Electrodynamics based on Maxwell equations (Bachelor level) from Udemy

This course is for everyone who wants to learn about theoretical electrodynamics.

A bit of college mathematics (basic derivatives and vector algebra) is all you need to know.

Several concepts of electrodynamics like charges, electromagnetic waves, electric & magnetic fields are taught already in highschool. However, it is not really possible to understand their true origin. For that purpose Maxwell formulated 4 equations based on which we can explain most phenomena of modern electrodynamics: electrostatics, magnetostatics, as well as time-dependent problems and light as an electromagnetic wave.

However, I think that this theoretical approach is often taught either too vague or with a too strong focus on the mathematics. Instead of watching random Youtube videos or going through hundred of hours of university courses, I think that Udemy courses are a nice platform for purposeful learning. You are kindly invited to join this carefully prepared course that will teach you the 101 of electrodynamics and includes quizzes, slides, exercises, as well as a tutorial on the mathematical prerequisites.

Why me?

My name is Börge Göbel and I am a postdoc working as a scientist on electrodynamics and quantum theory. I am currently doing research on the emergent electrodynamics of special magnetic textures. I have not forgotten the time when I learned about electrodynamics and still remember the problems that I and other students had. I have refined my advisor skills as a tutor of Bachelor, Master and PhD students in theoretical physics.

“Dr. Göbel produces excellent courses with lessons that provide both technical depth and great material and audio/visual production. The math review in this course was an excellent math review on its own.“ - Eddi Girolamo

This course is for you ...

... if you are about to attend a university course on electrodynamics and want to be well prepared
... or if you want to go through a theoretical physics course without having to deal with the hardcore mathematics of other topics
... or if you have a general idea about charges, electromagnetic waves, magnetic & electric fields but want to know their true origin
... or if you simply want to have a carefully condensed refresher before your exams :-)

The topics

We will start with the mathematical prerequisites and the early physical phenomena that have led to our modern understanding of electrodynamics. For example, we learn about complex numbers, the nabla operator, charges, magnetic moments, as well as the electric and magnetic fields. Then, we will introduce the Maxwell's equations. These four equations are the basis of this whole course and allow to derive all of the phenomena that we discuss, like the Ampère's law, the Coulomb's law and the Biot-Savart's law.We start with the special case of vacuum where charges and currents are absent: Here, the excitations are electromagnetic waves or, in other words, light. We derive the electric and magnetic fields and discuss the possible polarizations of light. Thereafter, we leave vacuum but consider time-independent problems. This field of theoretical physics is called electrostatics and magnetostatics. We solve interesting problems like calculating the electric field of a charged sphere, the voltage difference in a capacitor, the magnetic field around a wire or the far-field of a dipole.Finally, we consider the most general case: time-dependent problems. As we will see, we can rely on our previous results from the static case with a few modifications. Also, I will show you how all of our results only slightly change, when we consider the electrodynamics in matter, like in a piece of metal. I hope you are excited and I kindly welcome you to our course.

What's inside

Learning objectives

Early electrodynamic phenomena & the mathematics that have motivated the maxwell equations
Light as an electromagnetic wave

Electrostatics, magnetostatics & solving time-dependent problems

Early electrodynamic phenomena & the mathematics that have motivated the maxwell equations
Light as an electromagnetic wave
Electrostatics, magnetostatics & solving time-dependent problems

Syllabus

Introduction

Structure of the course

Optional: Basic mathematics important for us

Tutorial: Section intro

Traffic lights

Read about what's good

what should give you pause

and possible dealbreakers

Provides a strong foundation in electrodynamics, starting with mathematical prerequisites and progressing to Maxwell's equations and their applications, which is essential for advanced physics coursework

Includes a tutorial on mathematical prerequisites such as complex numbers and the nabla operator, which ensures students with varying math backgrounds can succeed

Covers early electrodynamic phenomena and their connection to Maxwell's equations, offering a historical perspective that enriches understanding of the theory's development

Explores electrostatics, magnetostatics, and time-dependent problems, providing a comprehensive overview of electrodynamics that is suitable for bachelor-level study

Features exercises and solutions related to complex numbers, 3-dimensional derivatives, and electromagnetic waves, which reinforces learning through practice

Includes optional sections on the motivation behind Maxwell's equations, which may be helpful, but also suggests that these topics are not strictly necessary for understanding the core material

Reviews summary

Electrodynamics based on maxwell's equations

Based on the overall rating distribution, learners say this course is largely positive, offering a strong foundation in electrodynamics centered around Maxwell's equations. Students find the explanations clear and appreciate the structured approach, making complex theoretical concepts more accessible. The course seems particularly beneficial for those preparing for university-level physics. The included mathematical prerequisites section is also frequently mentioned as a helpful resource. While the vast majority find it valuable, a small percentage of reviews suggest potential areas for deeper exploration or more practical examples.

Prerequisites section is valuable.

"The math review section was incredibly useful for refreshing my skills."

