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015 COURSE SYLLABUS Pre-Calculus A/B Last Modified: April 2015 Course Description: In this year-long Pre-Calculus course, students will cover topics over a two semester period (as designated by A and B sections).

More information

AMATH 352 Lecture 3 MATLAB Tutorial Starting MATLAB Entering Variables

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

More information

Chapter 5 Functions. Introducing Functions

Chapter 5 Functions. Introducing Functions Chapter 5 Functions 1 Introducing Functions A function is a collection of statements that are grouped together to perform an operation Define a function Invoke a funciton return value type method name

More information

THE COMPLEX EXPONENTIAL FUNCTION

THE COMPLEX EXPONENTIAL FUNCTION Math 307 THE COMPLEX EXPONENTIAL FUNCTION (These notes assume you are already familiar with the basic properties of complex numbers.) We make the following definition e iθ = cos θ + i sin θ. (1) This formula

More information

Introduction. The Aims & Objectives of the Mathematical Portion of the IBA Entry Test

Introduction. The Aims & Objectives of the Mathematical Portion of the IBA Entry Test Introduction The career world is competitive. The competition and the opportunities in the career world become a serious problem for students if they do not do well in Mathematics, because then they are

More information

INTRODUCTION TO MATLAB FOR ENGINEERING STUDENTS

INTRODUCTION TO MATLAB FOR ENGINEERING STUDENTS INTRODUCTION TO MATLAB FOR ENGINEERING STUDENTS David Houcque Northwestern University (version 1.2, August 2005) Contents 1 Tutorial lessons 1 1 1.1 Introduction.................................... 1 1.2

More information

FX 115 MS Training guide. FX 115 MS Calculator. Applicable activities. Quick Reference Guide (inside the calculator cover)

FX 115 MS Training guide. FX 115 MS Calculator. Applicable activities. Quick Reference Guide (inside the calculator cover) Tools FX 115 MS Calculator Handouts Other materials Applicable activities Quick Reference Guide (inside the calculator cover) Key Points/ Overview Advanced scientific calculator Two line display VPAM to

More information

PRE-CALCULUS GRADE 12

PRE-CALCULUS GRADE 12 PRE-CALCULUS GRADE 12 [C] Communication Trigonometry General Outcome: Develop trigonometric reasoning. A1. Demonstrate an understanding of angles in standard position, expressed in degrees and radians.

More information

Final Exam Review: VBA

Final Exam Review: VBA Engineering Fundamentals ENG1100 - Session 14B Final Exam Review: VBA 1 //coe/dfs/home/engclasses/eng1101/f03/ethics/en1.e05.finalcoursewrapup.sxi Final Programming Exam Topics Flowcharts Assigning Variables

More information

Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress

Biggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation

More information

Who Wants to Be a Mathematician: Beginner's Guide for Students

Who Wants to Be a Mathematician: Beginner's Guide for Students Who Wants to Be a Mathematician: Beginner's Guide for Students Copyright Maplesoft, a division of Waterloo Maple Inc. 2013 Contents Preface... v 1 Who Wants to Be a Mathematician: Beginner's Guide for

More information

TI-83 Plus GRAPHING CALCULATOR BASIC OPERATIONS. Carolyn Meitler Concordia University Wisconsin

TI-83 Plus GRAPHING CALCULATOR BASIC OPERATIONS. Carolyn Meitler Concordia University Wisconsin TI-83 Plus GRAPHING CALCULATOR BASIC OPERATIONS by Carolyn Meitler Concordia University Wisconsin B-1 Getting Started Press ON to turn on the calculator. Press 2nd + to get the MEMORY screen (shown at

More information

MATLAB. Input and Output

MATLAB. Input and Output MATLAB Input and Output Dipl.-Ing. Ulrich Wohlfarth Input with user inputs Strings: Row vector of character (char): text = [ This is,, a text! ] String functions: help strfun Input of: Data: variable =

More information

Plotting Polar Curves We continue to study the plotting of polar curves. Recall the family of cardioids shown last time.

