ECE 102 Engineering Computation
|
|
- Jeffery Houston
- 5 years ago
- Views:
Transcription
1 ECE 102 Engineering Computation Phillip Wong MATLAB XY Plots with Linear-Linear Scaling Formatting Plots XY Plots with Logarithmic Scaling Multiple Plots Printing and Saving Plots
2 Introduction to 2D Graphs MATLAB supports 2D and 3D graphs for visualizing data sets. Available 2D graph types include: XY Scatter Stem Line Pie Histogram Bar Polar Contour There are extensive options for customizing the appearance of a graph. 1
3 XY Plots with Linear-Linear Scaling Linear XY plots: plot(x,y) The axes are linear in both xand y. xand yare vectors of the same length. x contains the independent data values. y contains the dependent data values. The plot appears in the Figure Window. 2
4 Enhanced plot command: plot(x,y,'propertyname',value) -orplot(x,y,'specifiers') PropertyName, Value set individual line and marker properties (e.g., style, color). Specifiersquickly define line and marker properties in a single string. XY plot with primary and secondary Y axes: plotyy(x1,y1,x2,y2) 3
5 Line Property Names: LineStyle LineWidth Color Value Description Color 'b' 'r' blue (default) red Style Value '-' '--' ':' '-.' 'none' Description solid (default) dashed dotted dash-dot no line 'g' 'c' 'm' 'y' 'k' 'w' green cyan magenta yellow black white Width Value Description 1 thinnest (default) 2 to 100 thicker line [R,G,B] R = Red (0 to 1) G = Green (0 to 1) B = Blue (0 to 1) 4
6 Marker Property Names: Marker MarkerSize MarkerEdgeColor MarkerFaceColor Marker size is an integer starting at 1. Marker color values are the same as the line color values. Marker Value '+' 'o' '*' '.' 'x' 's' 'd' '^' 'v' '>' '<' 'p' 'h' Description plus sign circle asterisk point cross square diamond triangle-up triangle-down triangle-right triangle-left 5-point star 6-point star 5
7 Example: x = -2*pi:pi/24:2*pi; y = sinc(x); plot(x,y) Blue solid line, no markers plot(x,y,'linestyle',':','color','r') Red dotted line, no markers plot(x,y,':r') Red dotted line, no markers plot(x,y,'om') plot(x,y,'-sk') No line, magenta circle markers Black solid line, black square markers 6
8 plot(x,y) plot(x,y,'linestyle',':','color','r') -orplot(x,y,':r') 7
9 plot(x,y,'om') plot(x,y,'-sk') 8
10 Formatting Plots Clear Figure clf Erases the Figure window New Figure figure(n) Opens a new figure window (index n) (optional if only one figure needed) Axis Grid Lines grid on Adds major grid lines grid minor Toggles minor grid lines grid off Removes all grid lines 9
11 Axis Limits axis([xmin xmax ymin ymax]) xmin xmax ymaxorymin yminorymax Note: Limits are specified in a vector. All four limits must be present. If a particular limit is specified as +inf or inf, then its value is autoset. Variations: axis auto axis xy axis ij Sets both axes limits automatically Sets origin to lower left corner Sets origin to upper left corner 10
12 Axis Labels xlabel('x axis text string') ylabel('y axis text string') Title title('one line text string') title({'two lines', 'of text'}) brace comma Text Box text(xpos,ypos,'text string') brace Note: xposand yposare coordinates relative to the graph s origin where the text should appear. 11
13 Greek characters and subscripts/superscripts can be displayed in text by embedding special sequences in the string. Symbol Sequence Symbol Sequence Symbol Sequence α \alpha ρ \rho ϒ \Upsilon β \beta σ \sigma Φ \Phi γ \gamma τ \tau Ψ \Psi δ \delta υ \upsilon Ω \Omega ɛ \epsilon φ \phi ζ \zeta χ \chi η \eta ψ \psi θ \theta ω \omega ι \iota Γ \Gamma κ \kappa Δ \Delta λ \lambda Θ \Theta µ \mu Λ \Lambda ν \nu Ξ \Xi ξ \xi Π \Pi Subscript _{text} π \pi Σ \Sigma Superscript ^{text} 12
14 Text Font Property Names: FontName FontSize FontAngle FontWeight Name Value Description Angle Value Description 'Helvetica' 'Times' 'Courier' 'FixedWidth' Helvetica font Times font Courier font Localized fixed font 'normal' 'italic' 'oblique' normal (default) slanted font slanted font Size Value Description 1 to 128 font point size Weight Value 'normal' 'demi' 'bold' Description normal (default) bold font bold font 13
15 Example: Plot 2 α 0 = e where 20 α 0 5 I g 2 Before formatting % Initialize data alpha_0 = -20:0.1:5; Ig = 2 * exp(-alpha_0.^2); % Basic plot clf plot(alpha_0, Ig) % Formatting axis([ ]) title('graph of y = 2exp(-\alpha_{0}^{2})',... 'FontName', 'Helvetica', 'FontSize', 14) xlabel('position \alpha_{0} (mm)', 'FontWeight', 'Bold') ylabel('intensity I_g (mw/mm^2)') text(0.3, 2, 'Peak value') 14
16 After formatting 15
