Categories

## Taylor Series Matlab

The following article provides an outline for Taylor Series Matlab. Taylor series is used to expand a function into an infinite sum of terms. Taylor series expresses the function in terms of its derivative at a point.

## Example:

Taylor series of e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + x^5/5! + …

As can see in the above example, we have drilled down the function ‘e^x’ into a polynomial which is of infinite degree. It finds its application in modern day Physics to simplify complex calculations, by breaking them down into the simple sum of terms. In Matlab, we use the ‘taylor’ function to get taylor series of any function.

## Syntax:

`A = taylor (Fx, p)`

`A = taylor (Fx, p, a)`

`A = taylor (Fx, Name, Value)`

## Explanation:

• taylor (Fx, p) will compute the Taylor series for the input function. By default, the series is computed till the 5th order and at ‘p = 0’ as the point.
• taylor (Fx, p, a) will compute the Taylor series for input function at the point p = a.
• taylor (Fx, Name, Value) can be used to put additional conditions, which can be specified using pair arguments (Name, Value).

### Examples of Taylor Series Matlab

Let us now see the code to calculate in Matlab using ‘taylor (Fx, p) function’:

## Example 1:

In this example, we will use a simple cos function and will expand it using Taylor series function.

We will follow the following 2 steps:

• Create the cos function in Matlab.
• Calculate the Taylor series using ‘Taylor function’.

## Syntax:

`syms x[Initializing the variable ‘x’] A = taylor (5* cos (x))`

[Creating the cos function and passing it as an input to the taylor function] [Please note that, since we did not pass any value for point ‘p’, the Taylor series will be computed at the point p = 0, by default] [Mathematically, the Taylor series of 5*cos(x) is (5*x^4)/24 – (5*x^2)/2 + 5]

## Code:

``````syms x
A = taylor (5* cos (x))``````

## Output:

Let us now see how the code for Taylor series looks like in Matlab if we want to use the point of our choice for Taylor series. For this purpose, we will be using ‘taylor (Fx, p, a)’ function and will pass some value for ‘p’.

## Example 2:

In this example, we will use a function of sine and will find the Taylor series at the point p = 1.

We will follow the following 2 steps:

• Create the function of sine in Matlab.
• Calculate the Taylor series using ‘taylor (Fx, p, a) function’ and pass ‘p’ as 1.

## Syntax:

`syms x[Initializing the variable ‘x’] A = taylor(4*sin(x)) x, 1)`[Creating the polynomial function of sine and passing it as an input to the taylor function] [Please note that we have passed ‘x’, ‘1’ as arguments, which represent the point x = 1] [Mathematically, the Taylor series of 4*sin (x) at point x = 1 is4*sin(1) – 2*sin(1)*(x – 1)^2 + (sin(1)*(x – 1)^4)/6 + 4*cos(1)*(x – 1) – (2*cos(1)*(x – 1)^3)/3 + (cos(1)*(x – 1)^5)/30

## Code:

``````syms x
A = taylor(4*sin(x), x, 1)``````

## Output:

Let us now see how the code for Taylor series looks like if we need to add more conditions using the ‘Name’, ‘Value’ pair arguments. For this purpose, we use ‘taylor (Fx, Name, Value)’ function.

## Example 3:

In this example, we will use the same polynomial function as used in the above example but will find the Taylor series only till 2nd order.

We will follow the following 2 steps:

• Create the function of cos and sine.
• Calculate the Taylor series using the function ‘taylor (Fx, Name, Value)’.

## Syntax:

`syms x[Initializing the variable ‘x’] A = taylor ((5*cos (x) + 4*sin (x)), x, 1, 'Order', 2)`[Creating the polynomial function of cos & sine and passing it as an input to the taylor function] [Please note that we have passed ‘Order’, ‘2’ as name-value pair arguments] [Mathematically, the taylor series of 5*cos (x) + 4*sin (x) at point x = 1 and order 2 is 5*cos (1) + 4*sin (1) + (x – 1) * (4*cos (1) – 5*sin (1))]

