Applying Differential Equations and Inverse Models with R from Pluralsight

This course focuses on conceptually understanding and implementing numerical techniques to solve differential equations, including ordinary/partial/delay differential equations, and systems of equations known as Differential Algebraic Equations.

Differential equations are a topic rich in history - several important results date back to the 18th and 19th centuries - but their importance is not confined to the history books: Differential equations still have wide and varied applications: did you know, for instance, that the famous S-curve, which we often find using logistic regression, can also be obtained by solving a differential equation? Likewise, the Black Scholes Equation which lies at the foundation of modern quantitative finance can be solved conveniently by conversion to the heat equation.

In this course, Applying Differential Equations and Inverse Models in R, you will explore a wide variety of differential equations, as well as an unrelated technique known as inverse modeling, and learn how you can apply these techniques using the R programming language.

First, you will learn how many different physical, chemical, and financial phenomena can be modeled using Differential Equations. You will see how population growth, the spread of infectious diseases, the pricing of complex financial derivatives, and the equilibrium in a chemical reaction can all be modeled using Differential Equations.

Next, you will discover how different types of differential equations are modeled and solved numerically. You will see how a mix of algebraic and differential equations forms a system known as a DAE, or Differential Algebraic Equation; and how a time-varying relationship between the dependent and independent variables can be modeled using Delay Differential Equations.

Finally, you will explore how initial as well as boundary value differential equations. You will see how the temperature varies with time in a rod that is being heated by a heat source, has one end insulated, and has the other end exposed to the atmosphere. You might find this use-case arcane, but this is the famous diffusion equation, which is also the basis of the Black-Scholes PDE from quant finance. You will round off this course of by understanding even-determined, under-determined, and over-determined systems, and working with such systems using R programming

When you’re finished with this course, you will have the skills and knowledge to apply a variety of numerical procedures to solve differential equations using the R programming language.

What's inside

Syllabus

Course Overview

Getting Started with Differential Equations

Understanding Types of Differential Equations

Solving Differential Equations

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Teaches Differential Equations, which are a cornerstone in many scientific and engineering disciplines

Taught by Janani Ravi, who are known for their work in the field of numerical analysis

Examines Differential Equations, which is highly relevant in various industries like finance, biology, and chemistry

Develops numerical techniques for solving differential equations, which are essential skills for data scientists and analysts

Uses R programming, which is widely used in data science and machine learning

Covers a range of differential equations, including ordinary, partial, delay, and Differential Algebraic Equations

Reviews summary

Practical r applications for differential equations

According to learners, this course offers an excellent deep dive into differential equations, emphasizing practical application using R. Students highlight the instructor's clear explanations that effectively break down complex concepts and link them to real-world phenomena like disease spread and financial models. The hands-on R examples and code are frequently praised as invaluable and well-done, making it rewarding for those interested in computational modeling. While many found the course challenging but manageable, especially for those bridging theory to implementation, some mention that it assumes a very strong mathematical background and may be too fast for beginners or those rusty on calculus. Overall, it's considered a valuable course for quantitative analysts and engineers.

Instructor provides clear explanations for complex topics.

"The instructor's explanations were incredibly clear, breaking down complex concepts into manageable parts."

"The instructor clearly knows his subject and his passion for the subject really shone through."

"An absolute gem... This course helped me bridge the gap to practical implementation."

Strong emphasis on hands-on application with R code and examples.

"The practical examples and R code were invaluable, making it easy to follow along and apply the techniques."

"The R implementations were well-done... The hands-on exercises in R were crucial for my learning."

"The course isn't just about theory; it's about applying it. The R demonstrations are excellent."

"I learned a lot about how to numerically solve different types of differential equations. The real-world applications were a highlight."

Some found structure slightly disorganized or R code dense.

"The course has good content, but it felt a bit disorganized at times. Some parts jumped between topics."

"The R code was also a bit dense at times. It could use more comments for clarity for intermediate users."

"My only minor critique is that some explanations could be more concise."

Requires solid mathematical foundations; challenging for beginners.

"It assumes a very strong mathematical background. Not for beginners, for sure."

"The pacing was too fast for someone like me who hasn't touched differential equations in years."

"Perhaps a pre-requisite check or a more explicit warning about the mathematical rigor would be helpful."

"I came in with a decent understanding of calculus but limited R experience, and found it manageable."

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 Applying Differential Equations and Inverse Models with R with these activities:

Compile and organize course materials

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Organizing your course materials will help to avoid confusion and ensure that you have easy access to the materials you need.

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Gather all of your course materials, including notes, assignments, and slides.
Create a filing system or use a digital tool to organize your materials.
Label and categorize your materials for easy referencing.

Review topics in linear algebra

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Reviewing linear algebra will help you better understand matrix theory and numerical methods for solving differential equations.