17 XY Plots with Logarithmic Scaling XY plots with at least one log scale: semilogx(x,y) semilogy(x,y) loglog(x,y) log x, linear y linear x, log y log x, log y xand yare vectors of the same length. x contains the independent data values. y contains the dependent data values. 16
18 Example: Plot y = e x for 0 x 10. Try different scales. x = 1:10; y = exp(x); figure(1) plot(x,y,'-^','markerfacecolor','red'); grid on xlabel('x'); ylabel('y=exp(x)'); title('linear Scales') figure(2) semilogy(x,y,'-^','markerfacecolor','green'); grid on xlabel('x'); ylabel('y=exp(x)'); title('semilogy Scales') 17
19 18
20 Multiple Lines in the Same Plot Method #1: plot command plot(x1,y1,'spec',x2,y2,'spec', ) All the lines are overlaid on the same plot. Each line can have its own specifiers. 19
21 Adding a Legend legend('str1','str2', ) Variations: legend('str','location', Loc_Value) Loc_Value is a predefined value that puts the legend at a specific location on the plot. legend('off') legend('show') legend('boxoff') legend('boxon') Turn off legend Show legend Remove box from legend Add box around legend 20
22 Allowed legend location values: Location Value Description Location Value Description 'North' Inside top 'EastOutside' Outside right 'South' Inside bottom 'WestOutside' Outside left 'East' Inside right 'NorthEastOutside' Outside top right 'West' Inside left 'NorthWestOutside' Outside top left 'NorthEast' Inside top right 'SouthEastOutside' Outside bottom right 'NorthWest' Inside top left 'SouthWestOutside' Outside bottom left 'SouthEast' Inside bottom right 'Best' Least conflict 'SouthWest' Inside bottom left 'BestOutside' Least unused space 'NorthOutside' Outside top 'SouthOutside' Outside bottom 21
23 Example: Plot y 1 = 3x 3-26x + 10, y 2 = 9x 2-26, and y 3 = 18x over the interval-2 x 4. x = -2:0.01:4; y1 = 3*x.^3-26*x+10; y2 = 9*x.^2-26; y3 = 18*x; plot(x,y1,'-b', x,y2,'--r', x,y3,':k') xlabel('x') ylabel('y and its derivatives') title('multiple Graphs plot()') 22
24 23
25 Method #2: hold command hold on Each new plot command adds a graph that is overlaid on the current graph (Place this after the first plot command) hold off Turns off hold mode, so each plot command creates a new graph 24
26 Example: Plot sin(2πt) and cos(2πt) on the same graph over the interval -π t +π. t = -pi:0.01:pi; y1 = sin(2*pi*t); y2 = cos(2*pi*t); plot(t,y1,'r') axis([-pi pi ]) hold on plot(t,y2,':b') title('multiple Graphs - hold') xlabel('time (seconds)') ylabel('amplitude (Volts)') legend('sin','cos','location','northeastoutside') hold off 25
27 26
28 Example: VD = 0.6:0.005:0.8; % V : Applied diode voltage k = e-23; % J/K : Boltzmann's constant q = e-19; % C : Electric charge IS = 1.0e-12; % A : Reverse saturation current I1 = IS * (exp(vd / (k*250/q)) - 1); % A : Diode T = 250 K I2 = IS * (exp(vd / (k*255/q)) - 1); % A : Diode T = 255 K I3 = IS * (exp(vd / (k*260/q)) - 1); % A : Diode T = 260 K clf grid on plot(vd,i1,'r','linewidth',2) axis([ e3]) hold on plot(vd,i2,'--m','linewidth',2) plot(vd,i3,':b','linewidth',2) xlabel('applied diode voltage V_{D} (V)','FontSize',12) ylabel('diode current I_{D} (A)','FontSize',12) title({'dependence of diode current on temperature T',... 'Parameters: I_{S} = 1 pa, Ideality factor \eta = 1'},... 'FontSize',14) legend('t=250 K','T=255 K','T=260K','Location','Best') hold off I( V D ) = I S e V D kt q 1 27
29 28
30 Method #3: line command line(x,y,'propertyname',value) Adds an additional line to a pre-existing plot. 29
31 Example: Plot y 1 = x, y 2 = x 2, and y 3 = x 3 over -2 x 2. x = -2:0.01:2; y1 = x; y2 = x.^2; y3 = x.^3; plot(x,y1,'linestyle','-','color','r','linewidth',1) line(x,y2,'linestyle','--','color','c','linewidth',2) line(x,y3,'linestyle',':','color','m','linewidth',3) xlabel('x'); ylabel('powers of y') title('multiple Graphs line()') 30
32 31
33 Multiple Plots on the Same Page subplot command subplot(m,n,k) Places the plot as a tile at position kon an m ngrid Example: 2 2 grid: (2,2,1) (2,2,2) (2,2,3) (2,2,4) 2 3 grid: (2,3,1) (2,3,2) (2,3,3) (2,3,4) (2,3,5) (2,3,6) 32
34 Example: Plot y 1 = x 2 and y 2 = x sin(4x) as 1 2 tiled graphs over the interval 0 x 10. x = 0:0.1:10; y1 = x.^2; y2 = x.*sin(4*x); subplot(1,2,1); plot(x,y1,'--') xlabel('x'); ylabel('y1=x^2') title('tile 1 subplot(1,2,1)') subplot(1,2,2); plot(x,y2,':') xlabel('x'); ylabel('y2=xsin(4x)') title('tile 2 subplot(1,2,2)') 33
35 34
36 Printing and Saving Plots To send the current plot to the printer: print To save the current plot to an image file: print dtype filename type = ps, psc, eps, epsc, tiff, jpeg, png Example: print djpeg myplot Image files are saved to the current directory. 35
COMP MATLAB.
