Numerical Methods in MATLAB for Engineering Students Part 1 from Udemy

Numerical Methods (also known as Numerical Analysis) is required in many Engineering degree programs. This course will focus on the root finding and numerical integration techniques most frequently covered at the undergraduate level.

MATLAB is widely used in undergraduate engineering programs as well as in industry. Because of this, MATLAB is used in this course to demonstrate how to successfully code each of the methods presented. In addition, it should be noted that this course can be used to enhance your coding skills.

You will learn the theory behind the techniques as well as the coding aspects. We will work examples by hand and then follow those with MATLAB examples.

This course covers the following topics:

Root Finding:

Bisection Method
Newtons Method (also known as Newton-Raphson)
Secant Method
MATLAB coding of all methods

Numerical Integration:

Rectangle Method
Midpoint Method
Trapezoidal Method
Simpson's Method
MATLAB coding of all methods

Downloadable resources that come with the course:

Outline of notes with all example problem statements
MATLAB codes needed to run all the examples

What's inside

Learning objectives

Root finding techniques: bisection method, newton's method, secant method
Numerical integration techniques: rectangle & midpoint methods, trapezoidal & simpsons methods

Matlab coding skills: algortihms and example matlab codes are reviewed to enhance knowledge of matlab and the numerical techniques

Root finding techniques: bisection method, newton's method, secant method
Numerical integration techniques: rectangle & midpoint methods, trapezoidal & simpsons methods
Matlab coding skills: algortihms and example matlab codes are reviewed to enhance knowledge of matlab and the numerical techniques

Syllabus

Learn how to numerically solve fro roots using Bisection, Newtons and Secant methods

Intro Video

Error Calculations & Outline of Notes

Bisection Method

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Uses MATLAB, a widely adopted tool in undergraduate engineering programs and industry, for coding and demonstrating numerical methods

Covers root finding and numerical integration techniques, which are fundamental concepts in many engineering degree programs

Provides downloadable resources, including an outline of notes with example problem statements and the MATLAB codes needed to run all examples

Enhances coding skills by demonstrating how to successfully code each of the presented numerical methods in MATLAB

Requires access to MATLAB, which may require a license or subscription that could pose a barrier to some students

Focuses on older numerical methods, such as the rectangle method, which may not be as efficient or accurate as more modern techniques

Reviews summary

Numerical methods and matlab for engineers

According to students, this course provides a solid foundation (positive) in both numerical methods (neutral) and their implementation using MATLAB (neutral). Learners found the lectures (positive) and coding examples (positive) to be particularly helpful, enabling them to understand the theory (positive) and apply it practically (positive). The course is seen as a great introduction (positive) for those new to the topic or needing a refresher, especially for engineering students (positive). While some felt it moved quickly or desired more advanced topics, the general consensus highlights its clarity (positive) and effectiveness in teaching core concepts (positive).

Provides a strong basis for numerical methods.

"This course gave me a really solid foundation in numerical methods and MATLAB."

"It's a perfect starting point for anyone needing to learn these topics for engineering."

"I feel much more confident with numerical analysis after taking this course."

Methods and concepts are explained clearly.

"The explanations of the numerical methods were really clear and easy to follow."

"I found the way the instructor explained the theory behind each method to be excellent."

"The course does a great job of explaining complex topics in an understandable way."

Practical coding examples aid understanding.

"The MATLAB examples are super helpful for seeing how the methods work in practice."

"Having the MATLAB codes available and explained step-by-step was a huge plus."

"I really appreciated the hands-on coding examples after learning the theory."

Some find the pace fast or content challenging.

"The course sometimes moved a bit quickly through certain topics."

"I had to rewatch some lectures to fully grasp the concepts, especially the MATLAB parts."

"While great, this course assumes some basic familiarity with calculus and programming."

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Numerical Methods in MATLAB for Engineering Students Part 1 with these activities:

Review Calculus Fundamentals

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Strengthen your understanding of calculus concepts, which are essential for grasping numerical integration techniques.

Browse courses on Limits

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Review differentiation and integration rules.
Practice solving basic calculus problems.
Focus on understanding the concept of limits.