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Review matrix operations and properties.
Practice solving systems of linear equations.
Review vector spaces and subspaces.

Join a study group for the course

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Study groups provide opportunities to discuss the course material, ask questions, and learn from others.

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Find a study group or form one with classmates.
Meet regularly to discuss the course material.
Work together to solve problems and prepare for exams.

Two other activities

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Follow tutorials on solving differential equations with R

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Tutorials provide hands-on practice and reinforce the concepts you learn in the course.

Browse courses on R Programming

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Find tutorials on solving differential equations with R.
Follow the tutorials step-by-step.
Apply the techniques to solve your own differential equations.

Build a differential equation model for a real-world problem

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Applying differential equations to solve a real-world problem will reinforce your understanding and demonstrate the practical significance of the course.

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Identify a problem that can be modeled using differential equations.
Develop a mathematical model using differential equations.
Solve the differential equations to obtain a solution.
Interpret the solution and discuss its implications.

Career center

Learners who complete Applying Differential Equations and Inverse Models with R will develop knowledge and skills that may be useful to these careers:

Financial Analyst

Financial Analysts advise individuals and organizations on financial matters, including investment decisions. They use a variety of financial models and techniques to analyze and interpret financial data, including differential equations. This course can help Financial Analysts improve their understanding of differential equations and how they can use them to make better informed investment decisions. It may also help them develop new models and techniques for financial analysis.

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Quantitative Analyst

Quantitative Analysts use mathematical and statistical models to support investment and business decisions. They use a variety of techniques, including differential equations, to model and analyze financial and business data. This course can help Quantitative Analysts develop the skills they need to use differential equations to make better informed investment and business decisions.

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Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to help organizations improve their efficiency and effectiveness. They use a variety of techniques, including differential equations, to model and analyze complex systems. This course can help Operations Research Analysts develop the skills they need to use differential equations to solve real-world problems. It can also help them build a foundation for further study in operations research.

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Systems Engineer

Systems Engineers design and develop complex systems. They use a variety of techniques, including differential equations, to model and analyze these systems. This course can help Systems Engineers develop the skills they need to use differential equations to design and develop better systems.

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Control Systems Engineer

Control Systems Engineers design and develop systems that control the behavior of other systems. They use a variety of techniques, including differential equations, to model and analyze these systems. This course can help Control Systems Engineers develop the skills they need to use differential equations to design and develop better control systems.

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Chemical Engineer

Chemical Engineers design and develop chemical plants and processes. They use a variety of techniques, including differential equations, to model and analyze these systems. This course can help Chemical Engineers develop the skills they need to use differential equations to design and develop better chemical plants and processes.

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Mechanical Engineer

Mechanical Engineers design and develop mechanical systems. They use a variety of techniques, including differential equations, to model and analyze these systems. This course can help Mechanical Engineers develop the skills they need to use differential equations to design and develop better mechanical systems.

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Aerospace Engineer

Aerospace Engineers design and develop aircraft, spacecraft, and other aerospace systems. They use a variety of techniques, including differential equations, to model and analyze these systems. This course can help Aerospace Engineers develop the skills they need to use differential equations to design and develop better aerospace systems.

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Civil Engineer

Civil Engineers design and develop civil infrastructure, such as roads, bridges, and buildings. They use a variety of techniques, including differential equations, to model and analyze these systems. This course can help Civil Engineers develop the skills they need to use differential equations to design and develop better civil infrastructure.

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Environmental Engineer

Environmental Engineers design and develop systems to protect the environment. They use a variety of techniques, including differential equations, to model and analyze these systems. This course can help Environmental Engineers develop the skills they need to use differential equations to design and develop better environmental systems.

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Biomedical Engineer

Biomedical Engineers design and develop medical devices and systems. They use a variety of techniques, including differential equations, to model and analyze these systems. This course can help Biomedical Engineers develop the skills they need to use differential equations to design and develop better medical devices and systems.

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Materials Scientist

Materials Scientists develop new materials and study the properties of existing materials. They use a variety of techniques, including differential equations, to model and analyze these materials. This course can help Materials Scientists develop the skills they need to use differential equations to develop better materials.

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Mathematician

Mathematicians study the properties of numbers, sets, and other mathematical objects. They use a variety of techniques, including differential equations, to develop new mathematical theories. This course can help Mathematicians develop the skills they need to use differential equations to develop new mathematical theories.

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Physicist

Physicists study the laws of nature. They use a variety of techniques, including differential equations, to model and analyze physical phenomena. This course can help Physicists develop the skills they need to use differential equations to develop new physical theories.

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Data Scientist

Data Scientists use mathematical and statistical techniques to analyze and interpret data. They use a variety of techniques, including differential equations, to model and analyze complex systems. This course can help Data Scientists develop the skills they need to use differential equations to solve real-world problems. It can also help them build a foundation for further study in data science.

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