COMP1131 MATLAB chenyang@fudan.edu.cn 1 2 (x, y ) [(x 1,y 1 ) (x 2,y 2 ) (x n,y n )] Y=f(X) X [x 1,x 2,...,x n ] Y [y 1,y 2,,y n ] 3 MATLAB 4 figure figure figure(n): n figure(n) 5 y = x + sin x (x [ π
More informationMathematics Review Exercises. (answers at end)
Brock University Physics 1P21/1P91 Mathematics Review Exercises (answers at end) Work each exercise without using a calculator. 1. Express each number in scientific notation. (a) 437.1 (b) 563, 000 (c)
More informationEntities for Symbols and Greek Letters
Entities for Symbols and Greek Letters The following table gives the character entity reference, decimal character reference, and hexadecimal character reference for symbols and Greek letters, as well
More informationContents. basic algebra. Learning outcomes. Time allocation. 1. Mathematical notation and symbols. 2. Indices. 3. Simplification and factorisation
basic algebra Contents. Mathematical notation and symbols 2. Indices 3. Simplification and factorisation 4. Arithmetic of algebraic fractions 5. Formulae and transposition Learning outcomes In this workbook
More informationT m / A. Table C2 Submicroscopic Masses [2] Symbol Meaning Best Value Approximate Value
APPENDIX C USEFUL INFORMATION 1247 C USEFUL INFORMATION This appendix is broken into several tables. Table C1, Important Constants Table C2, Submicroscopic Masses Table C3, Solar System Data Table C4,
More information1 Integration of Rational Functions Using Partial Fractions
MTH Fall 008 Essex County College Division of Mathematics Handout Version 4 September 8, 008 Integration of Rational Functions Using Partial Fractions In the past it was far more usual to simplify or combine
More informationCSSS/STAT/SOC 321 Case-Based Social Statistics I. Levels of Measurement
CSSS/STAT/SOC 321 Case-Based Social Statistics I Levels of Measurement Christopher Adolph Department of Political Science and Center for Statistics and the Social Sciences University of Washington, Seattle
More informationAP Physics 1 Summer Assignment. Directions: Find the following. Final answers should be in scientific notation. 2.)
AP Physics 1 Summer Assignment DUE THE FOURTH DAY OF SCHOOL- 2018 Purpose: The purpose of this packet is to make sure that we all have a common starting point and understanding of some of the basic concepts
More informationQuantum Mechanics for Scientists and Engineers. David Miller
Quantum Mechanics for Scientists and Engineers David Miller Background mathematics Basic mathematical symbols Elementary arithmetic symbols Equals Addition or plus 3 5 Subtraction, minus or less 3 or Multiplication
More informationOutline. Logic. Definition. Theorem (Gödel s Completeness Theorem) Summary of Previous Week. Undecidability. Unification
Logic Aart Middeldorp Vincent van Oostrom Franziska Rapp Christian Sternagel Department of Computer Science University of Innsbruck WS 2017/2018 AM (DCS @ UIBK) week 11 2/38 Definitions elimination x φ
More informationPhysics 241 Class #10 Outline (9/25/2013) Plotting Handle graphics Numerical derivatives and functions Next time numerical integrals
Physics 241 Class #10 Outline (9/25/2013) Plotting Handle graphics Numerical derivatives and functions Next time numerical integrals Announcements HW4 grades are up. HW5a HW5 revised Same problems, now
More informationUKMT Junior Mentoring Scheme Notes
UKMT Junior Mentoring Scheme Notes. Even, odd and prime numbers If a sum or difference of a pair of numbers is even, then both numbers are even or both are odd. To get an odd sum, one must be even and
More informationGRAPHIC WEEK 7 DR. USMAN ULLAH SHEIKH DR. MUSA MOHD MOKJI DR. MICHAEL TAN LOONG PENG DR. AMIRJAN NAWABJAN DR. MOHD ADIB SARIJARI
GRAPHIC SKEE1022 SCIENTIFIC PROGRAMMING WEEK 7 DR. USMAN ULLAH SHEIKH DR. MUSA MOHD MOKJI DR. MICHAEL TAN LOONG PENG DR. AMIRJAN NAWABJAN DR. MOHD ADIB SARIJARI 1 OBJECTIVE 2-dimensional line plot function
More informationGeneral Physics. Prefixes. Aims: The Greek Alphabet Units. Provided Data
General Physics Aims: The Greek Alphabet Units Prefixes Provided Data Name Upper Case Lower Case The Greek Alphabet When writing equations and defining terms, letters from the Greek alphabet are often
More information2D Plotting with Matlab
GEEN 1300 Introduction to Engineering Computing Class Meeting #22 Monday, Nov. 9 th Engineering Computing and Problem Solving with Matlab 2-D plotting with Matlab Script files User-defined functions Matlab
More informationUsing Structural Equation Modeling to Conduct Confirmatory Factor Analysis
Using Structural Equation Modeling to Conduct Confirmatory Factor Analysis Advanced Statistics for Researchers Session 3 Dr. Chris Rakes Website: http://csrakes.yolasite.com Email: Rakes@umbc.edu Twitter:
More informationTwo Mathematical Constants
1 Two Mathematical Constants Two of the most important constants in the world of mathematics are π (pi) and e (Euler s number). π = 3.14159265358979323846264338327950288419716939937510... e = 2.71828182845904523536028747135266249775724709369995...
