Theoretical Classical Mechanics: From Beginner to Expert from Udemy

This course is for everyone who wants to learn about classical mechanic: Beginners to experts.

A bit of college mathematics (basic derivatives, integrals & vectors) is all you need to know.

Classical mechanics is the foundation of all disciplines in physics. It is typically at the very beginning of the university-level physics education. But that does not mean the classical physics is always super easy or even boring. Things become extremely complicated quickly and can lead to unexpected solutions. We can describe classical mechanics on different levels. I can guarantee that you will learn a lot no matter what your current skill level is.

You are kindly invited to join this carefully prepared course in which we derive the following concepts from scratch. I will present examples and have prepared quizzes and exercises for all topics.

[Level 1] Beginner: Kinematics (3 hours)

Overview & mathematical basics (derivatives, integrals, vectors)
Kinematics: Position, velocity & acceleration

[Level 2] Intermediate: Dynamics (9 hours)

Mathematics (Coordinate systems, multidimensional derivatives & integrals)
Dynamics: Forces & related quantities (work, potentials, energy, momentum)
Dynamics of the circular motion (torque, angular momentum)

[Level 3] Advanced: Theoretical mechanics (3.5 hours)

Lagrange’s approach (Constraints, action, Noether's theorem)
Hamilton’s approach & beyond (Legendre transformation, Hamilton's equations of motion)

[Level 4] Expert: Differential equations (8 hours)

Advanced mathematics (Complex numbers & matrices)
Differential equations: Analytical solution
Numerical solution with Python3

Why me?

My name is Börge Göbel and I am a postdoc working as a scientist in theoretical physics. Therefore, I use theoretical classical mechanics very often but I have not forgotten the time when I learned about it 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 and have other successful courses here on Udemy.

I hope you are excited and I kindly welcome you to our course.

What's inside

Learning objectives

Kinematics: position, velocity & acceleration are related by derivatives and integrals
Dynamics: forces, potentials, work, energy and momentum allow for a phenomenological description based on newton's laws
Circular motion: angular velocity, acceleration, centripetal and centrifugal forces, torque and angular momentum
Theoretical physics: lagrangian and hamiltonian approaches based on d'alembert's principle and hamilton's principle
Solving differential equations analytically

Programming & numerical simulations: solving differential equations in python3
Mathematical methods: derivatives, integrals, taylor expansions, coordinate systems, complex numbers & matrices
Conservation laws based on noether theorem and symmetries
Nice examples like: spinning top, kepler's laws of planetary motion, coupled, damped and driven oscillators, pulleys, levers, coriolis force and many more

Kinematics: position, velocity & acceleration are related by derivatives and integrals
Dynamics: forces, potentials, work, energy and momentum allow for a phenomenological description based on newton's laws
Circular motion: angular velocity, acceleration, centripetal and centrifugal forces, torque and angular momentum
Theoretical physics: lagrangian and hamiltonian approaches based on d'alembert's principle and hamilton's principle
Solving differential equations analytically
Programming & numerical simulations: solving differential equations in python3
Mathematical methods: derivatives, integrals, taylor expansions, coordinate systems, complex numbers & matrices
Conservation laws based on noether theorem and symmetries
Nice examples like: spinning top, kepler's laws of planetary motion, coupled, damped and driven oscillators, pulleys, levers, coriolis force and many more

Syllabus

[Level 1] Overview & Mathematical basics

Structure of this course

About the following videos

[Mathematical Basics] Derivatives

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Read about what's good

what should give you pause

and possible dealbreakers

Covers Lagrangian and Hamiltonian approaches, which are essential for advanced theoretical physics studies and research

Includes numerical solutions with Python3, a valuable skill for modern physics and engineering applications

Explores advanced mathematics, including complex numbers and matrices, which are crucial for theoretical physics

Requires a basic understanding of derivatives, integrals, and vectors, which may necessitate a review for some learners

Presents examples like the spinning top and Kepler's laws, which are standard topics in classical mechanics curricula

Teaches analytical solutions to differential equations, a skill that is foundational in physics and engineering

Reviews summary

Theoretical classical mechanics comprehensive overview

According to learners, this course offers a comprehensive journey through classical mechanics, covering topics from beginner kinematics to advanced Lagrangian and Hamiltonian mechanics. Many find the instructor's explanations clear and appreciate the rigorous mathematical derivations. However, some students highlight that despite the title, the course moves quickly and may require more than just basic math knowledge for true beginners, feeling more suited for those with some prior physics or strong math background. The inclusion of differential equations and Python for numerical solutions is seen as a valuable addition by some. Overall, it's considered a solid theoretical foundation.