## Code:

``````syms x
A = taylor ((5*cos (x) + 4*sin (x)), x, 1, 'Order', 2)``````

Categories

## Features of Matlab

In this article, we will see an outline on Matlab Features. MATLAB, which was developed in the late 70s in the Computer Sciences department at the University of New Mexico, finally became a full-blown software by the mid-80s. MATLAB was developed focusing on mathematical simulations and hence found applications in control systems engineering, mechanical systems analysis, image processing, and also in academics for learning linear algebra and running deep mathematical simulations. While MATLAB had been great for working with static numerical data in vectors and matrices, through decades of development, it can now read data from flat files, databases, cloud storage, data acquisition hardware and even live financial data feeds. Its capabilities have grown to allow users to perform data visualization and even run complex machine learning models, even create mobile and desktop apps.

What separates MATLAB from the most popular platforms R & Python is that this is not an open-source platform, limiting its use to the corporation, academic institutes, and research organizations. Let us take a look at the features in MATLAB that make it the platform of choice for professional applications.

## Top Features of Matlab:

MATLAB is very capable in the field of data science and is currently being widely applied in industries ranging from insurance, finance, energy, medical devices, industrial automation, automotive and aerospace in various purposes for business-critical functions. With the recent iterations of the software platform being even more capable of running complex machine learning algorithms, its relevance in data science is expected to increase as we explore applications of ML & AI in our daily lives.

Researchers, engineers, and scientists that are already using MATLAB find it quite easy to move to deep learning owing to the functionality. And this functionality is what could encourage new learners too.

## 1. High-Level Language:

This is a high-level programming language with data structures, control flow statements, functions, output/input, and object-oriented programming. It permits both, rapidly creating speedy throw-away programs, and creating complete, complex and large application programs.

## 2. Interactive Environment:

MATLAB provides an interactive environment that allows iterative exploration, design, and problem-solving. It is a bunch of tools that a programmer can use. It includes abilities for handling the variables in the workspace & importing/exporting data. It also contains tools for development, handling, debugging, and profiling MATLAB files.

## 3. Handling Graphics:

It offers built-in graphics useful for data visualizing, and tools for generating custom plots. MATLAB holds high-level instructions specially for creating two and three-dimensional data visualizations, animations, image processing, and graphical presentation. This moreover includes low-level instructions that allow users to fully modify the appearance of graphics on top of to build thorough GUIs (Graphical User Interfaces) on MATLAB.

## 4. Mathematical Functions Library:

It offers a huge library of mathematical functions needed for computing statistics, linear algebra, numerical integration, filtering, Fourier analysis, optimization and solving regular differential equations.

## 5. Application Program Interface (API):

MATLAB APIs allow users to write C / C++ and Fortran programs that directly interact with MATLAB. These include options for calling programs from MATLAB (dynamic linking), reading and writing MAT-files, and for calling MATLAB as a computational engine. The users can utilize MEX API and Matrix API functions to interact with data within the MATLAB workspace.

## 6. Toolboxes:

A ” Toolbox” is a set of functions designed for a specific purpose and compiled as a package. These Toolboxes include MATLAB code, apps, data, examples and the documentation which helps users to utilize each Toolbox. Users can compile MATLAB files to create toolboxes if they require sharing with others. There are separate Toolboxes available from Mathworks, to be used for specific purposes, for example, text analytics, image processing, signal processing, deep learning, statistic & machine learning, and many more.

## 7. Accessing Data:

MATLAB can natively support the sensor, video, image, telemetry, binary, and various real-time data from JDBC/ODBC databases. Reading data from different databases, CSV, audio, images, and video is super simple from an integrated environment.

## 8. Interfacing with Other Languages:

Libraries written in Perl, Java, ActiveX or .NET can be directly called from MATLAB, and many libraries for XML or SQL support can be employed as wrappers around Java or ActiveX libraries.

## 9. Data Processing:

A vast library of mathematical functions for linear algebra, Fourier analysis, filtering, statistics, optimization, numerical integration and solving ordinary differential equations. MATLAB’s numeric routines scale openly to parallel processing over clusters and clouds. Parallel Computing Toolbox distributes training across multicore CPUs graphical processing units (GPUs), and clusters of computers with multiple CPUs and GPUs.

