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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.
Read more
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.
Read more
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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OpenCourser.com/course/pex4m0/differential
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What's inside
Syllabus
Euler Equations
Power Series
Solutions about ordinary points
Read more
Syllabus
Euler Equations
Power Series
Solutions about ordinary points
Read more
Frobenius Theorem
Finding a Second Solution
Bessel Functions
Legendre Polynomials
Good to know
Good to know
Know what's good ,
what to watch for , and
possible dealbreakers
Suitable for individuals seeking practical applications of ordinary differential equations in their respective fields
Provides a foundation in terminology, concepts, and methods of solving various differential equations
Introduces fundamental theory and applications, catering to those with practical needs
Assumes prior knowledge of calculus and some basic matrix theory, setting clear prerequisites
Save this course
Save Differential Equations Part II Series Solutions to your list so you can find it easily later:
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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 II Series Solutions with these
activities:
Read the textbook
Show steps
Solidify your understanding of the fundamental concepts covered in the course by reading the textbook.
View
Differential Equations with Boundary-value...
on Amazon
Show steps
Find a mentor who can provide guidance on differential equations
Show steps
Enhance your learning journey by connecting with a mentor who can provide personalized guidance.
Show steps
-
Identify potential mentors who are experts in differential equations.
-
Reach out to the potential mentors and express your interest in their guidance.
-
Meet with your mentor regularly and discuss your progress and challenges.
Revisit matrices
Show steps
Refresh your understanding of matrices, determinants, Cramer's Rule, eigenvalues, and eigenvectors to strengthen your foundation for the course.
Browse courses on
Matrices
Show steps
-
Review notes or textbooks on matrix concepts.
-
Solve practice problems involving matrix operations and properties.
Nine other activities
Expand to see all activities and additional details
Show all 12 activities
Watch video tutorials on differential equations
Show steps
Supplement your learning by watching video tutorials on differential equations.
Show steps
-
Search for video tutorials on differential equations.
-
Watch the videos and take notes.
-
Review the videos as needed.
Create a study guide
Show steps
Deepen your understanding of the course material by creating a study guide.
Show steps
-
Identify the key concepts in each chapter.
-
Summarize the key concepts in your own words.
-
Add notes and examples to enhance your understanding.
-
Review your study guide regularly.
Attend a peer review session
Show steps
Gain feedback and insights from peers by attending a peer review session.
Show steps
-
Find a peer review group or session.
-
Submit your work to the group for review.
-
Attend the peer review session.
-
Provide feedback to others and accept feedback on your work.
Solve differential equations
Show steps
Enhance your problem-solving skills by practicing various types of differential equations, including Euler equations.
Browse courses on
Euler Equations
Show steps
-
Work through practice problems from the course materials or textbooks.
-
Utilize online resources or platforms for additional practice.
Solve practice problems
Show steps
Reinforce your understanding of the course material by solving practice problems.
Show steps
-
Identify the type of differential equation.
-
Determine the appropriate method for solving the equation.
-
Apply the method to solve the equation.
-
Check your answer.
Summarize lecture notes
Show steps
Reinforce your understanding of the course material by creating concise summaries of lecture notes.
Browse courses on
Differential Equations
Show steps
-
Attend lectures and take detailed notes.
-
Review and organize notes after each lecture.
-
Create short summaries that capture the key concepts.
Explore Bessel Functions
Show steps
Expand your knowledge of Bessel functions by seeking out and following specialized tutorials and resources.
Show steps
-
Search for online tutorials or courses on Bessel functions.
-
Follow the tutorials and complete any practice exercises.
Develop a differential equation model
Show steps
Demonstrate your understanding of the course material by developing a differential equation model.
Show steps
-
Identify a real-world scenario that can be modeled using a differential equation.
-
Translate the scenario into a mathematical model.
-
Solve the differential equation.
-
Validate your model using data.
-
Communicate your results effectively.
Contribute to an open-source differential equations project
Show steps
Gain practical experience and deepen your understanding by contributing to an open-source project.
Show steps
-
Identify an open-source differential equations project.
-
Review the project's documentation and code.
-
Make a contribution to the project.
-
Collaborate with other contributors and maintain the project.
Read the textbook
Show steps
Solidify your understanding of the fundamental concepts covered in the course by reading the textbook.
View
Differential Equations with Boundary-value...
on Amazon
Show steps
Show steps
Show steps
Find a mentor who can provide guidance on differential equations
Show steps
Enhance your learning journey by connecting with a mentor who can provide personalized guidance.
Show steps
Show steps
Show steps
- Identify potential mentors who are experts in differential equations.
- Reach out to the potential mentors and express your interest in their guidance.
- Meet with your mentor regularly and discuss your progress and challenges.
Revisit matrices
Show steps
Refresh your understanding of matrices, determinants, Cramer's Rule, eigenvalues, and eigenvectors to strengthen your foundation for the course.
