This document provides an introduction and overview of Matlab. It outlines what Matlab is, the main Matlab screen components, how to work with variables, arrays, matrices and perform indexing. It also covers basic arithmetic, relational and logical operators, different display facilities like plotting, and flow control structures like if/else statements and for loops. The document demonstrates how to use M-files to write scripts and user-defined functions in Matlab. It aims to introduce the key features and capabilities of the Matlab programming environment and language.
Arithmetic coding is an entropy encoding technique that maps a sequence of symbols to a numeric interval between 0 and 1. Each symbol maps to a sub-interval of the current interval based on the symbol probabilities. As symbols are processed, the interval boundaries are updated according to the cumulative distribution function of the symbol probabilities. Arithmetic coding achieves better compression than Huffman coding by allowing coding of variable-length blocks without pre-specifying code lengths. It also handles conditional probability models more efficiently by updating interval boundaries based on context without needing pre-specified codebooks for all contexts.
This document discusses arithmetic coding, an entropy encoding technique. It begins with an introduction comparing arithmetic coding to Huffman coding. The document then provides pseudocode for the basic encoding and decoding algorithms. It describes how scaling techniques like E1 and E2 scaling allow for incremental encoding and decoding as well as achieving infinite precision with finite-precision integers. The document outlines applications of arithmetic coding in areas like JBIG, H.264, and JPEG 2000.
This document is from a Calculus I class at New York University. It provides an overview of functions, including the definition of a function, different ways functions can be represented (formulas, tables, graphs, verbal descriptions), properties of functions like monotonicity and symmetry, and examples of determining domains and ranges of functions. It aims to help students understand functions and their representations as a foundation for calculus.
This document provides an overview of MATLAB, including:
- MATLAB is a software package for numerical computation, originally designed for linear algebra problems using matrices. It has since expanded to include other scientific computations.
- MATLAB treats all variables as matrices and supports various matrix operations like addition, multiplication, element-wise operations, and matrix manipulation functions.
- MATLAB allows plotting of 2D and 3D graphics, importing/exporting of data from files and Excel, and includes flow control statements like if/else, for loops, and while loops to structure code execution.
- Efficient MATLAB programming involves using built-in functions instead of custom functions, preallocating arrays, and avoiding nested loops where possible through matrix operations.
1. Python provides various built-in container types including lists, tuples, dictionaries, sets, and strings for storing and organizing data.
2. These container types support common operations like indexing, slicing, membership testing, and methods for insertion, deletion, and modification.
3. The document provides examples of using operators and built-in functions to perform tasks like formatting strings, file I/O, conditional logic, loops, functions, and exceptions.
The document discusses functional programming concepts like monads, functors, and for comprehensions in Scala. It provides definitions and laws for functors, monads, and monadic operations like map, flatMap, filter. It shows the equivalence between for comprehensions and flatMap/map implementations. It also discusses monadic zeros and filtering laws. Key concepts covered include the functor laws, monad laws, equivalence between map/flatMap and for comprehensions, and laws for operations like filter.
This document provides information on key concepts related to derivatives including:
1. Critical numbers and how to find them using the first derivative test
2. How the first derivative relates to intervals of increasing and decreasing functions
3. How to determine local maxima and minima using the first derivative test
4. How to find absolute maxima and minima on a closed interval
5. How to determine concavity using the second derivative test and identify inflection points. Worked examples are provided to demonstrate each concept.
Function Programming in Scala.
A lot of my examples here comes from the book
Functional programming in Scala By Paul Chiusano and Rúnar Bjarnason, It is a good book, buy it.
Arithmetic coding is an entropy encoding technique that maps a sequence of symbols to a numeric interval between 0 and 1. Each symbol maps to a sub-interval of the current interval based on the symbol probabilities. As symbols are processed, the interval boundaries are updated according to the cumulative distribution function of the symbol probabilities. Arithmetic coding achieves better compression than Huffman coding by allowing coding of variable-length blocks without pre-specifying code lengths. It also handles conditional probability models more efficiently by updating interval boundaries based on context without needing pre-specified codebooks for all contexts.
This document discusses arithmetic coding, an entropy encoding technique. It begins with an introduction comparing arithmetic coding to Huffman coding. The document then provides pseudocode for the basic encoding and decoding algorithms. It describes how scaling techniques like E1 and E2 scaling allow for incremental encoding and decoding as well as achieving infinite precision with finite-precision integers. The document outlines applications of arithmetic coding in areas like JBIG, H.264, and JPEG 2000.
This document is from a Calculus I class at New York University. It provides an overview of functions, including the definition of a function, different ways functions can be represented (formulas, tables, graphs, verbal descriptions), properties of functions like monotonicity and symmetry, and examples of determining domains and ranges of functions. It aims to help students understand functions and their representations as a foundation for calculus.
