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Differential Equations Part I Basic Theory

Kwon, Kil Hyun and Kil Hyun Kwon

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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What's inside

Syllabus

Introduction

First Order Differential Equation 1

FIRST ORDER DEFERENTIAL EQUATION 2

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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

Basic ordinary differential equations theory

According to learners, this course provides a solid introduction to the basic theory and practical methods for solving ordinary differential equations. Many found it useful for building a foundation, particularly those needing DEs for practical applications in their field. Some students noted the importance of having strong prerequisites in calculus and linear algebra, as the material builds directly upon these topics and can be challenging if unprepared. As Part I, it focuses on core concepts and common techniques, serving as a necessary first step before exploring more advanced topics.

Covers fundamentals, not advanced topics.

"Keep in mind this is just the first part; it covers the essential basics but not advanced DEs."

"It provides a good foundation but you'll need follow-up courses for broader coverage."

"The course focuses on first and second order equations as advertised."

"It's a necessary prerequisite for learning more complex differential equations."

Provides a foundational look at core concepts.

"I found this course great for understanding the fundamental concepts of differential equations for the first time."

"It covers the essential basic theory needed to get started with ODEs."

"The material provided a necessary introduction to the main types of first and second order equations."

"This course served as a good starting point for learning about ODEs."

Instruction helps in understanding complex topics.

"The instructor explained the concepts clearly, which was very helpful."

"I felt the teaching style made difficult ideas more accessible."

"The lectures were well-structured and easy to follow most of the time."

"Good explanations made learning the solving methods much smoother."

Emphasizes application rather than abstract proofs.

"This course was very helpful for seeing how differential equations are used in real-world problems."

"I appreciated the focus on practical use and solving methods relevant to applications."

"The way the course tied theory to applications made the concepts much clearer."

"It gave me the tools I needed to start using DEs in my own work."

Some learners found the concepts difficult.

"I found some of the topics quite challenging and needed to spend extra time on them."

"The problems required a good amount of critical thinking and practice."

"While basic, differential equations themselves are not always easy to grasp initially."

"Some sections were definitely more difficult than others."

Requires strong background in calculus and linear algebra.

"Make sure your calculus and linear algebra skills are solid before starting this course."

"I struggled at times because my understanding of the prerequisites wasn't strong enough."

"The course moves quickly, assuming you are comfortable with related math topics."

"Having a good grasp of matrices and derivatives is essential for success here."

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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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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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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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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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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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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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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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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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

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What's inside

Syllabus

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Reviews summary

Basic ordinary differential equations theory

Activities

Career center

Reading list

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