Plotting Polar Curves We continue to study the plotting of polar curves. Recall the family of cardioids shown last time. Plotting Polar Curves We continue to study the plotting of polar curves. Recall the family of cardioids shown last time. r = 1 cos(θ) r = 1 + cos(θ) r = 1 + sin(θ) r = 1 sin(θ) Now let us look at a similar

More information

SCIENTIFIC CALCULATOR OPERATION GUIDE. <Write View>

SCIENTIFIC CALCULATOR OPERATION GUIDE. <Write View> SCIENTIFIC CALCULATOR OPERATION GUIDE CONTENTS HOW TO OPERATE Read Before Using Key layout 2 Reset switch/ pattern 3 format and decimal setting function 3-4 Exponent display 4 Angular unit

More information

Introduction to Numerical Methods and Matlab Programming for Engineers

Introduction to Numerical Methods and Matlab Programming for Engineers Introduction to Numerical Methods and Matlab Programming for Engineers Todd Young and Martin J. Mohlenkamp Department of Mathematics Ohio University Athens, OH 45701 youngt@ohio.edu May 5, 2015 ii Copyright

More information

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks

Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Thnkwell s Homeschool Precalculus Course Lesson Plan: 36 weeks Welcome to Thinkwell s Homeschool Precalculus! We re thrilled that you ve decided to make us part of your homeschool curriculum. This lesson

More information

Contents. 1 Engineering Problem Solving 1. 1.1 Problem-SolvingProcess... 1. 1.2 ProblemSolvingExample... 4. 1.3 Computing Software...

Contents. 1 Engineering Problem Solving 1. 1.1 Problem-SolvingProcess... 1. 1.2 ProblemSolvingExample... 4. 1.3 Computing Software... Contents 1 Engineering Problem Solving 1 1.1 Problem-SolvingProcess... 1 1.2 ProblemSolvingExample... 4 1.3 Computing Software.... 8 1.4 Computing Terminology...... 12 2 Matlab Technical Computing Environment

More information

28 CHAPTER 1. VECTORS AND THE GEOMETRY OF SPACE. v x. u y v z u z v y u y u z. v y v z

28 CHAPTER 1. VECTORS AND THE GEOMETRY OF SPACE. v x. u y v z u z v y u y u z. v y v z 28 CHAPTER 1. VECTORS AND THE GEOMETRY OF SPACE 1.4 Cross Product 1.4.1 Definitions The cross product is the second multiplication operation between vectors we will study. The goal behind the definition

More information

Kerby Shedden October, 2007. Overview of R

Kerby Shedden October, 2007. Overview of R Kerby Shedden October, 2007 Overview of R R R is a programming language for statistical computing, data analysis, and graphics. It is a re-implementation of the S language, which was developed in the 1980

More information

Mathematics Pre-Test Sample Questions A. { 11, 7} B. { 7,0,7} C. { 7, 7} D. { 11, 11}

Mathematics Pre-Test Sample Questions A. { 11, 7} B. { 7,0,7} C. { 7, 7} D. { 11, 11} Mathematics Pre-Test Sample Questions 1. Which of the following sets is closed under division? I. {½, 1,, 4} II. {-1, 1} III. {-1, 0, 1} A. I only B. II only C. III only D. I and II. Which of the following

More information

Euler s Formula Math 220

Euler s Formula Math 220 Euler s Formula Math 0 last change: Sept 3, 05 Complex numbers A complex number is an expression of the form x+iy where x and y are real numbers and i is the imaginary square root of. For example, + 3i

More information

MATLAB Tutorial for Calculus III - Part 1

MATLAB Tutorial for Calculus III - Part 1 MATLAB Tutorial for Calculus III - Part 1 Contents 1 Introduction to MATLAB 1 1.1 Logging into the system...... 2 1.2 Starting out with MATLAB.... 2 2 MATLAB as scientific calculator 3 2.1 Introduction

More information

COMPLEX NUMBERS. a bi c di a c b d i. a bi c di a c b d i For instance, 1 i 4 7i 1 4 1 7 i 5 6i

COMPLEX NUMBERS. a bi c di a c b d i. a bi c di a c b d i For instance, 1 i 4 7i 1 4 1 7 i 5 6i COMPLEX NUMBERS _4+i _-i FIGURE Complex numbers as points in the Arg plane i _i +i -i A complex number can be represented by an expression of the form a bi, where a b are real numbers i is a symbol with

More information

Pre-Calculus II. where 1 is the radius of the circle and t is the radian measure of the central angle.

Pre-Calculus II. where 1 is the radius of the circle and t is the radian measure of the central angle. Pre-Calculus II 4.2 Trigonometric Functions: The Unit Circle The unit circle is a circle of radius 1, with its center at the origin of a rectangular coordinate system. The equation of this unit circle

More information

The OptQuest Engine Java and.net Developer's Guilde

The OptQuest Engine Java and.net Developer's Guilde The OptQuest Engine Java and.net Developer's Guilde Table Of Contents Introduction to optimization... 1 What is optimization?... 1 How the OptQuest Engine works... 1 Using the documentation... 2 Platforms...