This document provides an overview of MATLAB, including:
- MATLAB is a software package for numerical computation, originally designed for linear algebra problems using matrices. It has since expanded to include other scientific computations.
- MATLAB treats all variables as matrices and supports various matrix operations like addition, multiplication, element-wise operations, and matrix manipulation functions.
- MATLAB allows plotting of 2D and 3D graphics, importing/exporting of data from files and Excel, and includes flow control statements like if/else, for loops, and while loops to structure code execution.
- Efficient MATLAB programming involves using built-in functions instead of custom functions, preallocating arrays, and avoiding nested loops where possible through matrix operations.
1. Python provides various built-in container types including lists, tuples, dictionaries, sets, and strings for storing and organizing data.
2. These container types support common operations like indexing, slicing, membership testing, and methods for insertion, deletion, and modification.
3. The document provides examples of using operators and built-in functions to perform tasks like formatting strings, file I/O, conditional logic, loops, functions, and exceptions.
The document discusses functional programming concepts like monads, functors, and for comprehensions in Scala. It provides definitions and laws for functors, monads, and monadic operations like map, flatMap, filter. It shows the equivalence between for comprehensions and flatMap/map implementations. It also discusses monadic zeros and filtering laws. Key concepts covered include the functor laws, monad laws, equivalence between map/flatMap and for comprehensions, and laws for operations like filter.
This document provides information on key concepts related to derivatives including:
1. Critical numbers and how to find them using the first derivative test
2. How the first derivative relates to intervals of increasing and decreasing functions
3. How to determine local maxima and minima using the first derivative test
4. How to find absolute maxima and minima on a closed interval
5. How to determine concavity using the second derivative test and identify inflection points. Worked examples are provided to demonstrate each concept.
Function Programming in Scala.
A lot of my examples here comes from the book
Functional programming in Scala By Paul Chiusano and Rúnar Bjarnason, It is a good book, buy it.
1) Base types in Python include integers, floats, booleans, strings, bytes, lists, tuples, dictionaries, sets, and None. These types support various operations like indexing, slicing, membership testing, and type conversions.
2) Common loop statements in Python are for loops and while loops. For loops iterate over sequences, while loops repeat as long as a condition is true. Loop control statements like break, continue, and else can be used to control loop execution.
3) Functions are defined using the def keyword and can take parameters and return values. Functions allow for code reusability and organization. Built-in functions operate on containers to provide functionality like sorting, summing, and converting between types.
Principles of functional progrmming in scalaehsoon
a short outline on necessity of functional programming and principles of functional programming in Scala.
In the article some keyword are used but not explained (to keep the article short and simple), the interested reader can look them up in internet.
The document discusses various math and string classes in Java. It covers:
- Constructing objects using the new operator and passing parameters.
- Using the Random class to generate random numbers.
- Declaring constants using final and static final.
- Basic arithmetic, increment/decrement, and math methods.
- Creating and manipulating strings using methods like length(), substring(), and concatenation.
- Drawing shapes on a frame using Graphics2D methods in a JComponent's paintComponent method.
This document provides an overview of probabilistic programming in Scala. It discusses how probabilistic programming languages (PPLs) unify general purpose programming with probabilistic modeling. Functional PPLs extend the idea that any function operating on values can also operate on probability distributions. The document outlines how a PPL for Scala could be implemented by extending core functions like Boolean operations to work on distributions, and developing probabilistic data structures like lists and graphs. Examples are given for modeling boolean formulas, hidden Markov models, social networks, and dice problems to demonstrate the capabilities of a functional PPL in Scala.
The document discusses various topics related to machine learning including supervised learning, deep neural networks, reinforcement learning, and deep reinforcement learning. It provides code examples for building neural networks in TensorFlow and implementing reinforcement learning agents. It also discusses applications of machine learning like stock predictions, recommendations, and self-driving cars.
This document provides a concise reference card summarizing key aspects of the Python 2.5 programming language, including variable types, basic syntax, object orientation, modules, exceptions, input/output, and the standard library. It covers topics like numbers, sequences, dictionaries, sets, functions, classes, imports, exceptions, files, and common library modules.
This document provides an overview and summary of Numerical Python (NumPy), an extension to the Python programming language that adds support for large, multi-dimensional arrays and matrices, along with a large library of high-level mathematical functions to operate on these arrays. It describes how to install NumPy, test the installation, and introduces some of the key features like array objects, universal functions (ufuncs), and convenience functions for array creation and manipulation.
Here are the steps to solve this ODE problem:
1. Define the ODE function:
function dydt = odefun(t,y)
dydt = -t.*y/10;
end
2. Solve the ODE:
[t,y] = ode45(@odefun,[0 10],10);
3. Plot the result:
plot(t,y)
xlabel('t')
ylabel('y(t)')
This uses ode45 to solve the ODE dy/dt = -t*y/10 on the interval [0,10] with initial condition y(0)=10.