Brush Up on MATLAB Fundamentals

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Practice basic MATLAB commands and syntax to prepare for coding numerical methods.

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Complete online MATLAB tutorials.
Write simple MATLAB scripts.
Familiarize yourself with MATLAB's debugging tools.

Numerical Methods for Engineers

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Supplement your learning with a comprehensive textbook on numerical methods.

View Numerical Methods For Engineers on Amazon

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Read relevant chapters on root finding and numerical integration.
Work through the examples provided in the book.
Compare the book's explanations with the course materials.

Four other activities

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Implement Root Finding Algorithms

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Practice implementing the Bisection, Newton's, and Secant methods in MATLAB to solidify your understanding.

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Code each algorithm from scratch.
Test your implementations with various functions.
Compare the performance of each method.

Implement Numerical Integration Algorithms

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Practice implementing the Rectangle, Midpoint, Trapezoidal, and Simpson's rules in MATLAB.

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Code each integration rule from scratch.
Test your implementations with various functions.
Compare the accuracy of each method.

Project: Root Finding Comparison

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Develop a MATLAB program to compare the performance of different root-finding methods on a set of test functions.

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Select a set of test functions with known roots.
Implement the Bisection, Newton's, and Secant methods.
Measure the time and number of iterations required for each method to converge.
Present your results in a report or presentation.

Project: Numerical Integration Error Analysis

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Develop a MATLAB program to analyze the error of different numerical integration methods for various functions.

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Select a set of test functions with known integrals.
Implement the Rectangle, Midpoint, Trapezoidal, and Simpson's rules.
Calculate the error for each method with different step sizes.
Present your results in a report or presentation.

Career center

Learners who complete Numerical Methods in MATLAB for Engineering Students Part 1 will develop knowledge and skills that may be useful to these careers:

Computational Scientist

Computational Scientists develop and apply computational methods to solve complex scientific problems. These professionals often work with simulations and mathematical models, requiring a strong foundation in numerical methods. Gaining familiarity with techniques such as the Bisection, Newton's, and Secant methods, taught in this course, is invaluable for solving equations numerically. Also, understanding numerical integration techniques such as Rectangle, Midpoint, Trapezoidal, and Simpson's methods, covered in this course, helps build a strong understanding of scientific computation. The course's emphasis on the coding aspects using MATLAB directly benefits someone aiming to become a Computational Scientist, particularly the course's coverage of example MATLAB codes.

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Mechanical Engineer

Mechanical Engineers design, develop, and test mechanical and thermal devices. Numerical methods are required for simulations, such as finite element analysis. This course's coverage of root finding techniques, like the Secant method, and numerical integration techniques build a foundation for solving complex engineering problems. Specifically, the MATLAB coding examples and downloadable resources are useful for mechanical engineers to apply these methods in practice.

See salaries and explore the career path for Mechanical Engineer

Aerospace Engineer

An Aerospace Engineer designs and tests aircraft and spacecraft. Numerical methods are essential in this field for simulating fluid dynamics, structural analysis, and control systems. This course helps build a foundation in root finding and numerical integration techniques. Aerospace engineers frequently rely on software such as MATLAB to model and solve complex engineering problems, making this course helpful. The MATLAB coding examples, combined with the underlying theory, will provides a valuable aid for Aerospace Engineers.

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Electrical Engineer

Electrical Engineers design, develop, and test electrical equipment and systems. Numerical methods are essential for circuit simulation, signal processing, and control systems. This course covers root finding and numerical integration techniques, useful for electrical engineers. The focus on MATLAB coding directly contributes to the skills needed for simulation and analysis in electrical engineering, especially given the course's downloadable MATLAB codes.

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Robotics Engineer

A Robotics Engineer designs, builds, and programs robots for various applications. Numerical methods are essential for robot control, simulation, and optimization. This course helps build a foundation in these methods using MATLAB. Specifically, the course's discussion of root finding techniques like Newton's Method, and numerical integration techniques, such as the Trapezoidal method, provides the mathematical tools needed for trajectory planning and control algorithms. Furthermore, the course includes downloadable MATLAB codes and is directly applicable to implementing numerical solutions in robotics projects, making this course useful for Robotics Engineers.