Requires more than basic math prerequisites.

"While it says basic math is enough, you really need a solid grasp of calculus and vectors to keep up."

"The math required is quite rigorous, which is great for a theoretical course, but tough if your math is rusty."

"I struggled a bit with the multidimensional calculus parts; wish there was more review included."

"It assumes you're comfortable with derivatives, integrals, and vector calculus beyond just the basics taught briefly."

Introduction to numerical methods with Python.

"The section on using Python for differential equations was a valuable addition; it adds a practical skill."

"It gave a good introduction to numerical methods, though it's quite basic and you might need more resources for depth."

"Appreciated the practical aspect of using Python to solve problems covered theoretically."

"Useful section for seeing how computational tools apply to mechanics."

Practice problems aid learning and application.

"The exercises provided good practice for applying the concepts learned in the videos."

"I found the quiz questions helpful for checking my understanding before moving on to new topics."

"Working through the problems was crucial for solidifying the lessons and derivations."

"The examples and exercises reinforce the theoretical concepts well."

Instructor clarifies complex physics concepts.

"I found the instructor's explanations of the derivations to be very clear and easy to follow."

"He presents the material in a logical and structured way that really helps build understanding."

"The way the concepts were introduced built upon each other well and helped solidify my grasp."

"The instructor has a clear way of explaining difficult topics, making them accessible."

Broad coverage from foundational to advanced topics.

"I was impressed by how much material was covered, from Newton's laws all the way to Lagrangian and Hamiltonian mechanics."

"It's great that it includes theoretical mechanics like Lagrange and Hamilton, which many intro courses skip."

"You get a comprehensive overview of classical mechanics typically covered at a university level, which is valuable."

"Covers topics you'd see in both introductory and advanced undergraduate physics courses, offering great breadth."

Moves quickly for those new to the subject.

"As a beginner, I found the pace very fast, especially once it got past the initial kinematics."

"It covers a lot of ground very quickly; difficult to absorb everything the first time through the lectures."

"I feel this course is better suited for someone looking for a review or deeper dive, not a first introduction to the subject."

"Definitely not 'beginner' in the sense of someone with minimal prior physics knowledge; moves like a university course."

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 Theoretical Classical Mechanics: From Beginner to Expert with these activities:

Review Basic Calculus Concepts

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Strengthen your understanding of derivatives and integrals, which are fundamental to understanding kinematics and dynamics in classical mechanics.

Browse courses on Derivatives

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Review the definitions of derivatives and integrals.
Practice solving basic derivative and integral problems.
Understand the relationship between derivatives and integrals.

Review Basic Calculus Concepts

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Strengthen your understanding of derivatives and integrals, which are fundamental to understanding kinematics and dynamics in classical mechanics.

Browse courses on Derivatives

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Review the definitions of derivatives and integrals.
Practice solving basic derivative and integral problems.
Understand the relationship between derivatives and integrals.

Read 'Classical Mechanics' by John R. Taylor

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Gain a deeper understanding of classical mechanics concepts by studying a well-regarded textbook.

View Student Solutions to Accompany Taylor's an... on Amazon

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Read the chapters relevant to the course syllabus.
Work through the example problems in the book.
Attempt the end-of-chapter exercises.

Seven other activities

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Show all ten activities

Read 'Classical Mechanics' by John R. Taylor

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Supplement your learning with a comprehensive textbook that covers all the topics in the course in detail.

View Student Solutions to Accompany Taylor's an... on Amazon

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Read the chapters corresponding to the course syllabus.
Work through the examples and exercises in the book.
Compare the book's explanations with the course lectures.

Help Others in the Discussion Forums

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Reinforce your understanding by helping other students with their questions and problems.

Browse courses on Kinematics

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Regularly check the discussion forums for questions.
Provide clear and helpful answers to the questions.
Explain your reasoning and provide examples when possible.

Solve Problems on Newton's Laws

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Reinforce your understanding of dynamics by solving a variety of problems involving Newton's laws of motion.