More informationIntroductory Unit for A Level Physics
Introductory Unit for A Level Physics Name: 1 Physics Year 12 Induction Objectives: To give you the skills needed for the successful study of Physics at A level. To help you to identify areas in which
More informationThese variables have specific names and I will be using these names. You need to do this as well.
Greek Letters In Physics, we use variables to denote a variety of unknowns and concepts. Many of these variables are letters of the Greek alphabet. If you are not familiar with these letters, you should
More informationor R n +, R n ++ etc.;
Mathematical Prerequisites for Econ 7005, Microeconomic Theory I, and Econ 7007, Macroeconomic Theory I, at the University of Utah by Gabriel A Lozada The contents of Sections 1 6 below are required for
More information. var save filename var. y fprintf(fl,'%f %f\n',y) y ..TXT. . fprintf() .TXT. myf = fopen('nam.txt','w'); nam.txt myf.
y fprintf(fl,'%f %f\n',y) y. \n.txt. fprintf()..txt.. myf = fopen('nam.txt','w'); :. (1-4 )..TXT. % Optt.m av =[17.4537 4.57 15.3 17.869 3.7]; Tit = 'Students Average:'; myf = fopen('nam.txt','w'); fprintf(myf,'%s\n',tit);
More informationMI&CCMIllILIL&JN CHEMISTRY
MI&CCMIllILIL&JN IQ)llCClrll(Q)JN&IRl)1 @IF CHEMISTRY MACCMIIJ1J1A~ JTI)nCClln@~Aill)! (Q)]F CHEMISTRY D.B. HIBBERT & A.M. JAMES M MACMILLAN REFERENCE BOOKS The Macmillan Press Ltd, 1987 All rights reserved.
More informationMatlab for Review. NDSU Matlab Review pg 1
NDSU Matlab Review pg 1 Becoming familiar with MATLAB The console The editor The graphics windows The help menu Saving your data (diary) General environment and the console Matlab for Review Simple numerical
More informationFLUIDS Problem Set #3 SOLUTIONS 10/27/ v y = A A = 0. + w z. Y = C / x
FLUIDS 2009 Problem Set #3 SOLUTIONS 10/27/2009 1.i. The flow is clearly incompressible because iu = u x + v y + w z = A A = 0 1.ii. The equation for a streamline is dy dx = Y. Guessing a solution of the
More informationName: AST 114 Date: THE DEEP SKY
Name: AST 114 Date: THE DEEP SKY The purpose of this lab is to familiarize the student with the use of the planisphere, sky atlas, and coordinate systems for the night sky and introduce the student to
More informationEssential Maths 1. Macquarie University MAFC_Essential_Maths Page 1 of These notes were prepared by Anne Cooper and Catriona March.