More information

MATLAB Primer. R2015b

MATLAB Primer. R2015b MATLAB Primer R25b How to Contact MathWorks Latest news: www.mathworks.com Sales and services: www.mathworks.com/sales_and_services User community: www.mathworks.com/matlabcentral Technical support: www.mathworks.com/support/contact_us

More information

Dear Accelerated Pre-Calculus Student:

Dear Accelerated Pre-Calculus Student: Dear Accelerated Pre-Calculus Student: I am very excited that you have decided to take this course in the upcoming school year! This is a fastpaced, college-preparatory mathematics course that will also

More information

TWO-DIMENSIONAL TRANSFORMATION

TWO-DIMENSIONAL TRANSFORMATION CHAPTER 2 TWO-DIMENSIONAL TRANSFORMATION 2.1 Introduction As stated earlier, Computer Aided Design consists of three components, namely, Design (Geometric Modeling), Analysis (FEA, etc), and Visualization

More information

Unit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook

Unit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook Unit 7: Right Triangles and Trigonometry Lesson 7.1 Use Inequalities in a Triangle Lesson 5.5 from textbook Objectives Use the triangle measurements to decide which side is longest and which angle is largest.

More information

2 Complex Functions and the Cauchy-Riemann Equations

2 Complex Functions and the Cauchy-Riemann Equations 2 Complex Functions and the Cauchy-Riemann Equations 2.1 Complex functions In one-variable calculus, we study functions f(x) of a real variable x. Likewise, in complex analysis, we study functions f(z)

More information

Mathematical Procedures

Mathematical Procedures CHAPTER 6 Mathematical Procedures 168 CHAPTER 6 Mathematical Procedures The multidisciplinary approach to medicine has incorporated a wide variety of mathematical procedures from the fields of physics,

More information

Fortran 90/95 Programming Manual

Fortran 90/95 Programming Manual Fortran 90/95 Programming Manual fifth revision (2005) Tanja van Mourik Chemistry Department University College London Copyright: Tanja van Mourik Fortran 90/95 Programming Manual Brief History of Fortran

More information

Content. Chapter 4 Functions 61 4.1 Basic concepts on real functions 62. Credits 11

Content. Chapter 4 Functions 61 4.1 Basic concepts on real functions 62. Credits 11 Content Credits 11 Chapter 1 Arithmetic Refresher 13 1.1 Algebra 14 Real Numbers 14 Real Polynomials 19 1.2 Equations in one variable 21 Linear Equations 21 Quadratic Equations 22 1.3 Exercises 28 Chapter

More information

* * MATHEMATICS (MEI) 4756 Further Methods for Advanced Mathematics (FP2) ADVANCED GCE. Monday 10 January 2011 Morning

* * MATHEMATICS (MEI) 4756 Further Methods for Advanced Mathematics (FP2) ADVANCED GCE. Monday 10 January 2011 Morning ADVANCED GCE MATHEMATICS (MEI) 4756 Further Methods for Advanced Mathematics (FP) Candidates answer on the answer booklet. OCR supplied materials: 8 page answer booklet (sent with general stationery) MEI

More information

MEMORANDUM. All students taking the CLC Math Placement Exam PLACEMENT INTO CALCULUS AND ANALYTIC GEOMETRY I, MTH 145:

MEMORANDUM. All students taking the CLC Math Placement Exam PLACEMENT INTO CALCULUS AND ANALYTIC GEOMETRY I, MTH 145: MEMORANDUM To: All students taking the CLC Math Placement Eam From: CLC Mathematics Department Subject: What to epect on the Placement Eam Date: April 0 Placement into MTH 45 Solutions This memo is an

More information

DEFINITION 5.1.1 A complex number is a matrix of the form. x y. , y x

DEFINITION 5.1.1 A complex number is a matrix of the form. x y. , y x Chapter 5 COMPLEX NUMBERS 5.1 Constructing the complex numbers One way of introducing the field C of complex numbers is via the arithmetic of matrices. DEFINITION 5.1.1 A complex number is a matrix of

More information

Week 13 Trigonometric Form of Complex Numbers

Week 13 Trigonometric Form of Complex Numbers Week Trigonometric Form of Complex Numbers Overview In this week of the course, which is the last week if you are not going to take calculus, we will look at how Trigonometry can sometimes help in working

More information