Browse courses on
Matrices
Show steps
Show steps
Show steps
- Review notes or textbooks on matrix concepts.
- Solve practice problems involving matrix operations and properties.
Nine other activities
Expand to see all activities and additional details
Show all 12 activities
Watch video tutorials on differential equations
Show steps
Supplement your learning by watching video tutorials on differential equations.
Show steps
Show steps
Show steps
- Search for video tutorials on differential equations.
- Watch the videos and take notes.
- Review the videos as needed.
Create a study guide
Show steps
Deepen your understanding of the course material by creating a study guide.
Show steps
Show steps
Show steps
- Identify the key concepts in each chapter.
- Summarize the key concepts in your own words.
- Add notes and examples to enhance your understanding.
- Review your study guide regularly.
Attend a peer review session
Show steps
Gain feedback and insights from peers by attending a peer review session.
Show steps
Show steps
Show steps
- Find a peer review group or session.
- Submit your work to the group for review.
- Attend the peer review session.
- Provide feedback to others and accept feedback on your work.
Solve differential equations
Show steps
Enhance your problem-solving skills by practicing various types of differential equations, including Euler equations.
Browse courses on
Euler Equations
Show steps
Show steps
Show steps
- Work through practice problems from the course materials or textbooks.
- Utilize online resources or platforms for additional practice.
Solve practice problems
Show steps
Reinforce your understanding of the course material by solving practice problems.
Show steps
Show steps
Show steps
- Identify the type of differential equation.
- Determine the appropriate method for solving the equation.
- Apply the method to solve the equation.
- Check your answer.
Summarize lecture notes
Show steps
Reinforce your understanding of the course material by creating concise summaries of lecture notes.
Browse courses on
Differential Equations
Show steps
Show steps
Show steps
- Attend lectures and take detailed notes.
- Review and organize notes after each lecture.
- Create short summaries that capture the key concepts.
Explore Bessel Functions
Show steps
Expand your knowledge of Bessel functions by seeking out and following specialized tutorials and resources.
Show steps
Show steps
Show steps
- Search for online tutorials or courses on Bessel functions.
- Follow the tutorials and complete any practice exercises.
Develop a differential equation model
Show steps
Demonstrate your understanding of the course material by developing a differential equation model.
Show steps
Show steps
Show steps
- Identify a real-world scenario that can be modeled using a differential equation.
- Translate the scenario into a mathematical model.
- Solve the differential equation.
- Validate your model using data.
- Communicate your results effectively.
Contribute to an open-source differential equations project
Show steps
Gain practical experience and deepen your understanding by contributing to an open-source project.
Show steps
Show steps
Show steps
- Identify an open-source differential equations project.
- Review the project's documentation and code.
- Make a contribution to the project.
- Collaborate with other contributors and maintain the project.
Career center
Learners who complete Differential Equations Part II Series Solutions will develop knowledge and skills
that may be useful to these careers:
Data Scientist
Data Scientist
Data Scientists analyze data using advanced mathematical and statistical techniques to extract meaningful insights, and Differential Equations Part II Series Solutions may be useful in gaining a solid foundation in mathematical and statistical theories. This course covers topics such as Euler Equations, Power Series, and Bessel Functions, which are essential for understanding the underlying principles of data analysis.
Financial Analyst
Financial Analyst
Financial Analysts use mathematical and statistical techniques to evaluate and predict financial performance, and Differential Equations Part II Series Solutions may be useful for developing strong mathematical and analytical skills. This course covers essential topics such as Euler Equations, Power Series, and Legendre Polynomials, which provide a foundation for understanding financial models.
Operations Research Analyst
Operations Research Analyst
Operations Research Analysts use mathematical and analytical techniques to improve efficiency and productivity in organizations, and Differential Equations Part II Series Solutions may be useful for building a strong mathematical foundation. This course covers topics such as Euler Equations, Frobenius Theorem, and Bessel Functions, which are relevant to modeling and solving complex operational problems.
Actuary
Actuary
Actuaries use mathematical and statistical techniques to assess and manage financial risk, and Differential Equations Part II Series Solutions may be useful for building a solid mathematical foundation. This course covers topics such as Euler Equations, Power Series, and Legendre Polynomials, which are relevant to understanding actuarial models and techniques.
Statistician
Statistician
Statisticians use mathematical and statistical techniques to collect, analyze, and interpret data, and Differential Equations Part II Series Solutions may be useful for developing strong mathematical and analytical skills. This course covers topics such as Euler Equations, Power Series, and Frobenius Theorem, which are essential for understanding statistical models and methods.
Quantitative Analyst
Quantitative Analyst
Quantitative Analysts use mathematical and statistical techniques to analyze and predict financial markets, and Differential Equations Part II Series Solutions may be useful for developing strong mathematical and analytical skills. This course covers topics such as Euler Equations, Power Series, and Bessel Functions, which are relevant to understanding financial models and techniques.