Essential Maths 1 The information in this document is the minimum assumed knowledge for students undertaking the Macquarie University Masters of Applied Finance, Graduate Diploma of Applied Finance, and
More informationIntroduction to MatLab
Introduction to MatLab 1 Introduction to MatLab Graduiertenkolleg Kognitive Neurobiologie Friday, 05 November 2004 Thuseday, 09 Novemer 2004 Kurt Bräuer Institut für Theoretische Physik, Universität Tübingen
More informationThe statmath package
The statmath package Sebastian Ankargren sebastian.ankargren@statistics.uu.se March 8, 2018 Abstract Applied and theoretical papers in statistics usually contain a number of notational conventions which
More informationComputational Foundations of Cognitive Science
Computational Foundations of Cognitive Science Lecture 14: Inverses and Eigenvectors in Matlab; Plotting and Graphics Frank Keller School of Informatics University of Edinburgh keller@inf.ed.ac.uk February
More informationEEM Simple use of Matlab
EEM 123 - Simple use of Matlab 0) Starting Matlab and basic operations Matlab is a powerful engineering tool, specifically designed to allow engineers to make simulations closest to the real world while
More informationHow to Make or Plot a Graph or Chart in Excel
This is a complete video tutorial on How to Make or Plot a Graph or Chart in Excel. To make complex chart like Gantt Chart, you have know the basic principles of making a chart. Though I have used Excel
More informationCZECHOSLOVAK JOURNAL OF PHYSICS. Instructions for authors
CZECHOSLOVAK JOURNAL OF PHYSICS Instructions for authors The Czechoslovak Journal of Physics is published monthly. It comprises original contributions, both regular papers and letters, as well as review
More informationRun bayesian parameter estimation
Matlab: R11a IRIS: 8.11519 Run bayesian parameter estimation [estimate_params.m] by Jaromir Benes May 11 Introduction In this m-le, we use bayesian methods to estimate some of the parameters. First, we
More informationLab 2: Static Response, Cantilevered Beam
Contents 1 Lab 2: Static Response, Cantilevered Beam 3 1.1 Objectives.......................................... 3 1.2 Scalars, Vectors and Matrices (Allen Downey)...................... 3 1.2.1 Attribution.....................................
More informationAQA 7407/7408 MEASUREMENTS AND THEIR ERRORS
AQA 7407/7408 MEASUREMENTS AND THEIR ERRORS Year 12 Physics Course Preparation 2018 Name: Textbooks will be available from the school library in September They are AQA A level Physics Publisher: Oxford
More informationAn Introduction to MatLab
Introduction to MatLab 1 An Introduction to MatLab Contents 1. Starting MatLab... 3 2. Workspace and m-files... 4 3. Help... 5 4. Vectors and Matrices... 5 5. Objects... 8 6. Plots... 10 7. Statistics...
More informationJoy Allen. March 12, 2015
LATEX Newcastle University March 12, 2015 Why use L A TEX? Extremely useful tool for writing scientific papers, presentations and PhD Thesis which are heavily laden with mathematics You get lovely pretty
More informationHOMEWORK 3: Phase portraits for Mathmatical Models, Analysis and Simulation, Fall 2010 Report due Mon Oct 4, Maximum score 7.0 pts.
HOMEWORK 3: Phase portraits for Mathmatical Models, Analysis and Simulation, Fall 2010 Report due Mon Oct 4, 2010. Maximum score 7.0 pts. Three problems are to be solved in this homework assignment. The
More informationJanuary 18, 2008 Steve Gu. Reference: Eta Kappa Nu, UCLA Iota Gamma Chapter, Introduction to MATLAB,
Introduction to MATLAB January 18, 2008 Steve Gu Reference: Eta Kappa Nu, UCLA Iota Gamma Chapter, Introduction to MATLAB, Part I: Basics MATLAB Environment Getting Help Variables Vectors, Matrices, and
More informationHomework 1 Solutions
18-9 Signals and Systems Profs. Byron Yu and Pulkit Grover Fall 18 Homework 1 Solutions Part One 1. (8 points) Consider the DT signal given by the algorithm: x[] = 1 x[1] = x[n] = x[n 1] x[n ] (a) Plot
More informationAssignment 1b: due Tues Nov 3rd at 11:59pm
n Today s Lecture: n n Vectorized computation Introduction to graphics n Announcements:. n Assignment 1b: due Tues Nov 3rd at 11:59pm 1 Monte Carlo Approximation of π Throw N darts L L/2 Sq. area = N =
More informationDIRECTING SUN PANELS
sunpan, April 9, 2015 1 DIRECTING SUN PANELS GERRIT DRAISMA 1. Introduction The quantity of sun light captured by sun panels depends on intensity and direction of solar radiation, area of the panels, and
More informationVector Spaces. 1 Theory. 2 Matlab. Rules and Operations
Vector Spaces Rules and Operations 1 Theory Recall that we can specify a point in the plane by an ordered pair of numbers or coordinates (x, y) and a point in space with an order triple of numbers (x,
More informationV = IR. There are some basic equations that you will have to learn for the exams. These are written down for you at the back of the Physics Guide.
Physics Induction Please look after this booklet ypu will need to hand it in on your return to school in September and will need to get a pass to continue on the AS cours 1 Physics Induction Objectives:
More informationLab 6: Linear Algebra
6.1 Introduction Lab 6: Linear Algebra This lab is aimed at demonstrating Python s ability to solve linear algebra problems. At the end of the assignment, you should be able to write code that sets up
More informationIntroduction to GNU Octave
Introduction to GNU Octave A brief tutorial for linear algebra and calculus students by Jason Lachniet Introduction to GNU Octave A brief tutorial for linear algebra and calculus students Jason Lachniet
More information1.1 The Language of Mathematics Expressions versus Sentences
The Language of Mathematics Expressions versus Sentences a hypothetical situation the importance of language Study Strategies for Students of Mathematics characteristics of the language of mathematics
More informationS(c)/ c = 2 J T r = 2v, (2)
M. Balda LMFnlsq Nonlinear least squares 2008-01-11 Let us have a measured values (column vector) y depent on operational variables x. We try to make a regression of y(x) by some function f(x, c), where
More informationLaboratory handout 1 Mathematical preliminaries
laboratory handouts, me 340 2 Laboratory handout 1 Mathematical preliminaries In this handout, an expression on the left of the symbol := is defined in terms of the expression on the right. In contrast,
More informationAn area chart emphasizes the trend of each value over time. An area chart also shows the relationship of parts to a whole.