This document is a lecture on advanced MATLAB methods. It discusses probability and statistics, data structures like cells and structs, images and animation, debugging techniques, and online resources. Specific topics covered include random number generation, histograms, cells vs matrices, initializing and accessing structs, figure handles, reading/writing images, creating animations, using the debugger, and the MATLAB File Exchange website.
This document provides an overview of the Introduction to Programming in MATLAB course. It outlines the course layout including 5 lectures covering various MATLAB topics. Problem sets are due daily and students must complete all lectures and problem sets to pass. Basic MATLAB skills such as scripts, variables, arrays, and basic plotting are introduced. The document also provides instructions for getting started with MATLAB and accessing resources.
To plot graphs in MATLAB, you must:
1. Define the range of values for the x-axis variable
2. Define the function as y = f(x)
3. Use the plot command plot(x,y) to generate the graph
MATLAB allows adding titles, labels, grid lines, adjusting axis scales, and plotting multiple functions on the same graph. Subplot allows generating multiple plots in the same figure.
This document summarizes key points from Lecture 2 of the Introduction to Programming in MATLAB course. It discusses user-defined functions, including function declarations and overloading functions. Flow control statements like if/else and for loops are explained. Various plotting functions and options are covered, such as line, image, surface, and 3D plots. Advanced plotting exercises demonstrate modifying a plotting function to include conditionals and subplotting multiple axes. Specialized plotting functions like polar, bar, and quiver are also mentioned.
1. Monads are container types like Option and List that allow computation on the contained values.
2. Monads support higher-order functions like map and flatMap that can transform the contained values.
3. Monads can be combined through operations like flatMap and flatten that allow chaining computations together in a uniform way.
4. Different monads can be implemented in different ways but generally involve unit/return, map/fmap, and flatMap/bind operations.
This document discusses arrays and structures. It begins by defining an array as a set of index-value pairs where each index maps to a value. Arrays are commonly implemented using consecutive memory locations. Structures group related data and allow accessing members via dot notation. The document provides examples of one-dimensional arrays in C and comparing integer pointers to arrays. It also covers self-referential structures, ordered lists, polynomials represented as terms, and sparse matrices stored as row-column-value triples. Functions for each abstract data type are defined, such as adding and multiplying polynomials or transposing a sparse matrix.
The document describes research on using symbolic regression to infer mathematical models from experimental data. Symbolic regression evolves computer programs that best fit the data, such as equations composed of basic arithmetic operations and functions. The approach is able to recover known models of various physical systems from sample data alone. It can also infer novel models of biological networks and other complex systems directly from experimental measurements. The ability to distill natural laws from data has applications in scientific discovery, engineering design, and other fields.
This presentation takes you on a functional programming journey, it starts from basic Scala programming language design concepts and leads to a concept of Monads, how some of them designed in Scala and what is the purpose of them
Arrays are data structures that store a collection of data elements of the same type using a single variable name to represent the entire collection. Structures group together data of different types under one name. Sparse matrices represent matrices with many zero elements by only storing the non-zero elements, using triples of row, column, and value to represent each non-zero term. Transposing a sparse matrix involves taking each non-zero term <i,j,value> and storing it as <j,i,value> in the transpose.
The document describes using MATLAB to plot various two-dimensional and three-dimensional plots, generate different types of signals used in signal processing, compare discrete and continuous ramp signals, compute the linear convolution of two sequences, illustrate folding and time shifting of sequences. MATLAB commands like plot, plot3, stem, conv are used to generate graphs and signals. Various experiments are presented on plotting functions, signals, and operations like convolution in MATLAB.
A short list of the most useful R commands
reference: http://www.personality-project.org/r/r.commands.html
R programı ile ilgilenen veya yeni öğrenmeye başlayan herkes için hazırlanmıştır.
Matlab is a high-level programming language and environment used for numerical computation, visualization, and programming. The document outlines key Matlab concepts including the Matlab screen, variables, arrays, matrices, operators, plotting, flow control, m-files, and user-defined functions. Matlab allows users to analyze data, develop algorithms, and create models and applications.
This document provides an introduction to MATLAB over 30 slides. It outlines what MATLAB is, the MATLAB screen, variables, arrays, matrices, indexing, operators, plot functions, control structures, M-files, and other key concepts. The goal is to teach the reader about basic MATLAB usage and functionality through examples and explanations of commands.
1) Base types in Python include integers, floats, booleans, strings, bytes, lists, tuples, dictionaries, sets, and None. These types support various operations like indexing, slicing, membership testing, and type conversions.
2) Common loop statements in Python are for loops and while loops. For loops iterate over sequences, while loops repeat as long as a condition is true. Loop control statements like break, continue, and else can be used to control loop execution.
3) Functions are defined using the def keyword and can take parameters and return values. Functions allow for code reusability and organization. Built-in functions operate on containers to provide functionality like sorting, summing, and converting between types.