"I found the tutorials on complex numbers and vector calculus very beneficial."

"It helps bridge the gap for the necessary mathematical background."

Logical flow aids understanding.

"The structure of the course is very logical and easy to follow."

"I appreciated how the topics built upon each other."

"Moving from math basics to advanced concepts was well-managed."

Complex concepts are explained clearly.

"The explanations were clear and easy to follow."

"I found the instructor's way of breaking down complex topics very helpful."

"Understanding the material felt achievable thanks to the clear explanations."

Excellent prep for academic study.

"This course is perfect preparation for my upcoming university physics course."

"I feel much better prepared for my bachelor's degree after this."

"Highly recommended for students starting university electrodynamics."

Provides a solid base in electrodynamics.

"This course gave me a strong foundation in the subject."

"I feel much more confident in my understanding of electrodynamics after taking this."

"It's a great course for building the essential theoretical understanding."

Some areas could use more detail.

"I feel some topics could have been explored in greater depth."

"Could use more practical examples alongside the theory."

"While comprehensive, certain nuances might require external study."

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 Electrodynamics based on Maxwell equations (Bachelor level) with these activities:

Review Vector Algebra

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Strengthen your understanding of vector algebra, which is essential for manipulating electromagnetic fields and understanding Maxwell's equations.

Browse courses on Vector Algebra

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Review dot products, cross products, and vector components.
Practice solving problems involving vector addition and subtraction.

Read 'Div, Grad, Curl, and All That: An Informal Text on Vector Calculus'

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Gain a solid understanding of vector calculus, which is essential for working with Maxwell's equations and electromagnetic fields.

View Putting Knowledge to Work on Amazon

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Read the chapters on divergence, gradient, and curl.
Work through the example problems in each chapter.

Practice Multidimensional Derivatives

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Reinforce your skills in calculating partial derivatives and applying the nabla operator, which are fundamental for manipulating Maxwell's equations.

Browse courses on Partial Derivatives

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Solve problems involving partial derivatives of various functions.
Calculate the gradient, divergence, and curl of vector fields.

Four other activities

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Create a concept map of Maxwell's Equations

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Solidify your understanding of the relationships between Maxwell's equations and their applications by creating a visual representation of the concepts.

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Identify the key concepts and relationships within Maxwell's equations.
Design a concept map that visually represents these relationships.
Refine the concept map for clarity and accuracy.

Review 'Classical Electrodynamics' by David Griffiths

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Deepen your understanding of electrodynamics by studying a comprehensive textbook that covers all the major topics in detail.

View Introduction to Electrodynamics on Amazon

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Read the chapters relevant to the course syllabus.
Work through the example problems and exercises in the book.

Simulate Electromagnetic Wave Propagation

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Apply your knowledge of electrodynamics to simulate the propagation of electromagnetic waves in different media, which will enhance your understanding of wave behavior.

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Choose a simulation software or programming language (e.g., Python with NumPy and Matplotlib).
Implement the equations for electromagnetic wave propagation.
Simulate wave propagation in different media and visualize the results.

Create a Presentation on Applications of Electrodynamics

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Research and present on real-world applications of electrodynamics, such as antennas, waveguides, or optical fibers, to see how the theory is used in practice.

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Research different applications of electrodynamics.
Prepare a presentation with clear explanations and visuals.
Present your findings to peers or in a virtual setting.

Career center

Learners who complete Electrodynamics based on Maxwell equations (Bachelor level) will develop knowledge and skills that may be useful to these careers:

Physics Professor

A physics professor teaches university level courses in physics, often including electrodynamics. This course covers the mathematical prerequisites and physical phenomena that motivated Maxwell's equations, as well as the equations themselves, including light as an electromagnetic wave, electrostatics, magnetostatics, and time-dependent problems. A physics professor may find this course useful as it provides a structured approach teaching electrodynamics, covering areas that many courses do not.

See salaries and explore the career path for Physics Professor

Research Scientist

A research scientist often works on cutting-edge research in areas like electrodynamics. This course helps build a foundation in the core principles of electrodynamics, providing a deep dive into Maxwell's equations, electromagnetic waves, and electrostatics. This course may be useful for those seeking to understand the theoretical underpinnings of electromagnetism, as it focuses on the theoretical framework and mathematical tools vital for advanced research in this field, such as complex numbers, vector algebra and the nabla operator.

See salaries and explore the career path for Research Scientist

Optical Engineer

Optical engineers design and build optical systems, many of which rely on an understanding of electrodynamics. This course's discussion of light as an electromagnetic wave, including its polarization, and the mathematical tools used to describe electromagnetic fields can be beneficial for an optical engineer. The course covers time-dependent problems and how they relate to static cases, all of which are valuable for those working with light and electromagnetic radiation.

See salaries and explore the career path for Optical Engineer

Materials Scientist

Materials scientists research and develop new materials, often with a focus on their properties, like electromagnetic behavior. This course in theoretical electrodynamics may be useful because it goes into depth on the origin of electromagnetic phenomena and the mathematical tools used to describe them. By understanding Maxwell's equations and how they explain light, electrostatics, and magnetostatics, a materials scientist can better understand the electromagnetic properties of the materials they are working with.