## 10. Machine Learning, Neural Networks, Beyond Statistics:

Deep Learning Toolbox provides simple MATLAB commands for creating and interconnecting the layers of a deep neural network. MATLAB provides an ML-rich language library, allowing the script to be very short and equally effective as compared to other languages. Automated feature selection and built-in hyper-parameter tuning make fine-tuning the machine learning and deep learning models easy.

## 11. Text Analytics:

Text Analytics Toolbox offers algorithms for pre-processing, visualizing, analyzing, and modeling textual data. It contains tools for handling raw textual data from sources such as news feeds, equipment logs, surveys, social media, and even operator reports. Models created with this toolbox can be used in applications such as sentiment analysis, and topic modeling. Models created with the Text Analytics Toolbox can also be combined with features from other data sources for building machine learning models that use numeric, textual and other data types.

## 12. Multi-Platform Deployment:

MATLAB allows to ‘export’ machine learning models anywhere including Java, Microsoft .NET, Excel, Python, C/C++, CUDA (parallel computing platform and programming model developed by Nvidia), enterprise IT systems, or the cloud. Or deploy models to MATLAB Production Server for integration with web, desktop, database, and enterprise applications.

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## Matlab Introduction

Matlab is a programming language similar to other well-known languages such as Java, C#, etc., which comes with its own IDE (that is Integrated Development Environment) and set of libraries. Matlab is an abbreviation of the term “Matrix Laboratory” since it was initially referred to as the matrix programming language. It is a fourth-generation programming language. It was first discovered by Cleve Moler, who at the time was the Chairman of the Computer Science department at the University of New Mexico. His goal was to find an alternative way to perform linear algebra and numerical computation for his students without them having to use Fortran. Later in 1984, Cleve Molar along with Steve Bangart and Jack Little – who recognized Matlab’s commercial potential, found MathWorks. MathWorks released its first official version of Matlab in 1984.

### Uses :

1. Performing numerical linear algebra
2. Numerical computation of Matrices
3. Data analysis and visualization
4. Plotting graphs for larger data sets
5. Developing algorithms
6. Creating interfaces for the user that is the GUI- Graphical User Interface and other applications that is the API – Application Programming Interface.

### Understanding the Matlab

In simple words, It is an advanced and more sophisticated version of a calculator that can be run on your computer or mobile device. One can use it to perform operations by making use of the command line interface as well as a text editor. It can also be used for writing programs and functions that perform continual tasks. The Matlab IDE contains a “help” icon, which consists of a detailed explanation of its workings. This feature is highly beneficial for people just getting started with Matlab.

### How does Matlab make Working so Easy?

It makes your code fast. Your code is compiled using JIT- just-in-time compiler, library calls are optimized and tasks to perform math operations are distributed among the computer’s cores. With Matlab, one can run algorithms in parallel making the execution faster. As compared to Java, the development of algorithms in Matlab is much faster and more robust. It allows you to load data from different sources and visualize them. Matlab’s IDE provides access to interactive applications that enable you to perform computational operations interactively by providing you visuals of these operations. Allowing you to visualize how different algorithms interpret your data. One could also design their own customized applications as well as use applications designed by other Matlab users.

### What can you do with Matlab?

Using Matlab you can implement and design different algorithms. You can load data from different sources such as files, databases or the web to analyze your data and visualize it using Matlab visualization application which gives you a wide range of graph plots to choose from. It also makes it easier to work with larger data sets. It as a math product contains a mathematical function library that allows you to perform linear algebra and computation of matrices. This also helps to facilitate data analysis. Creating data models, prototypes, and simulations of data can be achieved. You can also design interfaces for both users as well as other programming applications to make working with Matlab easier.

### Advantages

1. It provides the fastest IDE for the mathematical computation of matrices and linear algebra.
2. Contains the best mathematical package libraries to provide support for all fields of mathematics, ranging from simple summation to matrix inversion, etc.
3. It provides multi-threading support and garbage collection to facilitate the parallel execution of algorithms.
4. Its graphics system (Simulink) includes commands for two-dimensional and three-dimensional data visualization, image processing, graphics presentation, and animation providing high-quality visualization of plots and charts.

### Required skills

In order to get started with Matlab, one should have knowledge of basic object-oriented programming language and be aware of Matlab’s syntax. Have a good knowledge of the workings of Simulink. One should also possess a good understanding of advanced mathematics. Being familiar with its set of libraries and packages are required to carry out various mathematical operations. Knowing how to use the various built-in tools provided by the Matlab IDE to make one’s work faster.