Principles of functional progrmming in scalaehsoon
a short outline on necessity of functional programming and principles of functional programming in Scala.
In the article some keyword are used but not explained (to keep the article short and simple), the interested reader can look them up in internet.
The document discusses various math and string classes in Java. It covers:
- Constructing objects using the new operator and passing parameters.
- Using the Random class to generate random numbers.
- Declaring constants using final and static final.
- Basic arithmetic, increment/decrement, and math methods.
- Creating and manipulating strings using methods like length(), substring(), and concatenation.
- Drawing shapes on a frame using Graphics2D methods in a JComponent's paintComponent method.
This document provides an overview of probabilistic programming in Scala. It discusses how probabilistic programming languages (PPLs) unify general purpose programming with probabilistic modeling. Functional PPLs extend the idea that any function operating on values can also operate on probability distributions. The document outlines how a PPL for Scala could be implemented by extending core functions like Boolean operations to work on distributions, and developing probabilistic data structures like lists and graphs. Examples are given for modeling boolean formulas, hidden Markov models, social networks, and dice problems to demonstrate the capabilities of a functional PPL in Scala.
The document discusses various topics related to machine learning including supervised learning, deep neural networks, reinforcement learning, and deep reinforcement learning. It provides code examples for building neural networks in TensorFlow and implementing reinforcement learning agents. It also discusses applications of machine learning like stock predictions, recommendations, and self-driving cars.
This document provides a concise reference card summarizing key aspects of the Python 2.5 programming language, including variable types, basic syntax, object orientation, modules, exceptions, input/output, and the standard library. It covers topics like numbers, sequences, dictionaries, sets, functions, classes, imports, exceptions, files, and common library modules.
This document provides an overview and summary of Numerical Python (NumPy), an extension to the Python programming language that adds support for large, multi-dimensional arrays and matrices, along with a large library of high-level mathematical functions to operate on these arrays. It describes how to install NumPy, test the installation, and introduces some of the key features like array objects, universal functions (ufuncs), and convenience functions for array creation and manipulation.
Here are the steps to solve this ODE problem:
1. Define the ODE function:
function dydt = odefun(t,y)
dydt = -t.*y/10;
end
2. Solve the ODE:
[t,y] = ode45(@odefun,[0 10],10);
3. Plot the result:
plot(t,y)
xlabel('t')
ylabel('y(t)')
This uses ode45 to solve the ODE dy/dt = -t*y/10 on the interval [0,10] with initial condition y(0)=10.
This document is a lecture on advanced MATLAB methods. It discusses probability and statistics, data structures like cells and structs, images and animation, debugging techniques, and online resources. Specific topics covered include random number generation, histograms, cells vs matrices, initializing and accessing structs, figure handles, reading/writing images, creating animations, using the debugger, and the MATLAB File Exchange website.
This document provides an overview of the Introduction to Programming in MATLAB course. It outlines the course layout including 5 lectures covering various MATLAB topics. Problem sets are due daily and students must complete all lectures and problem sets to pass. Basic MATLAB skills such as scripts, variables, arrays, and basic plotting are introduced. The document also provides instructions for getting started with MATLAB and accessing resources.
To plot graphs in MATLAB, you must:
1. Define the range of values for the x-axis variable
2. Define the function as y = f(x)
3. Use the plot command plot(x,y) to generate the graph
MATLAB allows adding titles, labels, grid lines, adjusting axis scales, and plotting multiple functions on the same graph. Subplot allows generating multiple plots in the same figure.
This document summarizes key points from Lecture 2 of the Introduction to Programming in MATLAB course. It discusses user-defined functions, including function declarations and overloading functions. Flow control statements like if/else and for loops are explained. Various plotting functions and options are covered, such as line, image, surface, and 3D plots. Advanced plotting exercises demonstrate modifying a plotting function to include conditionals and subplotting multiple axes. Specialized plotting functions like polar, bar, and quiver are also mentioned.
1. Monads are container types like Option and List that allow computation on the contained values.
2. Monads support higher-order functions like map and flatMap that can transform the contained values.
3. Monads can be combined through operations like flatMap and flatten that allow chaining computations together in a uniform way.
4. Different monads can be implemented in different ways but generally involve unit/return, map/fmap, and flatMap/bind operations.
This document discusses arrays and structures. It begins by defining an array as a set of index-value pairs where each index maps to a value. Arrays are commonly implemented using consecutive memory locations. Structures group related data and allow accessing members via dot notation. The document provides examples of one-dimensional arrays in C and comparing integer pointers to arrays. It also covers self-referential structures, ordered lists, polynomials represented as terms, and sparse matrices stored as row-column-value triples. Functions for each abstract data type are defined, such as adding and multiplying polynomials or transposing a sparse matrix.
