A Beginner's Guide to Numerical Methods in MATLAB from Udemy

What's inside

Learning objectives

Understand about the ways computer store numbers
Choose the right numerical methods to solve a problem

Measure (and avoid) the errors inherent in numeric calculations
See how algorithms are implemented in matlab

Understand about the ways computer store numbers
Choose the right numerical methods to solve a problem
Measure (and avoid) the errors inherent in numeric calculations
See how algorithms are implemented in matlab

Syllabus

Undestand the key ideas and concepts behind numerical methods

Some motivating examples of what the course can help you do.

Understand how computers store numbers and what can go wrong

How do you store numbers using only 0s and 1s?

How computers actually store numbers. A discussion of mantissa, exponent and bias.

We talk about the notion of the machine epsilon and the fact that it's not really that useful when specifying calculation tolerances.

The two types of errors that reduce the accuracy of numerical methods.

Use MATLAB to calculate round-off and truncation errors.

What makes a function continuous?

The claim that a differentiable function that has equal states at two distinct point has a stationary point somewhere in between.

Another theorem you need to be aware of.

If a<b and f(a)f(b)<0 then the root of f(x) = 0 lies between a and b.

What are one-point iterative methods and what are they used for?

The notion of convergence (and divergence, too).

A look at Aitken's Δ² process and Steffensen's method.

Use MATLAB to fast solve the root-finding problem.

What is the order of convergence and why do we care?

An extremely efficient and popular root finding method. Quadratic convergence, woo-hoo!

Use MATLAB to solve the root-finding problem.

Newton's method applied in many dimensions. Useful for solving systems of non-linear equations!

What kind of simplicifications can be made to divided differences if we assume the points are equally spaced?

What if you cannot get the Jacobian matrix in analytic form? Use finite differences! (Note: finite differences are actually discussed in a later section, so you can come back to this clip later.)

Use MATLAB to solve a root-finding problem.

A way of speeding up polynomial evaluations.

Use MATLAB to evaluate polynomial.

A very simple method that leverages Bolzano's theorem.

Similar to the Bisection method, Regula Falsi can, in most cases, provide faster convergence than the Bisection method.

An interpolation formula for Lagrange polynomial.

Yet another single-point iteration method.

An introduction to the concept of interpolation, with a simple example.

A better way of defining the interpolating polynomial.

Did you think the Newton basis was cool? With divided difference, you don't even have to solve the triangular set of equations!

The derivations of divided differences took too much time, so the examples get their own separate lesson.

Use MATLAB to determite the interpolated value of a point.

An improvement of Lagrangian interpolation.

Finite difference approximations of derivatives - forward, backward and central differences.

Now a formula for the 2nd derivative approximation.

A look that the error terms in first and second derivatives that arise from using finite difference methods.

A method of combining approximations for improving accuracy.

Why would we want to integrate things numerically?

The simplest way of estimating the value of an integral.

Subdivide an integral into several strips, evaluate functions as midpoints, treat strips as rectangles. Profit!

A way of numerically calculating a specific type of integral.

Another numeric procedure for a very specific integral. Usable for calculating the Gamma function!

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Uses MATLAB, a widely used software in both academia and industry, making it easier to translate theoretical knowledge into practical problem-solving skills

Covers error analysis, which is crucial for understanding the limitations and reliability of numerical methods in real-world applications

Includes quizzes and downloadable MATLAB files, which facilitates hands-on learning and reinforces theoretical concepts through practical application

Requires access to MATLAB software, which may involve a purchase or subscription, potentially posing a barrier for some learners

Focuses on specific numerical methods like interpolation and curve fitting, which are essential for data analysis and modeling in various fields

Reviews summary

Introductory numerical methods with matlab

According to learners, this course provides a solid introduction to the concepts of numerical methods and their implementation in MATLAB. Many students found the explanations of theoretical concepts to be clear and well-structured. The inclusion of practical MATLAB code and examples was frequently highlighted as a major strength, making the application of the methods understandable. However, some learners felt the pace could be challenging for absolute beginners without some prior mathematical or programming background. There were also comments suggesting the depth of coverage varied for different topics and that more challenging exercises would be beneficial. Overall, it is considered a good starting point for applying numerical techniques using MATLAB.

Some topics covered more deeply than others.

"The sections on root-finding and interpolation were very thorough, but I felt numerical differentiation and integration could have gone a bit deeper."

"It's a good survey of different methods, but don't expect exhaustive coverage of every technique."

"Provides a solid overview of the key areas mentioned in the syllabus."

Quizzes are okay, but more practice needed.