Excel 2003 Creating a Chart Introduction Page 1 By the end of this lesson, learners should be able to: Identify the parts of a chart Identify different types of charts Create an Embedded Chart Create a
More information. α β γ δ ε ζ η θ ι κ λ μ Aμ ν(x) ξ ο π ρ ς σ τ υ φ χ ψ ω. Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω. Friday April 1 ± ǁ
. α β γ δ ε ζ η θ ι κ λ μ Aμ ν(x) ξ ο π ρ ς σ τ υ φ χ ψ ω. Α Β Γ Δ Ε Ζ Η Θ Ι Κ Λ Μ Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω Friday April 1 ± ǁ 1 Chapter 5. Photons: Covariant Theory 5.1. The classical fields 5.2. Covariant
More informationTikZ Tutorial. KSETA Doktorandenworkshop 2014 Christian Amstutz, Tanja Harbaum, Ewa Holt July 21,
TikZ Tutorial KSETA Doktorandenworkshop 2014 Christian Amstutz, Tanja Harbaum, Ewa Holt July 21, 2014 KIT University of the State of Baden-Wuerttemberg and National Laboratory of the Helmholtz Association
More informationSolving Differential Equations on 2-D Geometries with Matlab
Solving Differential Equations on 2-D Geometries with Matlab Joshua Wall Drexel University Philadelphia, PA 19104 (Dated: April 28, 2014) I. INTRODUCTION Here we introduce the reader to solving partial
More information1 Mathematical styles
1 Mathematical styles Inline mathematics is typeset using matched pairs of dollar signs $. An alternate punctuation is \( and \) which are better suited for editors with syntax highlighting. We now introduce
More information2.1 Identifying Patterns
I. Foundations for Functions 2.1 Identifying Patterns: Leaders' Notes 2.1 Identifying Patterns Overview: Objective: s: Materials: Participants represent linear relationships among quantities using concrete
More informationL3: Review of linear algebra and MATLAB
L3: Review of linear algebra and MATLAB Vector and matrix notation Vectors Matrices Vector spaces Linear transformations Eigenvalues and eigenvectors MATLAB primer CSCE 666 Pattern Analysis Ricardo Gutierrez-Osuna
More informationComplex Numbers. Visualize complex functions to estimate their zeros and poles.
Lab 1 Complex Numbers Lab Objective: Visualize complex functions to estimate their zeros and poles. Polar Representation of Complex Numbers Any complex number z = x + iy can be written in polar coordinates
More informationEEE161 Applied Electromagnetics Laboratory 1
Dr. Milica Marković Applied Electromagnetics Laboratory page 1 EEE161 Applied Electromagnetics Laboratory 1 Instructor: Dr. Milica Marković Office: Riverside Hall 3028 Email: milica@csus.edu Web:http://gaia.ecs.csus.edu/
More informationComplex Numbers. A complex number z = x + iy can be written in polar coordinates as re i where
Lab 20 Complex Numbers Lab Objective: Create visualizations of complex functions. Visually estimate their zeros and poles, and gain intuition about their behavior in the complex plane. Representations
More informationFurther Maths A2 (M2FP2D1) Assignment ψ (psi) A Due w/b 19 th March 18
α β γ δ ε ζ η θ ι κ λ µ ν ξ ο π ρ σ τ υ ϕ χ ψ ω The mathematician s patterns, like the painter s or the poet s, must be beautiful: the ideas, like the colours or the words, must fit together in a harmonious
More informationPhysics 1114 Chapter 0: Mathematics Review
Physics 1114 Chapter 0: Mathematics Review 0.1 Exponents exponent: in N a, a is the exponent base number: in N a, N is the base number squared: when the exponent is 2 cube: when the exponent is 3 square
More informationProduction of this 2015 edition, containing corrections and minor revisions of the 2008 edition, was funded by the sigma Network.
About the HELM Project HELM (Helping Engineers Learn Mathematics) materials were the outcome of a three- year curriculum development project undertaken by a consortium of five English universities led
More informationCSE 1400 Applied Discrete Mathematics Definitions
CSE 1400 Applied Discrete Mathematics Definitions Department of Computer Sciences College of Engineering Florida Tech Fall 2011 Arithmetic 1 Alphabets, Strings, Languages, & Words 2 Number Systems 3 Machine
More informationMatlab Sheet 3 - Solution. Plotting in Matlab
f(x) Faculty of Engineering Spring 217 Mechanical Engineering Department Matlab Sheet 3 - Solution Plotting in Matlab 1. a. Estimate the roots of the following equation by plotting the equation. x 3 3x
More informationand in each case give the range of values of x for which the expansion is valid.