The document describes research on using symbolic regression to infer mathematical models from experimental data. Symbolic regression evolves computer programs that best fit the data, such as equations composed of basic arithmetic operations and functions. The approach is able to recover known models of various physical systems from sample data alone. It can also infer novel models of biological networks and other complex systems directly from experimental measurements. The ability to distill natural laws from data has applications in scientific discovery, engineering design, and other fields.
This presentation takes you on a functional programming journey, it starts from basic Scala programming language design concepts and leads to a concept of Monads, how some of them designed in Scala and what is the purpose of them
Arrays are data structures that store a collection of data elements of the same type using a single variable name to represent the entire collection. Structures group together data of different types under one name. Sparse matrices represent matrices with many zero elements by only storing the non-zero elements, using triples of row, column, and value to represent each non-zero term. Transposing a sparse matrix involves taking each non-zero term <i,j,value> and storing it as <j,i,value> in the transpose.
The document describes using MATLAB to plot various two-dimensional and three-dimensional plots, generate different types of signals used in signal processing, compare discrete and continuous ramp signals, compute the linear convolution of two sequences, illustrate folding and time shifting of sequences. MATLAB commands like plot, plot3, stem, conv are used to generate graphs and signals. Various experiments are presented on plotting functions, signals, and operations like convolution in MATLAB.
A short list of the most useful R commands
reference: http://www.personality-project.org/r/r.commands.html
R programı ile ilgilenen veya yeni öğrenmeye başlayan herkes için hazırlanmıştır.
Matlab is a high-level programming language and environment used for numerical computation, visualization, and programming. The document outlines key Matlab concepts including the Matlab screen, variables, arrays, matrices, operators, plotting, flow control, m-files, and user-defined functions. Matlab allows users to analyze data, develop algorithms, and create models and applications.
This document provides an introduction to MATLAB over 30 slides. It outlines what MATLAB is, the MATLAB screen, variables, arrays, matrices, indexing, operators, plot functions, control structures, M-files, and other key concepts. The goal is to teach the reader about basic MATLAB usage and functionality through examples and explanations of commands.
MIT OpenCourseWare provides course materials for the free online course 6.094 Introduction to MATLAB taught in January 2009. The course covers topics like linear algebra, polynomials, optimization, differentiation and integration, and solving differential equations using MATLAB. Lecture 3 focuses on solving systems of linear equations, matrix operations, polynomial fitting to data, nonlinear root finding, function minimization, and numerical methods for differentiation, integration, and solving ordinary differential equations.
The name MATLAB stands for MATrix LABoratory.MATLAB is a high-performance language for technical computing.
It integrates computation, visualization, and programming environment. Furthermore, MATLAB is a modern programming language environment: it has sophisticated data structures, contains built-in editing and debugging tools, and supports object-oriented programming.
These factor make MATLAB an excellent tool for teaching and research.
MatLab is a matrix-based program used for numeric computation and visualization. It contains functions for creating matrices and performing operations on them like addition, subtraction, multiplication, etc. It also allows plotting of functions and special matrices like magic squares, identity matrices, and Toeplitz matrices. Polynomial operations can also be performed such as addition, multiplication, differentiation and evaluation.
Here are the steps to solve this problem in MATLAB:
1. Create a matrix A with the marks data:
A = [24 44 36 36;
52 57 68 76;
66 53 69 73;
85 40 86 72;
15 47 25 28;
79 72 82 91];
2. Define the column labels:
subjects = {'Math','Programming','Thermodynamics','Mechanics'};
3. Find the total marks of each subject:
totals = sum(A)
4. Find the average marks of each subject:
averages = mean(A)
5. Find the highest marks scored in each subject:
maxMarks = max
This document provides an introduction to MATLAB. It covers MATLAB basics like arithmetic, variables, vectors, matrices and built-in functions. It also discusses plotting graphs, programming in MATLAB by creating functions and scripts, and solving systems of linear equations. The document is compiled by Endalkachew Teshome from the Department of Mathematics at AMU for teaching MATLAB.
Computers and Programming , Programming Languages Types, Problem solving, Introduction to the MATLAB environment, Using MATLAB Documentation
Introduction to the course, Operating methodology-Installation Procedure
1. Compare a sample code in C with MATLAB
2. Trajectory of a particle in projectile motion ( solving quadratic equations)
3. Ideal gas law problem to find volume
The document discusses various topics related to graphics and plotting in MATLAB including: the plot command for creating 2D and 3D plots; options for specifying line styles; using linspace to generate uniformly spaced vectors; adding labels, titles, and text to figures; displaying data using plots, stem plots, bar charts; and including multiple graphs in the same figure. Key graphing functions covered are plot, stem, bar, title, xlabel, ylabel, text, and linspace. The document also includes examples of MATLAB code for generating various types of graphs and annotating them.
This document provides an overview of basic MATLAB concepts including:
1. Creating variables and performing basic arithmetic operations
2. Generating and manipulating matrices using built-in functions
3. Plotting graphs of simple functions like sine and cosine waves
4. Solving linear equations and finding the inverse and determinant of matrices
It includes sample exercises demonstrating these MATLAB skills.