Browse courses on Newton's Laws

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Find a collection of problems on Newton's laws.
Solve problems of varying difficulty levels.
Check your solutions against the provided answers.

Solve Kinematics and Dynamics Problems

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Reinforce your understanding of kinematics and dynamics by solving a variety of problems.

Browse courses on Kinematics

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Find practice problems in textbooks or online resources.
Solve the problems independently, showing all your work.
Check your answers and review the solutions if needed.

Read 'Analytical Mechanics' by Hand and Finch

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Deepen your understanding of analytical mechanics with a more advanced textbook.

View Analytical Mechanics on Amazon

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Read the chapters on Lagrangian and Hamiltonian mechanics.
Work through the examples and exercises in the book.
Compare the book's approach with the course lectures.

Create a Video Explaining a Mechanics Concept

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Solidify your understanding by explaining a complex concept in your own words through a video.

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Choose a concept from the course that you find challenging.
Research the concept thoroughly and prepare a script.
Record a video explaining the concept clearly and concisely.
Edit the video and share it with your peers for feedback.

Simulate a Physical System in Python

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Apply your knowledge of differential equations and Python programming to simulate a physical system.

Browse courses on Python

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Choose a physical system, such as a pendulum or a spring-mass system.
Derive the equations of motion for the system.
Write a Python program to solve the equations numerically.
Visualize the results of the simulation.

Career center

Learners who complete Theoretical Classical Mechanics: From Beginner to Expert will develop knowledge and skills that may be useful to these careers:

Computational Physicist

Computational physicists use numerical methods to solve problems in physics, often involving complex systems described by classical mechanics. This course's inclusion of numerical solutions to differential equations with Python, along with the focus on theoretical concepts, helps computational physicists in their daily work. The course's progression from beginner concepts to expert level knowledge assists one who is entering this field. This course is directly related to the work of a computational physicist.

See salaries and explore the career path for Computational Physicist

Research Scientist

A research scientist conducts experiments and theoretical investigations in various fields. This course's coverage of classical mechanics provides a strong theoretical foundation, which is highly valuable. The course's focus on advanced topics like Lagrangian and Hamiltonian mechanics, along with differential equations, which are needed for various models, and numerical simulations, which are also relevant for research. This course helps researchers build a foundation in many areas.

See salaries and explore the career path for Research Scientist

Physicist

A physicist utilizes the principles of classical mechanics, as covered in this course, to understand and model the physical world. This role requires a deep understanding of kinematics, dynamics, and advanced theoretical mechanics to conduct experiments, develop theoretical models, and analyze data. The course's progression from basic concepts to advanced topics like Lagrangian and Hamiltonian mechanics, differential equations, and numerical simulations in Python directly aligns with the skills needed by a physicist. This course helps build a foundation for those who wish to become physicists.

See salaries and explore the career path for Physicist

Astronautical Engineer

An astronautical Engineer designs, develops, and tests spacecraft and related technologies. This job uses classical mechanics to understand orbital mechanics, propulsion, and spacecraft dynamics. This course, with its focus on kinematics, dynamics, rotational motion, and differential equations, provides a solid foundational understanding. This course can help someone who wishes to become an astronautical engineer.

See salaries and explore the career path for Astronautical Engineer

Aerospace Engineer

Aerospace engineering applies the concepts of classical mechanics to design and analyze aircraft, spacecraft, and related systems. This course, with its focused content on kinematics, dynamics, rotational motion, and differential equations, provides a critical foundation for many core aerospace engineering tasks. The course's discussion of topics like circular motion, forces, and energy are directly applicable to aerospace engineering. One who wants to become an aerospace engineer may find this course very useful.

See salaries and explore the career path for Aerospace Engineer

Mechanical Engineer

Mechanical engineers use principles of classical mechanics to design, develop, and test mechanical devices and systems. This course covers foundational concepts like forces, motion, energy, and differential equations, which are essential for designing machinery, tools, and mechanical systems. The course's modules on rotational motion, torque, and angular momentum are particularly relevant to mechanical engineering. This course may be useful for those that wish to become a mechanical engineer.

See salaries and explore the career path for Mechanical Engineer

Control Systems Engineer

Control system engineers design and implement systems that manage the behavior of dynamic systems. This work requires a strong knowledge of classical mechanics, particularly dynamics and differential equations, which are covered in this course. The course's focus on forces, motion, and energy, and how they interact, is essential for the work of a control systems engineer. The theoretical framework built by this course provides a strong foundation.