Mathematician
Mathematician
Mathematicians use mathematical principles to solve problems and develop new theories, and Differential Equations Part II Series Solutions may be useful for building a strong mathematical foundation. This course covers topics such as Euler Equations, Frobenius Theorem, and Bessel Functions, which are fundamental to mathematical research.
Software Engineer
Software Engineer
Software Engineers design, develop, and maintain software systems, and Differential Equations Part II Series Solutions may be useful for developing strong analytical and problem-solving skills. This course covers topics such as Euler Equations, Power Series, and Legendre Polynomials, which can be applied to software design and development.
Computer Scientist
Computer Scientist
Computer Scientists design, develop, and analyze computer systems and software, and Differential Equations Part II Series Solutions may be useful for developing strong analytical and problem-solving skills. This course covers topics such as Euler Equations, Power Series, and Legendre Polynomials, which can be applied to computer science research and development.
Data Analyst
Data Analyst
Data Analysts collect, analyze, and interpret data to extract meaningful insights, and Differential Equations Part II Series Solutions may be useful for developing strong analytical and problem-solving skills. This course covers topics such as Euler Equations, Power Series, and Legendre Polynomials, which can be applied to data analysis.
Business Analyst
Business Analyst
Business Analysts analyze business processes and data to identify areas for improvement, and Differential Equations Part II Series Solutions may be useful for developing strong analytical and problem-solving skills. This course covers topics such as Euler Equations, Power Series, and Legendre Polynomials, which can be applied to business analysis.
Systems Analyst
Systems Analyst
Systems Analysts design, develop, and implement computer systems, and Differential Equations Part II Series Solutions may be useful for developing strong analytical and problem-solving skills. This course covers topics such as Euler Equations, Power Series, and Legendre Polynomials, which can be applied to systems analysis and design.
Market Researcher
Market Researcher
Market Researchers conduct research to understand market trends and consumer behavior, and Differential Equations Part II Series Solutions may be useful for developing strong analytical and problem-solving skills. This course covers topics such as Euler Equations, Power Series, and Legendre Polynomials, which can be applied to market research.
Technical Writer
Technical Writer
Technical Writers create and edit technical documentation, and Differential Equations Part II Series Solutions may be useful for developing strong writing and communication skills. This course covers topics such as Euler Equations, Power Series, and Legendre Polynomials, which can be used to explain complex technical concepts.
Science Writer
Science Writer
Science Writers create and edit scientific and technical content, and Differential Equations Part II Series Solutions may be useful for developing strong writing and communication skills. This course covers topics such as Euler Equations, Power Series, and Legendre Polynomials, which can be used to explain complex scientific concepts.
For more career information including salaries, visit:
OpenCourser.com/course/pex4m0/differential
Reading list
We've selected 13 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 II Series Solutions.
This textbook provides a comprehensive and rigorous treatment of the theory of partial differential equations, making it a valuable resource for advanced students and researchers.
This textbook provides a comprehensive and rigorous treatment of the theory of nonlinear partial differential equations, making it a valuable resource for advanced students and researchers.
Provides a rigorous and in-depth treatment of the theory of ordinary differential equations, making it a valuable resource for advanced students and researchers.
This textbook provides a thorough introduction to the theory of differential equations and dynamical systems, with a focus on qualitative methods and applications.
This textbook provides a comprehensive introduction to the concepts and methods of ordinary differential equations, addressing the needs of undergraduate mathematics, science, and engineering students.
This textbook covers a wide range of topics in differential equations, with a focus on applications to engineering, science, and mathematics.
Provides a comprehensive treatment of applied differential equations, with a focus on numerical methods and applications in engineering and science.
This textbook provides a comprehensive treatment of applied partial differential equations, with a focus on numerical methods and applications in engineering and science.
Provides an accessible introduction to the theory and applications of differential equations, with a focus on real-world examples.
While this book covers linear algebra as well, it provides a thorough introduction to the theory and applications of differential equations, making it a useful resource for this course.
This textbook provides a modern and accessible introduction to the theory of differential equations, with a focus on dynamical systems and applications.
While this book classic, it is more comprehensive than this course and thereby offers many supplementary topics to the learner. It is written in a clear manner and makes a good reference book.
While this book focuses on nonlinear dynamical systems and chaos, it provides a solid foundation in the theory of differential equations, making it a useful reference for this course.
For more information about how these books relate to this course, visit:
OpenCourser.com/course/pex4m0/differential
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Level
Introductory
Via
Coursera
Institution
Korea Advanced Institute of Science and Technology(KAIST)
Instructor
Kil Hyun Kwon
Language
English
Good to know
Suitable for individuals seeking practical applications of ordinary differential equations in their respective fields
Provides a foundation in terminology, concepts, and methods of solving various differential equations
Introduces fundamental theory and applications, catering to those with practical needs
Assumes prior knowledge of calculus and some basic matrix theory, setting clear prerequisites
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