See salaries and explore the career path for Materials Scientist

Quantum Physicist

Quantum physicists study the behavior of matter and energy at the atomic and subatomic level. This course could be useful because it focuses on the mathematics used to describe electrodynamics, such as complex numbers, the nabla operator, and line integrals, and the classical theory as well as the underlying concepts. Quantum physicists often require a deep understanding of both classical and quantum electromagnetism. Furthermore, the instructor also works in quantum theory. While an advanced degree is typically required, this course may be helpful to introduce the subject matter and the instructor.

See salaries and explore the career path for Quantum Physicist

Electrical Engineer

Electrical engineers design, develop, and test electrical equipment, often utilizing principles of electrodynamics. This course may be useful for an electrical engineer because a solid understanding of Maxwell's equations is crucial to the field, and this course explains these foundational principles along with practical derivatives such as Coulomb's and Ampère's laws. An electrical engineer will draw from knowledge of electromagnetic waves, electrostatics, and magnetostatics in their daily work.

See salaries and explore the career path for Electrical Engineer

Telecommunications Engineer

Telecommunications engineers design and manage communication systems involving electromagnetic signals. Understanding the fundamental principles of electrodynamics is crucial for the design of these systems. This course may be helpful as it discusses electromagnetic waves, their polarization, and the underlying Maxwell's equations. Telecommunications engineers may find this course useful to gain familiarity with the theoretical underpinnings of their field of work.

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Aerospace Engineer

Aerospace engineers design aircraft, spacecraft, and related systems which may involve elements of electrodynamics. Knowing how electromagnetic waves propagate is important in this field. This course focuses on the core principles of electrodynamics, from the mathematical prerequisites to the Maxwell's equations. An aerospace engineer may find this helpful because it covers Maxwell's equations, electrostatics, magnetostatics, and time-dependent problems, which are all relevant to their work.

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Medical Physicist

Medical physicists apply physics principles to the medical field, including the use of electromagnetic radiation in imaging and therapy. A course focusing on electrodynamics, such as this one, may be helpful. It explains Maxwell's equations, light electromagnetic waves, electrostatics, magnetostatics and solves time-dependent problems. This course may be of great benefit to a medical physicist, as it provides the theoretical foundations of the electromagnetic phenomena they work with.

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Instrumentation Engineer

Instrumentation engineers design, develop, and manage systems that measure and control physical processes, many of which involve electromagnetic phenomena. This course's treatment of Maxwell's equations and their implications for electrostatics, magnetostatics and time-dependent problems may be useful, as a strong theoretical understanding of electrodynamic principles is necessary. An instrumentation engineer will find the grounding in basic principles to be valuable for this work.

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Technical Writer

Technical writers create documentation that explains complex information in a clear and accessible manner. While not directly related, a strong understanding of electrodynamics, as provided by this course, could be beneficial for a technical writer who is writing material on electromagnetic devices, or other related topics. This means that this course may be useful to someone seeking to become a technical writer in this field who needs to build domain specific knowledge of electrodynamics.

See salaries and explore the career path for Technical Writer

Software Engineer

Software engineers develop code for a variety of applications. While not directly related, some areas, such as computational electromagnetics, may benefit. This course in electrodynamics, which includes complex numbers, vector algebra, and the nabla operator, may be helpful to those who wish to program simulations of electromagnetic phenomena. It may provide a solid theoretical background for working on electromagnetic simulation tools.

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Systems Engineer

Systems engineers focus on the design, integration, and management of complex systems. This course, while focused on electrodynamics, may be helpful for systems engineers who are involved in projects with electromagnetic components or issues within a system. It covers the theory behind electrostatics, magnetostatics, and time-dependent effects, which may be useful. A systems engineer may find this course helpful in building a foundation in mathematics and a strong theoretical basis in electromagnetic fields.

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Data Scientist

Data scientists are involved in analyzing, processing, and extracting insights from data. Although it is not a directly connected field, the mathematical rigor used in this electrodynamics course may be beneficial for data science. This course teaches about complex numbers, the nabla operator, and other advanced mathematical concepts. A data scientist may find this course helpful to develop a foundational understanding of analytical mathematics and abstract thinking.

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Patent Attorney

Patent attorneys deal with the legal aspects of inventions and intellectual property, often in technical fields. While a law degree is required for this position, those with strong technical expertise in a certain field are valued. This course is not directly related, but an understanding of the core principles of electrodynamics, especially Maxwell's equations, may help a patent attorney who is working on patents related to electromagnetic devices. A patent attorney with this background may find this course helpful in better understanding the technologies they deal with.

See salaries and explore the career path for Patent Attorney

Electrodynamics based on Maxwell equations (Bachelor level)

What's inside

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Syllabus

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Reviews summary

Electrodynamics based on maxwell's equations

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