Here are the steps to solve this problem numerically in MATLAB:
1. Define the 2nd order ODE for the pendulum as two first order equations:
y1' = y2
y2' = -sin(y1)
2. Create an M-file function pendulum.m that returns the right hand side:
function dy = pendulum(t,y)
dy = [y(2); -sin(y(1))];
end
3. Use an ODE solver like ode45 to integrate from t=0 to t=6pi with initial conditions y1(0)=pi, y2(0)=0:
[t,y] = ode45
This document provides an overview of mathematical functions in MATLAB, including:
1) Common math functions such as absolute value, rounding, floor/ceiling, exponents, logs, and trigonometric functions.
2) How to write custom functions and use programming constructs like if/else statements and for loops.
3) Data analysis functions including statistics and histograms.
4) Complex number representation and basic complex functions in MATLAB.
MATLAB/SIMULINK for Engineering Applications day 2:Introduction to simulinkreddyprasad reddyvari
The document provides an introduction to MATLAB and Simulink through a presentation. It discusses what MATLAB and Simulink are, their basic functions and capabilities, and how to get started using them. The presentation covers topics such as vectors, matrices, plotting, control structures, M-files, and writing user-defined functions. The goal is to help attendees gain basic knowledge of MATLAB/Simulink and be able to explore them on their own.
This document provides an introduction and overview of MATLAB. It defines MATLAB as an interactive system for technical computing with matrices as the basic data type. It describes how MATLAB is used in mathematics, industry, and research for numeric computation and visualization. The document outlines MATLAB's toolboxes for specialized applications and provides examples of using matrices, vectors, operators, and functions in MATLAB. It demonstrates how to perform operations like matrix addition and inversion, solve systems of linear equations, and analyze arrays with built-in functions.
Matlab is an interactive computing environment for numerical computation, visualization, and programming. The document provides an introduction and overview of Matlab, including what Matlab is, the Matlab screen interface, variables and arrays, basic math operations, plotting functions, control structures like if/else and for loops, using m-files, and writing user-defined functions. Key features of Matlab covered are the command window, workspace, command history, generating matrices and vectors, element-wise operations, relational and logical operators, and file input/output statements.
SAMPLE QUESTIONExercise 1 Consider the functionf (x,C).docxagnesdcarey33086
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: __________________________
LAB DAY and TIME:______________
Instructor: _______________________
Exercise 1
(a)
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
f= @(x,C) sin(C*x)./(C*x) % C will be just a constant, no need for ".*"
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % supressing the y's
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
Command window output:
f =
@(x,C)sin(C*x)./(C*x)
C1 =
1
C2 =
2
C3 =
3
(b)
M-file of structure function+function
function ex1
x = linspace(-3*pi,3*pi); % generating x vector - default value for number
% of pts linspace is 100
C1 = 1, C2 = 2, C3 = 3 % Using commans to separate commands
y1 = f(x,C1); y2 = f(x,C2); y3 = f(x,C3); % function f is defined below
plot(x,y1,'b.-', x,y2,'ro-', x,y3,'ks-') % using different markers for
% black and white plots
xlabel('x'), ylabel('y') % labeling the axis
title('f(x,C) = sin(Cx)/(Cx)') % adding a title
legend('C = 1','C = 2','C = 3') % adding a legend
grid on
end
function y = f(x,C)
y = sin(C*x)./(C*x);
end
Command window output:
C1 =
1
C2 =
2
C3 =
3
Joe Bob
Mon lab: 4:30-6:50
Lab 3
Exercise 1
(a) Create function M-file for banded LU factorization
function [L,U] = luband(A,p)
% LUBAND Banded LU factorization
% Adaptation to LUFACT
% Input:
% A diagonally dominant square matrix
% Output:
% L,U unit lower triangular and upper triangular such that LU=A
n = length(A);
L = eye(n); % ones on diagonal
% Gaussian Elimination
for j = 1:n-1
a = min(j+p.
This document provides an introduction to MATLAB programming. It discusses resources for the course including the course web page and slides. It then explains what MATLAB is, how to get started using it on Windows and Linux systems, and how to get help. It also covers the MATLAB desktop environment, performing calculations on the command line, entering numeric arrays, indexing into matrices, basic plotting commands, and logical indexing.
Amth250 octave matlab some solutions (1)asghar123456
This document contains the solutions to 5 questions regarding numerical integration and differential equations. Question 1 involves numerically evaluating several integrals. Question 2 computes the Fresnel integrals. Question 3 uses Monte Carlo integration to estimate volumes. Question 4 examines the convergence and stability of the Euler method. Question 5 simulates the Lorenz system and demonstrates its sensitivity to initial conditions.