"The quizzes tested basic understanding, but I wish there were more hands-on coding exercises or problem sets."

"While the quizzes are helpful for checking comprehension, they don't fully prepare you for applying the methods to complex problems."

"Could benefit from more challenging assignments to really test the understanding of the concepts and MATLAB implementation."

The course provides a good foundation in the theory.

"The theoretical explanations for the numerical methods covered were surprisingly clear and easy to follow, which is often difficult with this subject."

"I really appreciated how the course broke down the mathematical concepts before diving into the code."

"The lectures on floating point errors and convergence were particularly well-explained and helped solidify my understanding."

Practical examples and code in MATLAB are helpful.

"The MATLAB examples provided were extremely useful. Seeing the methods implemented step-by-step made a huge difference."

"Having the actual MATLAB files available for download allowed me to run and experiment with the code myself."

"The practical application in MATLAB helped me connect the theory to real-world problem solving."

Pace may be fast for some beginners.

"While the course is titled 'Beginner's Guide', I felt the pace was a bit fast at times, assuming some prior knowledge I didn't have."

"If you are completely new to both numerical methods AND MATLAB, you might find yourself needing to pause and rewatch sections frequently."

"I think a basic understanding of calculus and linear algebra is helpful, even though it's marketed for beginners."

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 A Beginner's Guide to Numerical Methods in MATLAB with these activities:

Review Calculus Fundamentals

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Reinforce your understanding of calculus concepts, as numerical methods often rely on these principles. This will help you better understand the underlying theory and limitations of the methods.

Browse courses on Limits

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Review key concepts like limits, derivatives, and integrals.
Work through practice problems to solidify your understanding.
Focus on the Fundamental Theorem of Calculus.

Brush Up on MATLAB Fundamentals

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Practice basic MATLAB commands and syntax to ensure you can effectively implement the numerical methods taught in the course. This will reduce frustration and allow you to focus on the numerical concepts.

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Review basic syntax and data types in MATLAB.
Practice writing simple functions and scripts.
Familiarize yourself with plotting and debugging tools.

Numerical Methods with MATLAB: Implementations and Applications

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Supplement your learning with a comprehensive textbook that provides detailed explanations and MATLAB examples. This will give you a deeper understanding of the methods and their practical applications.

View Numerical Methods with MATLAB 2nd (second)... on Amazon

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Read the chapters corresponding to the course topics.
Work through the examples and exercises in the book.
Compare the book's approach to the course's approach.

Four other activities

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Show all seven activities

Implement Root-Finding Algorithms

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Practice implementing root-finding algorithms like Bisection, Newton-Raphson, and Secant methods in MATLAB. This will solidify your understanding of these methods and improve your coding skills.

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Choose a root-finding algorithm (e.g., Bisection, Newton-Raphson).
Implement the algorithm in MATLAB.
Test the algorithm with different functions and initial guesses.
Compare the performance of different algorithms.

Create a Numerical Methods Cheat Sheet

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Compile a cheat sheet summarizing the key formulas, algorithms, and error analysis techniques covered in the course. This will serve as a valuable reference for future use.

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Review the course materials and identify key concepts.
Organize the information into a concise and easy-to-read format.
Include formulas, algorithms, and error analysis techniques.

Solve a Real-World Problem with Numerical Methods

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Apply the numerical methods learned in the course to solve a real-world problem from your field of interest. This will demonstrate your understanding of the methods and their practical applications.

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Identify a real-world problem that can be solved with numerical methods.
Choose appropriate numerical methods to solve the problem.
Implement the methods in MATLAB and analyze the results.
Write a report summarizing your findings.

Applied Numerical Methods with MATLAB for Engineers and Scientists

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Explore a textbook that emphasizes the application of numerical methods in engineering and science. This will broaden your understanding of how these methods are used in practice.

View Spreadsheet Problem Solving and Programming for... on Amazon

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Browse through the book and identify relevant chapters.
Study the examples and try to implement them in MATLAB.
Compare the book's examples to the problems covered in the course.

Career center

Learners who complete A Beginner's Guide to Numerical Methods in MATLAB will develop knowledge and skills that may be useful to these careers:

Simulation Engineer

A simulation engineer develops and uses computer simulations to model and analyze physical systems or processes. Numerical methods are at the heart of simulation engineering, enabling engineers to approximate solutions to complex equations and predict system behavior. This course helps to develop fundamental knowledge of numerical methods, particularly with the focus on MATLAB. With simulation engineering, accuracy is paramount, so the course's emphasis on error analysis helps improve the reliability of simulations. The content on iterative methods, interpolation, and numerical integration are also beneficial.

