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Differential Equations Part I Basic Theory

This introductory courses on (Ordinary) Differential Equations are mainly for the people, who need differential equations mostly for the practical use in their own fields. So we try to provide basic terminologies, concepts, and methods of solving various types of differential equations as well as a rudimentary but indispensable knowledge of the underlying theory and some related applications.

The prerequisites of the courses is one- or two- semester calculus course and some exposure to the elementary theory of matrices like determinants, Cramer’s Rule for solving linear systems of equations, eigenvalues and eigenvectors.

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Syllabus

Introduction

First Order Differential Equation 1

FIRST ORDER DEFERENTIAL EQUATION 2

Mathematical Modeling and Applications

LINEAR SECOND ORDER EQUATIONS 1

Linear Second order equations 2

Linear Second order equations 3

Linear Second order equations 4

APPLICATIONS OF SECOND ORDER EQUATIONS

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This course delves into differential equations, which serve as essential tools for various fields, including science, engineering, and technology

Designed for learners seeking practical applications rather than solely theoretical knowledge

Builds a strong foundation in differential equations for students with calculus backgrounds

Offered by instructors Kil Hyun Kwon and Kil Hyun Kwon

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Reviews summary

Differential equations i: well-explained, engaging

Learners say that Differential Equations Part I Basic Theory is a well-received course, featuring a great instructor, engaging assignments, and easy-to-understand lectures. While this course is considered quite difficult, learners generally enjoyed it and found it to be informative and worthwhile. Students particularly appreciated the practical nature of this course, which helped them to understand how differential equations are applied in real-world situations. However, some learners did have difficulty understanding the instructor's accent.

The course includes many practical applications of differential equations.

"This course is so much important for me.by the course i learn many new things & many solving problem system.The instructor of this course is so much expert in teachin."

"Suitable concepts about ordinary differential equations and its concepts , with a little touch of applications just like pendulum, spring mass system.Especially, the lectures were well explained.I really very much happy to be as a learner of this course."

"this course teach me so much about differential equations and there application"

"The contents and concepts are very good and examples are very useful in real life"

The instructor is well-respected and engaging

"Thank you Professor Kwon, Kim Hyun for your distinguished tutorials and attention. I am better prepared with differential equations."

"I have enjoyed taking this course. The topics have been divided very well in that they are not too long and hard just the right amount. The lecturer was delightful and easy to understand."

"The Korean accent was quite hard to understand. So I had to repeat some of the clips over and over again. But overall, it is an effective online learning course program"

"An excellent platform for the subject knowledge. Coursera teaches the different types of learning methods .in this couse I learned about differential equations applicable to physical concepts"

Some learners found the instructor's accent difficult to understand.

"The Korean accent was quite hard to understand. So I had to repeat some of the clips over and over again. But overall, it is an effective online learning course program"

"The English accent of the professor is not understandable,which makes it difficult to understand what he is explaining."

The course is generally considered to be difficult.

"It was quite difficult but worth it!"

"Gives you in-depth knowledge of Differential equations but there is a little bit less explaination in WEEK-7 topic- ANNIHILATOR. But overall the course is very good to study."

"I liked the presenter and assume most of my problems caused by the decades since I last studied calculus. (I had forgotten lots about integration and imaginery numbers). Can I still buy the certificate?"

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 Differential Equations Part I Basic Theory with these activities:

Read and Review 'Ordinary Differential Equations' by Tenenbaum and Pollard

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This book provides a solid foundation in differential equations and is highly recommended as a reference text for this course.

View Ordinary Differential Equations (Dover Books on... on Amazon

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Read the introductory chapter to familiarize yourself with the basic concepts of differential equations.
Work through the examples and exercises in each chapter to reinforce your understanding.
Use the book as a reference when working on assignments and projects throughout the course.

Join a study group

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Discussing the course material with peers can help you understand different perspectives and identify areas where you need additional support.

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Find a group of classmates who are also taking the course.
Meet regularly to discuss the course material, work on assignments together, and quiz each other.
Be an active participant in the group and contribute to the discussions.

Attend a Differential Equations Workshop

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Attending a differential equations workshop can provide an opportunity to learn from experts and ask questions in a focused setting.

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Find a differential equations workshop that is offered in your area.
Register for the workshop and attend all the sessions.
Take notes during the workshop and ask questions to the instructors.

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Career center

Learners who complete Differential Equations Part I Basic Theory will develop knowledge and skills that may be useful to these careers:

Professor

A professor conducts research in their field and often teaches at a higher education institution. To be successful in this career, you need a strong foundation in the theories, concepts, and methodologies of your field and must be able to effectively teach students. This course will provide you with important foundational knowledge in the field of differential equations that is often required for advanced research.

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Physicist

A physicist explores the forces, energy, and matter that make up the universe. This course may be useful for those wanting to work with differential equations, which are used heavily in modeling physical phenomena to generate testable predictions.

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Epidemiologist

An epidemiologist investigates patterns and causes of disease and other health problems in populations. This course may be useful for those wanting to work with differential equations, which are useful in modeling the spread of diseases and other phenomena.

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Data Scientist

A data scientist analyzes data to extract meaningful insights and develop solutions to business problems. This course may be useful for those wanting to learn about differential equations, which can be used to model various types of data.

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Financial Analyst

A financial analyst provides investment advice to individuals and institutions, making recommendations on stocks, bonds, and other financial instruments. This course may be useful for those wanting to learn about differential equations, which can be used to model financial data.

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Systems Analyst

A systems analyst designs, develops, and implements computer systems to meet the needs of an organization. Differential equations are used in modeling for systems analysis, and may be useful to someone working in this field.

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Mathematician

A mathematician develops and applies mathematical principles to solve problems in various fields, including science, engineering, and business. A strong foundation in differential equations may be useful to someone pursuing this career.

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Operations Research Analyst

An operations research analyst develops and applies analytical methods to help organizations make better decisions. Some operations research analysts use differential equations to build models for optimization.

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Engineer

An engineer designs, builds, and maintains machines, structures, and systems. Differential equations are used heavily in engineering to model physical systems.

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Software Developer

A software developer designs, develops, and maintains software systems. Differential equations can be used to model software behavior.

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Actuary

An actuary uses mathematical and statistical methods to assess risk and uncertainty. Differential equations may be useful in this career, as they are often used to model risk and uncertainty

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Market Researcher

A market researcher conducts research to understand market trends and consumer behavior. Differential equations can be used to model market behavior.

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Biostatistician

A biostatistician uses statistical methods to design and analyze studies in the health sciences. Differential equations may be useful to a biostatistician because they are often used to model biological systems.

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Economist

An economist studies the production, distribution, and consumption of goods and services. Differential equations may be useful in this career, as they are often used to model economic systems.

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Statistician

A statistician collects, analyzes, interprets, and presents data. Differential equations may be useful in this career, as they are often used to model statistical models.

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Reading list

We've selected 14 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 Differential Equations Part I Basic Theory.

Squigonometry: The Study of Imperfect Circles

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Provides a clear and comprehensive introduction to differential equations and their applications. It is written in a conversational style and provides many examples and exercises to help students understand the concepts.

Differential Equations Part I Basic Theory

Here's a deal for you

What's inside

Syllabus

Good to know

Save this course

Reviews summary

Differential equations i: well-explained, engaging

Activities

Career center

Reading list

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