More instructions for the lab write-up1) You are not obli.docxgilpinleeanna
More instructions for the lab write-up:
1) You are not obligated to use the 'diary' function. It was presented only for you convenience. You
should be copying and pasting your code, plots, and results into some sort of "Word" type editor that
will allow you to import graphs and such. Make sure you always include the commands to generate
what is been asked and include the outputs (from command window and plots), unless the problem
says to suppress it.
2) Edit this document: there should be no code or MATLAB commands that do not pertain to the
exercises you are presenting in your final submission. For each exercise, only the relevant code that
performs the task should be included. Do not include error messages. So once you have determined
either the command line instructions or the appropriate script file that will perform the task you are
given for the exercise, you should only include that and the associated output. Copy/paste these into
your final submission document followed by the output (including plots) that these MATLAB
instructions generate.
3) All code, output and plots for an exercise are to be grouped together. Do not put them in appendix, at
the end of the writeup, etc. In particular, put any mfiles you write BEFORE you first call them.
Each exercise, as well as the part of the exercises, is to be clearly demarked. Do not blend them all
together into some sort of composition style paper, complimentary to this: do NOT double space.
You can have spacing that makes your lab report look nice, but do not double space sections of text
as you would in a literature paper.
4) You can suppress much of the MATLAB output. If you need to create a vector, "x = 0:0.1:10" for
example, for use, there is no need to include this as output in your writeup. Just make sure you
include whatever result you are asked to show. Plots also do not have to be a full, or even half page.
They just have to be large enough that the relevant structure can be seen.
5) Before you put down any code, plots, etc. answer whatever questions that the exercise asks first.
You will follow this with the results of your work that support your answer.
SAMPLE QUESTION:
Exercise 1: Consider the function
f (x,C)=
sin(C x)
Cx
(a) Create a vector x with 100 elements from -3*pi to 3*pi. Write f as an inline or anonymous function
and generate the vectors y1 = f(x,C1), y2 = f(x,C2) and y3 = f(x,C3), where C1 = 1, C2 = 2 and
C3 = 3. Make sure you suppress the output of x and y's vectors. Plot the function f (for the three
C's above), name the axis, give a title to the plot and include a legend to identify the plots. Add a
grid to the plot.
(b) Without using inline or anonymous functions write a function+function structure m-file that does
the same job as in part (a)
SAMPLE LAB WRITEUP:
MAT 275 MATLAB LAB 1 NAME: ...
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Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
2. Outline:
What is Matlab?
Matlab Screen
Variables, array, matrix, indexing
Operators (Arithmetic, relational, logical )
Display Facilities
Flow Control
Using of M-File
Writing User Defined Functions
Conclusion
3. What is Matlab?
Matlab is basically a high level language
which has many specialized toolboxes for
making things easier for us
How high?
Matlab
High Level
Languages such as
C, Pascal etc.
Assembly
4. What are we interested in?
Matlab is too broad for our purposes in this
course.
The features we are going to require is
Matlab
Series of
Matlab
commands
Command
m-files mat-files
Line
functions Command execution Data
Input like DOS command storage/
Output window loading
capability
5. Matlab Screen
Command Window
type commands
Current Directory
View folders and m-files
Workspace
View program variables
Double click on a variable
to see it in the Array Editor
Command History
view past commands
save a whole session
using diary
6. Variables
No need for types. i.e.,
int a;
double b;
float c;
All variables are created with double precision unless
specified and they are matrices.
Example:
>>x=5;
>>x1=2;
After these statements, the variables are 1x1 matrices
with double precision
7. Array, Matrix
a vector x = [1 2 5 1]
x =
1 2 5 1
a matrix x = [1 2 3; 5 1 4; 3 2 -1]
x =
1 2 3
5 1 4
3 2 -1
transpose y = x’ y =
1
2
5
1
8. Long Array, Matrix
t =1:10
t =
1 2 3 4 5 6 7 8 9 10
k =2:-0.5:-1
k =
2 1.5 1 0.5 0 -0.5 -1
B = [1:4; 5:8]
x =
1 2 3 4
5 6 7 8
9. Generating Vectors from functions
zeros(M,N) MxN matrix of zeros x = zeros(1,3)
x =
0 0 0
ones(M,N) MxN matrix of ones
x = ones(1,3)
x =
1 1 1
rand(M,N) MxN matrix of uniformly
distributed random x = rand(1,3)
numbers on (0,1) x =
0.9501 0.2311 0.6068
10. Matrix Index
The matrix indices begin from 1 (not 0 (as in C))
The matrix indices must be positive integer
Given:
A(-2), A(0)
Error: ??? Subscript indices must either be real positive integers or logicals.
A(4,2)
Error: ??? Index exceeds matrix dimensions.
11. Concatenation of Matrices
x = [1 2], y = [4 5], z=[ 0 0]
A = [ x y]
1 2 4 5
B = [x ; y]
1 2
4 5
C = [x y ;z]
Error:
??? Error using ==> vertcat CAT arguments dimensions are not consistent.