α β γ δ ε ζ η θ ι κ λ µ ν ξ ο π ρ σ τ υ ϕ χ ψ ω Mathematics is indeed dangerous in that it absorbs students to such a degree that it dulls their senses to everything else P Kraft Further Maths A (MFPD)
More informationLAB 1: MATLAB - Introduction to Programming. Objective:
LAB 1: MATLAB - Introduction to Programming Objective: The objective of this laboratory is to review how to use MATLAB as a programming tool and to review a classic analytical solution to a steady-state
More informationExperiment 1: Linear Regression
Experiment 1: Linear Regression August 27, 2018 1 Description This first exercise will give you practice with linear regression. These exercises have been extensively tested with Matlab, but they should
More informationECE2111 Signals and Systems UMD, Spring 2013 Experiment 1: Representation and manipulation of basic signals in MATLAB
ECE2111 Signals and Systems UMD, Spring 2013 Experiment 1: Representation and manipulation of basic signals in MATLAB MATLAB is a tool for doing numerical computations with matrices and vectors. It can
More information. D CR Nomenclature D 1
. D CR Nomenclature D 1 Appendix D: CR NOMENCLATURE D 2 The notation used by different investigators working in CR formulations has not coalesced, since the topic is in flux. This Appendix identifies the
More informationTRANSITION GUIDE
HEATHCOTE SCHOOL & SCIENCE COLLEGE AQA A LEVEL PHYSICS TRANSITION GUIDE 2017-2018 Name: Teacher/s: 1 Transition guide: Physics We have created this student support resource to help you make the transition
More informationEquation Sheet For Quizzes and Tests
hapter : Aluminum.70 g/cm 3 opper 8.96 g/cm 3 Iron 7.87 g/cm 3 Equation Sheet For Quizzes and Tests You must have memorized the unit prefix values and the formulas related to circles, spheres, and rectangles.
More informationLinear Algebra. Jim Hefferon. x x x 1
Linear Algebra Jim Hefferon ( 1 3) ( 2 1) 1 2 3 1 x 1 ( 1 3 ) ( 2 1) x 1 1 2 x 1 3 1 ( 6 8) ( 2 1) 6 2 8 1 Notation R real numbers N natural numbers: {, 1, 2,...} C complex numbers {......} set of... such
More informationSupplementary Figures
Supplementary Figures Supplementary Figure 1: Primary DEER data for the complexes of the RsmE protein dimer bound to two stem-loop RNAs singly spin-labelled at positions A to H (corresponding distance
More informationIntroduction to Computational Neuroscience
CSE2330 Introduction to Computational Neuroscience Basic computational tools and concepts Tutorial 1 Duration: two weeks 1.1 About this tutorial The objective of this tutorial is to introduce you to: the
More informationSession 3. Question Answers
Session 3 Question Answers Question 1 Enter the example code and test the program. Try changing the step size 0.01 and see if you get a better results. The code for the example %Using Euler's method to
More informationENED 1091 HW#3 Due Week of February 22 nd
ENED 1091 HW#3 Due Week of February 22 nd Problem 1: The graph below shows position measurements (in cm) collected every 0.5 seconds over a 10 second interval of time. (a) Using linear interpolation, estimate
More informationlast name ID 1 c/cmaker/cbreaker 2012 exam version a 6 pages 3 hours 40 marks no electronic devices SHOW ALL WORK
last name ID 1 c/cmaker/cbreaker 2012 exam version a 6 pages 3 hours 40 marks no electronic devices SHOW ALL WORK 8 a b c d e f g h i j k l m n o p q r s t u v w x y z 1 b c d e f g h i j k l m n o p q
More informationMatlab Section. November 8, 2005
Matlab Section November 8, 2005 1 1 General commands Clear all variables from memory : clear all Close all figure windows : close all Save a variable in.mat format : save filename name of variable Load
More informationEpsilon-Delta Window Challenge Name Student Activity
Open the TI-Nspire document Epsilon-Delta.tns. In this activity, you will get to visualize what the formal definition of limit means in terms of a graphing window challenge. Informally, lim f( x) Lmeans
More informationComputer simulation of radioactive decay
Computer simulation of radioactive decay y now you should have worked your way through the introduction to Maple, as well as the introduction to data analysis using Excel Now we will explore radioactive
More information(f P Ω hf) vdx = 0 for all v V h, if and only if Ω (f P hf) φ i dx = 0, for i = 0, 1,..., n, where {φ i } V h is set of hat functions.