See salaries and explore the career path for Simulation Engineer

Computational Scientist

A computational scientist develops and applies computational models and simulations to solve complex scientific problems. This often involves using numerical methods to analyze data, simulate physical systems, and make predictions. This course helps develop a strong foundation in numerical methods, particularly with its focus on MATLAB, a common tool in computational science. The course's modules on error analysis and minimization are particularly relevant for creating reliable and accurate scientific simulations. Furthermore, the skills gained in interpolation, curve fitting, numerical differentiation, and integration covered in this course help to provide a comprehensive toolkit for any aspiring computational scientist.

See salaries and explore the career path for Computational Scientist

Research Scientist

A research scientist plans and conducts experiments, analyzes data, and publishes findings in a specific field of science. Numerical methods are often used in research to simulate complex systems, analyze experimental data, and develop theoretical models. This course helps build a solid foundation in numerical methods, equipping research scientists with the tools needed to perform advanced data analysis and modeling. The course's emphasis on error analysis is crucial for ensuring the reliability and validity of research findings. The MATLAB focus of the course aligns with a common tool for scientific computation. This course is particularly relevant for research scientists in fields such as physics, engineering, and computational biology. Many research scientist positions require an advanced degree.

See salaries and explore the career path for Research Scientist

Quantitative Analyst

A quantitative analyst, often working in the financial industry, develops and implements mathematical models for pricing derivatives, managing risk, and making trading decisions. These models rely heavily on numerical methods for solving complex equations and simulating market behavior. This course helps provide a strong foundation in these numerical methods, essential for any aspiring quantitative analyst. The exploration of iterative methods, interpolation, numerical differentiation, and integration covered provides valuable insights into the tools used in quantitative finance. Furthermore, the MATLAB-based approach of the course aligns with a standard programming environment in the field. Quantitative analyst positions typically require an advanced degree.

See salaries and explore the career path for Quantitative Analyst

Modeling Analyst

A modeling analyst builds and uses mathematical or computational models to analyze data, simulate scenarios, and make predictions in many different industries. This course provides a foundation in numerical methods that are essential for creating and validating these models. As a modeling analyst, the course helps develop an understanding of interpolation and curve fitting to help you represent complex relationships between variables. The emphasis on error analysis helps modeling analysts ensure the accuracy and reliability of their models. You will likely be using software like MATLAB to implement these models.

See salaries and explore the career path for Modeling Analyst

Algorithm Developer

An algorithm developer designs and implements algorithms for various applications, such as search engines, data compression, and machine learning. This course provides a strong foundation in numerical methods, which are essential for developing efficient and accurate algorithms. This is especially true for the kinds of algorithm developers who focus on numerical computing. The course's coverage of iterative methods, interpolation, and numerical integration directly translates to the development of algorithms for optimization, approximation, and simulation. The MATLAB-based examples in the course help algorithm developers to rapidly prototype and test their ideas. An algorithm developer wanting to go into numerical computing should take this course.

See salaries and explore the career path for Algorithm Developer

Statistician

A statistician collects, analyzes, and interprets data to draw conclusions and make predictions. Numerical methods are used extensively in statistics for tasks such as parameter estimation, model fitting, and hypothesis testing. This course helps build a strong foundation in numerical methods, equipping statisticians with a broader range of tools for analyzing data. The topics of error analysis, interpolation, and curve fitting covered in the course offer the ability critically evaluate statistical models. The hands-on MATLAB examples in this course further solidify one's understanding of these concepts.

See salaries and explore the career path for Statistician

Biostatistician

A biostatistician applies statistical methods to solve problems in biology, medicine, and public health. Numerical methods are often used in biostatistics for tasks such as analyzing clinical trial data, modeling disease progression, and predicting treatment outcomes. This course helps provide a foundation in numerical methods, which are often used in statistical analysis and data modeling. The MATLAB examples can also be useful as you become a biostatistician. In particular, the discussion of the ways that computers store numerical data and the possible errors that can arise can be greatly beneficial.

See salaries and explore the career path for Biostatistician

Data Scientist

A data scientist uses statistical methods, machine learning algorithms, and data visualization techniques to extract insights from data. Numerical methods are used extensively in data science for tasks such as model training, optimization, and simulation. This course helps provide a foundation in these key numerical methods. The course's coverage of interpolation and curve fitting is particularly relevant for building predictive models and handling missing data. Given this course's practical approach in MATLAB, this learning experience can become very helpful for data scientists.