14. Operators (Element by Element)
.* element-by-element multiplication
./ element-by-element division
.^ element-by-element power
15. The use of “.” – “Element” Operation
A = [1 2 3; 5 1 4; 3 2 1]
A=
1 2 3
5 1 4
3 2 -1
b = x .* y c=x./y d = x .^2
x = A(1,:) y = A(3 ,:)
b= c= d=
x= y= 3 8 -3 0.33 0.5 -3 1 4 9
1 2 3 3 4 -1
K= x^2
Erorr:
??? Error using ==> mpower Matrix must be square.
B=x*y
Erorr:
??? Error using ==> mtimes Inner matrix dimensions must agree.
16. Basic Task: Plot the function sin(x)
between 0≤x≤4π
Create an x-array of 100 samples between 0
and 4π.
>>x=linspace(0,4*pi,100);
Calculate sin(.) of the x-array1
0.8
0.6
>>y=sin(x); 0.4
0.2
0
Plot the y-array -0.2
-0.4
-0.6
>>plot(y) -0.8
-1
0 10 20 30 40 50 60 70 80 90 100
17. Plot the function e-x/3sin(x) between
0≤x≤4π
Create an x-array of 100 samples between 0
and 4π.
>>x=linspace(0,4*pi,100);
Calculate sin(.) of the x-array
>>y=sin(x);
Calculate e-x/3 of the x-array
>>y1=exp(-x/3);
Multiply the arrays y and y1
>>y2=y*y1;
18. Plot the function e-x/3sin(x) between
0≤x≤4π
Multiply the arrays y and y1 correctly
>>y2=y.*y1;
Plot the y2-array
0.7
>>plot(y2) 0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
0 10 20 30 40 50 60 70 80 90 100
20. Display Facilities
title(.)
>>title(‘This is the sinus function’)
This is the sinus function
1
0.8
xlabel(.) 0.6
0.4
>>xlabel(‘x (secs)’) 0.2
sin(x)
0
ylabel(.)
-0.2
-0.4
-0.6
-0.8
>>ylabel(‘sin(x)’) -1
0 10 20 30 40 50 60 70 80 90 100
x (secs)
21. Operators (relational, logical)
== Equal to
~= Not equal to
< Strictly smaller
> Strictly greater
<= Smaller than or equal to
>= Greater than equal to
& And operator
| Or operator
23. Control Structures
Some Dummy Examples
If Statement Syntax
if ((a>3) & (b==5))
Some Matlab Commands;
if (Condition_1) end
Matlab Commands
if (a<3)
elseif (Condition_2) Some Matlab Commands;
Matlab Commands elseif (b~=5)
Some Matlab Commands;
elseif (Condition_3) end
Matlab Commands
if (a<3)
else Some Matlab Commands;
Matlab Commands else
Some Matlab Commands;
end end
24. Control Structures
Some Dummy Examples
For loop syntax for i=1:100
Some Matlab Commands;
end
for i=Index_Array for j=1:3:200
Some Matlab Commands;
Matlab Commands end
end for m=13:-0.2:-21
Some Matlab Commands;
end
for k=[0.1 0.3 -13 12 7 -9.3]
Some Matlab Commands;
end
25. Control Structures
While Loop Syntax
Dummy Example
while (condition)
Matlab Commands while ((a>3) & (b==5))
Some Matlab Commands;
end end
26. Use of M-File
Click to create
a new M-File
• Extension “.m”
• A text file containing script or function or program to run
27. Use of M-File Save file as Denem430.m
If you include “;” at the
end of each statement,
result will not be shown
immediately
28. Writing User Defined Functions
Functions are m-files which can be executed by
specifying some inputs and supply some desired outputs.
The code telling the Matlab that an m-file is actually a
function is
function out1=functionname(in1)
function out1=functionname(in1,in2,in3)
function [out1,out2]=functionname(in1,in2)
You should write this command at the beginning of the
m-file and you should save the m-file with a file name
same as the function name
29. Writing User Defined Functions
Examples
Write a function : out=squarer (A, ind)
Which takes the square of the input matrix if the input
indicator is equal to 1
And takes the element by element square of the input
matrix if the input indicator is equal to 2
Same Name
30. Writing User Defined Functions
Another function which takes an input array and returns the sum and product
of its elements as outputs
The function sumprod(.) can be called from command window or an m-file as
31. Notes:
“%” is the neglect sign for Matlab (equaivalent
of “//” in C). Anything after it on the same line
is neglected by Matlab compiler.
Sometimes slowing down the execution is
done deliberately for observation purposes.
You can use the command “pause” for this
purpose
pause %wait until any key
pause(3) %wait 3 seconds
32. Useful Commands
The two commands used most by Matlab
users are
>>help functionname
>>lookfor keyword