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Chemical Engineer

Chemical Engineers design and operate chemical plants. Numerical methods are used to simulate chemical reactions, optimize processes, and analyze transport phenomena. This course may be useful in that it teaches root finding and numerical integration techniques, applicable to solving chemical engineering problems. The MATLAB coding skills enhanced in the course are valuable for implementing simulations, making the course useful to chemical engineers.

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Data Scientist

A Data Scientist uses programming skills and statistical knowledge to collect, analyze, and interpret large datasets. This course may be helpful to a budding Data Scientist because it enhances coding skills, particularly in MATLAB, which is used for numerical computation. The root finding and numerical integration techniques covered are also relevant for statistical modeling and analysis. Familiarity with the algorithms discussed in the course, alongside experience using MATLAB, builds a foundation for implementing data science methodologies. This course is useful, specifically, because it provides MATLAB codes needed to run all of the examples.

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Civil Engineer

Civil Engineers design, construct, and maintain infrastructure projects. Numerical methods are used to model structural behavior, simulate fluid flow, and optimize designs. This course may provide an understanding of these methods, and hands-on experience with MATLAB, useful for civil engineers. In particular, the course covers MATLAB coding of root finding and numerical intergration techniques.

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Atmospheric Scientist

Atmospheric Scientists study weather, climate, and air quality. They rely heavily on numerical models to simulate atmospheric processes and predict future conditions. An Atmospheric Scientist benefits from the root finding and numerical integration techniques taught in this course. The use of MATLAB, combined with the theoretical knowledge presented, provides a foundation for implementing and analyzing atmospheric models. The downloadable MATLAB codes included in the course could prove quite helpful to an Atmospheric Scientist.

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Biomedical Engineer

Biomedical Engineers apply engineering principles to solve medical and healthcare-related problems. Numerical methods can be used to model physiological systems, analyze medical images, and design medical devices. This course may be useful because it provides a foundation in root finding and numerical integration techniques, particularly in MATLAB. The ability to code and implement these methods, which this course is designed to enhance, may be valuable for biomedical engineers working with quantitative data and simulations.

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Geophysicist

Geophysicists study the physical properties and processes of the Earth. They use numerical methods for seismic data processing, gravity and magnetic field modeling, and geothermal simulations. This course may be useful because it covers root finding and numerical integration techniques using MATLAB. This course, in particular, builds experience with algorithms and enhances the knowledge of MATLAB.

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Hydrologist

Hydrologists study the distribution, circulation, and properties of water. They use numerical models to simulate groundwater flow, surface water runoff, and water quality. The numerical integration techniques and MATLAB coding skills that this course enhances will helps build the ability to develop and implement these models. The included MATLAB codes, in particular, should be beneficial to a practicing Hydrologist.

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Statistician

Statisticians collect, analyze, and interpret data to inform decision-making. While this role typically requires an advanced degree, statisticians use numerical methods for statistical modeling, simulation, and optimization. This course may be useful in that it enhances coding skills, particularly in MATLAB, which is used for statistical computing. The numerical integration techniques covered are also relevant for statistical inference and modeling. The theory behind the techniques, as well as the coding aspects, is specifically beneficial.

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Financial Analyst

A Financial Analyst analyzes financial data, provides forecasts, and advises on investment strategies. Numerical methods, such as those discussed in this course, can be applied to model financial markets and price derivatives. While this course might not directly cover finance-specific models, the root finding and numerical integration techniques presented are fundamental to many financial algorithms. This course may equip financial analysts with the quantitative skills needed to implement and understand these models in MATLAB. The fact that the course provides MATLAB codes to run all its examples help further.

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Data Analyst

Data Analysts interpret data to identify trends, patterns, and insights. While this role may not always require an advanced degree, numerical methods play a role in various analytical techniques. This course may be useful to a data analyst to enhance coding skills, particularly in MATLAB, and to learn numerical techniques. The course's examples and downloadable MATLAB codes can be used to build custom tools for data processing and analysis.

See salaries and explore the career path for Data Analyst

Numerical Methods in MATLAB for Engineering Students Part 1

What's inside

Learning objectives

Syllabus

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Reviews summary

Numerical methods and matlab for engineers

Activities

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