### Why should we use Matlab?

Matlab is one of the best technologies available in the market for mathematical operations performed on matrices and linear algebra. It also provides the best support for faster and better algorithm design and testing. It makes analyzing data with different algorithms and studying the changes in behavior easy. It also provides flexibility to design new interfaces as per ones need.

### Scope

Matlab has its application across various functional fields such as finance, business, science, and engineering.

### Why do we need Matlab?

Using MATLAB allows us several advantages over other languages and methods.

1. By using toolboxes one could greatly enhance Matlab’s functionalities. For example, Statistics Toolbox facilitates specialized statistical manipulation of data, Excel link lets the data to be written in a format which is readable by Excel.
2. MATLAB considers every single data element as a matrix. For example, an integer would be treated as a matrix of one row and one column. It provides built-in functions for matrix-based operations such as matrix addition, multiplication, inversion, etc.
3. It considerably reduces the size of the code by using Vectorized operations.
4. Simulink – Matlab’s graphics system provides optimized output for interaction. Making it easier to plot data and allowing one to customize its size and color.

### Who is the right audience for learning Matlab technologies?

Engineers in the field of Data Science will find it useful for data analysis, data plotting and other detailed data related study. It is also for Scientists and research scholars dealing with advanced mathematical studies.

### How this technology will help you in career growth?

Looking at the current boom in jobs for data analysis and data science, This could help you advance your career in these fields as it provides excellent features for analyzing data. It is also applicable in fields of deep learning, machine learning, signal processing and communication, computational finance, image and signal processing to name a few.

Categories

## Introduction to Matlab

Matlab or Matrix Laboratory is a high-level programming language consisting of an interactive environment mainly used for numeric computation, programming, and visualization. It has been developed by MathWorks. The basic functions of Matlab are plotting of functions and data, the creation of user interfaces, matrix manipulations. It also provides support for interfacing with other programming languages in C, C++, Fortran, and Java. Besides, it is also used to analyze data, create models and applications, and also develop algorithms. Along with all this, introduction to Matlab also provides numerous built-in functions for mathematical operations involving numerous calculations, performing numerical methods, generating plots, and a lot of other functions. Matlab also has a very good scope in the automotive domain using Rapid control Prototyping or RCP used extensively in medical, automotive, and aerospace domains.

## Main components / highlights:

In the above section, we studied the introduction to Matlab, so now we’re going to learn the components of Matlab. Matlab provides a lot of functionalities that can help in computational mathematics. Below are the most common functions and mathematical calculations used in Matlab –

1. Dealing with Matrices and Arrays
2. 2-D and 3-D Plotting and graphics
3. Linear Algebra
4. Algebraic Equations
5. Non-linear Functions
6. Statistics
7. Data Analysis
8. Calculus and Differential Equations
9. Numerical Calculations
10. Integration
11. Transforms
12. Curve Fitting
13. Various other special functions

## Characteristics:

Matlab is a versatile tool designed for computational mathematics and supports lots of other operations. Below given are a few of the characteristics that make Matlab an intelligent tool –

1. Matlab contents are a huge library of built-in functions providing support for various mathematical functions like filtering, optimization, Fourier analysis, linear algebra, statistics, numerical integration, and solving differential equations.
2. Matlab is a high-level language used for visualization, application development, and numerical computation.
3. Matlab provides support for creating custom plots and data visualization with its built-in support for graphics.
4. Matlab also supports an iterative environment helping to design and problem solving along with iterative exploration.
5. Matlab provides integration support with other languages like C, Java, Microsoft Excel, and .NET for integrating Matlab-based algorithms with external applications.
6. With its uniquely designed programming interface, Matlab helps its users with development tools for maximizing performance and improving code maintainability.
7. Matlab also supports building applications with custom graphical interfaces.

### Applications of Matlab:

As we discussed in the introduction to Matlab, we will now learn about Matlab’s applications which are as follows: Matlab is widely used in the industry as a tool for mathematical computation and different streams of studies like physics chemistry, engineering, mathematics, Etc. The various applications involving Matlab are below –

1. Computational Finance
2. Control systems
3. Signal Processing and communication
4. Test and Measurement
5. Image and video processing
6. Computational biology