See salaries and explore the career path for Control Systems Engineer

Robotics Engineer

A robotics engineer uses their understanding of mechanics to design, build, and program robots. This course provides a strong base in classical mechanics, including kinematics and dynamics, which is essential for modeling robot motion. The course's focus on mathematical methods, differential equations, and numerical solutions in Python are directly relevant to the modeling and simulation aspects of robotics. This course may assist in becoming a robotics engineer.

See salaries and explore the career path for Robotics Engineer

Simulation Specialist

A simulation specialist develops and uses computer simulations to model real world systems. Concepts from classical mechanics, like forces, motion, and energy, are very useful to develop these simulations. The course teaches numerical solutions using Python, which is a key skill for a simulation specialist. A strong foundation in mechanics, as provided by this course, helps build the right skills for simulation specialists.

See salaries and explore the career path for Simulation Specialist

Applied Mathematician

An applied mathematician uses mathematical principles to solve complex real-world problems. The deep mathematical treatment of classical mechanics in this course, including derivatives, integrals, differential equations, and linear algebra, are extremely useful. The concepts of coordinate systems, vectors, and forces are relevant in a variety of applications that an applied mathematician may encounter. This course may be useful for those who wish to become an applied mathematician.

See salaries and explore the career path for Applied Mathematician

Software Engineer

Some software engineers work in fields that require knowledge of physics. This course may be useful to those who wish to become a software engineer in a related field, particularly with its Python-based numerical solutions. The course can provide a conceptual framework for understanding the simulations and modeling work done by those involved in software engineering projects with a physics component. This course may be useful in this role.

See salaries and explore the career path for Software Engineer

Data Scientist

Data scientists apply mathematical and statistical techniques to extract insights from data. While not directly focused on classical mechanics, this course can help build a foundation in mathematical methods, including derivatives, integrals, and differential equations. The numerical simulation component using Python may also be useful, showing how theoretical concepts can be put into practice. This course may be helpful for those who wish to go into data science.

See salaries and explore the career path for Data Scientist

Biomedical Engineer

Biomedical engineers apply engineering principles to biological and medical systems. While not directly focused on living systems, a background in mechanics helps one to understand biomechanics and the physics of medical devices. This course may be useful for those who seek to understand the mechanics of movement and force. The mathematical methods in the course may allow for a more robust understanding. This course may be helpful for one who wants to become a biomedical engineer.

See salaries and explore the career path for Biomedical Engineer

Financial Quant

Financial quants apply mathematical and statistical methods to model financial markets. While this course focuses on classical mechanics, the mathematical rigor and problem-solving mindset may be useful. The course's deep dive into derivatives, integrals, and differential equations provides a good background for mathematical modeling. The problem solving aspects of the course may also be useful to financial quants. This course may be helpful to enter financial fields.

See salaries and explore the career path for Financial Quant

Game Developer

Game developers use physics to create realistic simulations within games. While most game engines handle physics calculations, a strong understaning of classical mechanics can be useful. This course can allow game developers to understand what goes on behind those calculations and possibly develop their own systems. Those who wish to become game developers may find this course useful.

See salaries and explore the career path for Game Developer

Reading list

We've selected two 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 Theoretical Classical Mechanics: From Beginner to Expert.

Student Solutions Manual to Accompany Taylor's...

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Provides a comprehensive introduction to classical mechanics, covering topics from Newtonian mechanics to Lagrangian and Hamiltonian formalisms. It is widely used as a textbook in undergraduate physics courses. Reading this book will provide a solid foundation and deeper understanding of the concepts covered in the course. It is particularly helpful for understanding the mathematical formalisms used in theoretical mechanics.

Student Solutions to Accompany Taylor's an...

Paperback

Analytical Mechanics

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Provides a more advanced treatment of classical mechanics, focusing on analytical techniques such as Lagrangian and Hamiltonian mechanics. It is suitable for students who want to delve deeper into the theoretical aspects of the subject. This book is best used as additional reading to expand on the concepts introduced in the course. It is often used in graduate-level courses.

Analytical Mechanics

Kindle Edition

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Theoretical Classical Mechanics

From Beginner to Expert

What's inside

Learning objectives

Syllabus

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Reviews summary

Theoretical classical mechanics comprehensive overview

Activities

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Reading list

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