Differential Equations Part III Systems of Equations from Coursera

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.

Table of Contents

Differential Equations Part I Basic Theory

Chapter 1 Introduction

Chapter 2 First Order Differential Equations

Chapter 3 Mathematical Modelling and Applications

Chapter 4 Linear Second Order Equations

Chapter 5 Applications of Second Order Equations

Differential Equations Part II Series Solutions

Chapter 1 Euler Equations

Chapter 2 Series Solutions of Linear Equations

Chapter 3 Special Functions: Bessel Functions and Legendre Polynomials

Differential Equations Part III Systems of Differential Equations

Chapter 1 Systems of Linear Equations

Chapter 2 Stability of Autonomous Systems

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What's inside

Syllabus

Introduction

Week 2

Week 3

Week 4. Stability of Autonomous Systems

Week 5

Week 6

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Explores differential equations, which is a foundational topic in advanced mathematics

Examines mathematical modeling and applications of differential equations, which can be useful in various fields

Covers linear second order equations and their applications, which are essential for understanding many physical phenomena

Provides a rudimentary but indispensable knowledge of the underlying theory of differential equations, which is beneficial for further study

Emphasizes practical use of differential equations, catering to learners interested in applying them in their fields

Requires prerequisites in calculus and matrix theory, indicating a suitable level of mathematical maturity for the audience

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 III Systems of Equations with these activities:

Review matrix theory and determinants

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Refreshes your memory on matrices and determinants if you studied these topics over two semesters ago.

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Review notes
Review textbooks

Watch video tutorials on eigenvalue problems

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Provides a visual demonstration of how to solve eigenvalue problems.

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Find video tutorials on eigenvalue problems
Make notes of important points
Solve similar eigenvalue problems on your own

Review 'Linear Differential Equations and Boundary Value Problems'

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Provides additional context on linear differential equations and boundary value problems.

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Read through the book
Highlight important concepts
Attempt the practice problems

Three other activities

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Create a mind map of the applications of differential equations

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Helps visualize and organize the practical uses of differential equations.

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List down the applications of differential equations
Create a mind map using the list

Develop a mathematical model using differential equations

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Provides an opportunity to apply differential equations to a real-world problem.

Browse courses on Mathematical Modeling

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Choose a real-world problem
Develop a mathematical model using differential equations
Solve the differential equations
Analyze the results

Participate in a study group to discuss autonomous systems

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Provides a platform for discussing and clarifying concepts related to autonomous systems.

Browse courses on Autonomous Systems

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Form a study group with peers
Discuss the key concepts of autonomous systems
Solve problems and case studies together

Career center

Learners who complete Differential Equations Part III Systems of Equations will develop knowledge and skills that may be useful to these careers:

Physicist

Physicists study the fundamental laws of nature and the physical properties of matter and energy. This course in Differential Equations Part III Systems of Equations is a great foundation for Physicists, as it provides them with the mathematical tools to model and analyze physical systems and phenomena.

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Mechanical Engineer

Mechanical Engineers design, develop, and build mechanical systems and components. Differential Equations is an essential tool for Mechanical Engineers, as it helps them analyze and design systems involving motion, forces, and energy.

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Systems Engineer

Systems Engineers design, develop, and manage complex systems, such as aircraft, satellites, and computer networks. This course will help Systems Engineers understand Systems of Differential Equations which are used to model and analyze the behavior of complex systems, enabling them to design and manage systems that are reliable, efficient, and meet performance requirements.

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Aerospace Engineer

Aerospace Engineers plan, design, develop, and oversee the testing and manufacturing of aircraft, missiles, and spacecraft as well as their structural and propulsion components. This course in Differential Equations Part III Systems of Equations is a great introduction to the complex mathematical concepts and theories that Aerospace Engineers need to understand to do their jobs effectively.

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Geophysicist

Geophysicists study the physical properties of the Earth and its atmosphere using mathematical and computational models. This course will introduce Systems of Differential Equations, which are used by Geophysicists to model and analyze geophysical phenomena such as地震 waves, fluid flow in the Earth's mantle, and the dynamics of the atmosphere.

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Biomedical Engineer

Biomedical Engineers apply engineering principles and design concepts to medicine and biology for healthcare purposes. They research, design, develop, and evaluate systems and products such as artificial organs, prosthetics, and medical imaging systems. This course will teach about Systems of Differential Equations and provides valuable knowledge of the underlying theory and applications, which is useful for Biomedical Engineers in modeling and analyzing biological systems and processes.

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Chemical Engineer

Chemical Engineers apply scientific and mathematical principles to design, operate, and maintain chemical plants and other industrial processes. Differential Equations is a vital subject for Chemical Engineers as they design chemical processes and equipment.

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Civil Engineer

Civil Engineers design, construct, and oversee the maintenance of infrastructure projects like bridges, buildings, dams, and roads. They also manage environmental issues such as water treatment and air pollution control. This course will provide a solid understanding of Systems of Differential Equations and their applications, which is important for Civil Engineers when designing and analyzing various infrastructure systems, such as bridges, buildings, and dams.

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Electrical Engineer

Electrical Engineers design, develop, test, and supervise the installation and maintenance of electrical systems and equipment. This course will familiarize Electrical Engineers with Systems of Differential Equations, which are widely used in various fields such as power systems, control systems, and signal processing, helping them to design and analyze electrical systems more effectively.

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Industrial Engineer

Industrial Engineers design, improve, and install integrated systems for managing industrial production and operations. Differential Equations are used in Industrial Engineering to model and analyze complex systems, such as production lines and supply chains, to optimize efficiency and productivity.

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Operations Research Analyst

Operations Research Analysts use mathematical and analytical techniques to improve decision-making and solve complex problems in various industries. Systems of Differential Equations are used in Operations Research to model and analyze dynamic systems, such as supply chains, inventory management, and scheduling, to optimize performance and efficiency.

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Materials Scientist

Materials Scientists research and develop new materials with improved properties for various applications. This course can provide Materials Scientists with a solid understanding of Systems of Differential Equations which are used to model and analyze the behavior of materials under different conditions, helping them design and develop new materials with desired properties.

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Computer Scientist

Computer Scientists design, develop, and implement computer systems and applications. This course can teach Systems of Differential Equations which are used to model many real-world systems and processes, providing valuable knowledge for Computer Scientists who work in various fields such as artificial intelligence, computer graphics, and scientific computing.

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Data Scientist

Data Scientists use mathematical and statistical techniques to extract insights from data. This course in Differential Equations Part III Systems of Equations may provide a helpful foundation for understanding complex systems and processes, which is essential for Data Scientists when working with large and complex datasets.

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Financial Analyst

Financial Analysts use mathematical and statistical techniques to analyze financial data and make investment recommendations. This course can provide a foundation in Systems of Differential Equations which are used in financial modeling to predict future trends and make informed decisions.

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