See salaries and explore the career path for Data Scientist

Econometrician

An econometrician uses statistical and mathematical models to analyze economic data and test economic theories. Numerical methods are widely used in econometrics for tasks such as parameter estimation, model simulation, and forecasting. This course helps provide practical skills in numerical methods, including interpolation, curve fitting, and numerical integration. The hands-on experience with MATLAB provides the ability to implement econometric models and analyze data effectively, which is critical to this career. An econometrician must be able to analyze errors and their impact.

See salaries and explore the career path for Econometrician

Data Analyst

A data analyst examines and interprets data to identify trends, patterns, and insights. This often involves using numerical methods to clean, process, and analyze large datasets. This course may be helpful in developing a foundational understanding of numerical methods, which are often used in statistical analysis and data modeling. With content on interpolation and curve fitting, this course equips aspiring data analysts with the ability to create accurate models from potentially noisy real-world data. Additionally, the course's focus on error analysis helps data analysts to critically evaluate the reliability of their findings. Data that is processed inside of MATLAB, as the course uses, is a big part of a data analyst's job.

See salaries and explore the career path for Data Analyst

Machine Learning Engineer

A machine learning engineer develops and deploys machine learning models for various applications. While not every aspect of machine learning directly involves numerical methods, many core algorithms rely on techniques such as optimization, linear algebra, and numerical integration. This course helps improve proficiency in these numerical techniques, which are crucial for understanding and implementing machine learning algorithms. The course's MATLAB examples provide a practical foundation for prototyping and testing machine learning models. The emphasis on iterative methods, interpolation, and numerical integration may be particularly useful in the field of machine learning.

See salaries and explore the career path for Machine Learning Engineer

Financial Analyst

A financial analyst evaluates financial data, such as market trends and company performance, to provide investment recommendations. Quantitative analysis, which relies heavily on numerical methods, is a core component of this role. This course helps build a foundation in numerical methods, providing the tools needed to model financial instruments, forecast market behavior, and assess risk. The course's exploration of interpolation and curve fitting is particularly relevant for building predictive models based on historical data. Moreover, the MATLAB focus of this course aligns with the tools commonly used in the financial industry. Aspiring financial analysts looking to enhance their quantitative skills may find this course compelling.

See salaries and explore the career path for Financial Analyst

Software Engineer

A software engineer designs, develops, and tests software applications. While not all software engineering roles require extensive knowledge of numerical methods, some specialized areas, such as scientific computing and data analysis, certainly do. This course may be useful for software engineers working on applications that involve numerical computations, simulations, or data processing. The focus on MATLAB provides practical experience with a widely used programming environment for scientific computing. In particular, the content on avoiding errors inherent in numeric calculations may be useful.

See salaries and explore the career path for Software Engineer

Systems Engineer

A systems engineer focuses on the design, integration, and management of complex systems. In many engineering applications, numerical methods are used to simulate system behavior, optimize performance, and analyze stability. This course may be useful for systems engineers seeking to enhance their analytical skills and gain a deeper understanding of numerical modeling. The coursework on differential equations, root finding and numerical integration helps expand your capabilities as a systems engineer. Familiarity with MATLAB and understanding of numerical methods are very useful for this technical role.

See salaries and explore the career path for Systems Engineer

Reading list

We've selected two books that we think will supplement your learning. Use these to develop background knowledge, enrich your coursework, and gain a deeper understanding of the topics covered in A Beginner's Guide to Numerical Methods in MATLAB.

Numerical Methods with MATLAB

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Provides a comprehensive overview of numerical methods with a strong focus on MATLAB implementations. It covers a wide range of topics relevant to the course, including root-finding, interpolation, numerical differentiation and integration, and more. The book is valuable as a reference text and provides additional depth to the course material. It is commonly used as a textbook in numerical methods courses.

Numerical Methods with MATLAB 2nd (second) edition...

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Spreadsheet Problem Solving and Programming for...

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Widely used textbook that covers a broad range of numerical methods with a focus on engineering and scientific applications. It provides clear explanations, numerous examples, and MATLAB code snippets. This book is particularly helpful for understanding the practical applications of numerical methods and can serve as a valuable reference for solving real-world problems. It adds breadth to the course by showcasing diverse applications.

Spreadsheet Problem Solving and Programming for...

Paperback

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Spreadsheet Problem Solving and Programming for...

Kindle Edition

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A Beginner's Guide to Numerical Methods in MATLAB

What's inside

Learning objectives

Syllabus

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Reviews summary

Introductory numerical methods with matlab

Activities

Career center

Reading list

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