Answer ALL FOUR Questions Question 1 Let I = [, 2] and f(x) = (x 1) 3 for x I. (a) Let V h be the continous space of linear piecewise function P 1 (I) on I. Write a MATLAB code to compute the L 2 -projection
More informationY1 Double Maths Assignment λ (lambda) Exam Paper to do Core 1 Solomon C on the VLE. Drill
α β γ δ ε ζ η θ ι κ λ µ ν ξ ο π ρ σ τ υ ϕ χ ψ ω Nature is an infinite sphere of which the centre is everywhere and the circumference nowhere Blaise Pascal Y Double Maths Assignment λ (lambda) Tracking
More informationBayesian Analysis - A First Example
Bayesian Analysis - A First Example This script works through the example in Hoff (29), section 1.2.1 We are interested in a single parameter: θ, the fraction of individuals in a city population with with
More informationBfh Ti Control F Ws 2008/2009 Lab Matlab-1
Bfh Ti Control F Ws 2008/2009 Lab Matlab-1 Theme: The very first steps with Matlab. Goals: After this laboratory you should be able to solve simple numerical engineering problems with Matlab. Furthermore,
More informationLAB # 5 HANDOUT. »»» The N-point DFT is converted into two DFTs each of N/2 points. N = -W N Then, the following formulas must be used. = k=0,...
EEE4 Lab Handout. FAST FOURIER TRANSFORM LAB # 5 HANDOUT Data Sequence A = x, x, x, x3, x4, x5, x6, x7»»» The N-point DFT is converted into two DFTs each of N/ points. x, x, x4, x6 x, x3, x5, x7»»» N =e
More informationIntegration by Parts Logarithms and More Riemann Sums!
Integration by Parts Logarithms and More Riemann Sums! James K. Peterson Department of Biological Sciences and Department of Mathematical Sciences Clemson University September 16, 2013 Outline 1 IbyP with
More informationISIS/Draw "Quick Start"
ISIS/Draw "Quick Start" Click to print, or click Drawing Molecules * Basic Strategy 5.1 * Drawing Structures with Template tools and template pages 5.2 * Drawing bonds and chains 5.3 * Drawing atoms 5.4
More informationQuick-Guide to SATAID
Quick-Guide to SATAID Japan Meteorological Agency Updated as of 2017/07/24 What is SATAID? SATAID (SATellite Animation and Interactive Diagnosis) is a sophisticated display program that enables visualization
More information2 Getting Started with Numerical Computations in Python
1 Documentation and Resources * Download: o Requirements: Python, IPython, Numpy, Scipy, Matplotlib o Windows: google "windows download (Python,IPython,Numpy,Scipy,Matplotlib" o Debian based: sudo apt-get
More informationCustomizing pgstar for your models
MESA Summer School 10Aug2015 Customizing pgstar for your models Monique Windju / Frank Timmes/ Emily Leiner SI 2 SPIDER Color coded notation used throughout this lecture + lab: Things you do are in yellow,
More informationQuality Report Generated with Pix4Dmapper Pro version
Quality Report Generated with Pix4Dmapper Pro version 3.0.13 Important: Click on the different icons for: Help to analyze the results in the Quality Report Additional information about the sections Click
More informationSolutions. Chapter 1. Problem 1.1. Solution. Simulate free response of damped harmonic oscillator
Chapter Solutions Problem. Simulate free response of damped harmonic oscillator ẍ + ζẋ + x = for different values of damping ration ζ and initial conditions. Plot the response x(t) and ẋ(t) versus t and
More informationLecture 5b: Starting Matlab
Lecture 5b: Starting Matlab James K. Peterson Department of Biological Sciences and Department of Mathematical Sciences Clemson University August 7, 2013 Outline 1 Resources 2 Starting Matlab 3 Homework
More informationwww.goldensoftware.com Why Create a Thematic Map? A thematic map visually represents the geographic distribution of data. MapViewer will help you to: understand demographics define sales or insurance territories
More informationMatlab homework assignments for modeling dynamical systems
Physics 311 Analytical Mechanics - Matlab Exercises C1.1 Matlab homework assignments for modeling dynamical systems Physics 311 - Analytical Mechanics Professor Bruce Thompson Department of Physics Ithaca
More informationChapter 2 A Mathematical Toolbox
Chapter 2 Mathematical Toolbox Vectors and Scalars 1) Scalars have only a magnitude (numerical value) Denoted by a symbol, a 2) Vectors have a magnitude and direction Denoted by a bold symbol (), or symbol
More informationExperiment: Oscillations of a Mass on a Spring
Physics NYC F17 Objective: Theory: Experiment: Oscillations of a Mass on a Spring A: to verify Hooke s law for a spring and measure its elasticity constant. B: to check the relationship between the period
More informationMATLAB crash course 1 / 27. MATLAB crash course. Cesar E. Tamayo Economics - Rutgers. September 27th, /27
1/27 MATLAB crash course 1 / 27 MATLAB crash course Cesar E. Tamayo Economics - Rutgers September 27th, 2013 2/27 MATLAB crash course 2 / 27 Program Program I Interface: layout, menus, help, etc.. I Vectors
More informationPHYS 114 Exam 1 Answer Key NAME:
PHYS 4 Exam Answer Key AME: Please answer all of the questions below. Each part of each question is worth points, except question 5, which is worth 0 points.. Explain what the following MatLAB commands
More informationElectric Fields and Equipotentials
OBJECTIVE Electric Fields and Equipotentials To study and describe the two-dimensional electric field. To map the location of the equipotential surfaces around charged electrodes. To study the relationship
More information