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My #100 course certificate from Coursera
Understanding Modern Physics I: Relativity and CosmologyThe Hong Kong University of Science and Technology I am thrilled to...
![Olbers paradox, Friedmann equation, Hubble Law, Matter](https://kzhu.ai/wp-content/uploads/2022/07/Understanding-Modern-Physics-1-18.jpg)
Cosmology
Cosmology is the science of studying our universe. Being different from astronomy, which corresponds to studying some particular...
![Equivalence principle, Light bending, Gravitational time dilation](https://kzhu.ai/wp-content/uploads/2022/07/Understanding-Modern-Physics-1-16.jpg)
General Relativity: Gravity and Black Holes
Previously, in special relativity, we have found that the concepts of space and time are relative. When you...
![Generalization of Geometry, Spacetime Diagram](https://kzhu.ai/wp-content/uploads/2022/07/Understanding-Modern-Physics-1-14.jpg)
Special Relativity: Geometry, Momentum and Energy
In 3-dimensional space, when we are looking at an object, what we see depends on the angle, the...
![Lorentz Transformation](https://kzhu.ai/wp-content/uploads/2022/06/Understanding-Modern-Physics-1-10.jpg)
Lorentz Transformation
Lorentz transformation is the central question in the mathematical structure of special relativity. Simply put, given the coordinate...
![Length contraction, Spacetime diagram, Light speedmeter](https://kzhu.ai/wp-content/uploads/2022/06/Understanding-Modern-Physics-1-5.jpg)
Special Relativity: Length and Simultaneity
The concept of “length” and “the same time” have to be reconsidered in special relativity. Light Ruler and...
![Certificate Vector Calculus for Engineers](https://kzhu.ai/wp-content/uploads/2021/12/Coursera-5J9M3UBGSGSX-1024x791.jpg)
My #81 course certificate from Coursera
Vector Calculus for EngineersThe Hong Kong University of Science and Technology We can’t emphasize enough the importance of...
![Newton's second law, Light clock, Time dilation](https://kzhu.ai/wp-content/uploads/2021/12/Understanding-Modern-Physics-1-2.jpg)
Special Relativity: Space and Time
For hundreds years, space and time were absolute in the concept of Newton, they are something that can...
![Certificate Differential Equations for Engineers](https://kzhu.ai/wp-content/uploads/2021/12/Coursera-FVEGAX3XS994-1024x791.jpg)
My #80 course certificate from Coursera
Differential Equations for EngineersThe Hong Kong University of Science and Technology By highlighting both theories and applications in...
![Gradient theorem, Conservative vector fields](https://kzhu.ai/wp-content/uploads/2021/12/Vector-Calculus-28-724x1024.jpg)
Vector Calculus: Fundamental Theorems
Gradient Theorem The fundamental theorem of single variable calculus was the one that told you “the integral of the...
![Line integrals of scalar fields, Line integral of vector fields](https://kzhu.ai/wp-content/uploads/2021/12/Vector-Calculus-24-724x1024.jpg)
Line and Surface Integrals
Line Integrals Scalar Fields We have a curve C in the x-y plane, we can represent a point...
![Fourier series](https://kzhu.ai/wp-content/uploads/2021/12/Differential-Equations-For-Engineers-43-793x1024.jpg)
The Diffusion Equation of a Dye
Fourier Series Sometimes complicated motions can actually be composed of motions of many different frequencies. The type of mathematical analysis...
![System of linear first order ODEs, Distinct real eigenvalues](https://kzhu.ai/wp-content/uploads/2021/12/Differential-Equations-For-Engineers-39-793x1024.jpg)
Systems of Differential Equations
Systems of Homogeneous Linear First-order ODEs The system of linear first order homogeneous equations can be written in matrix...
![Double triple integrals, Polar coordinates](https://kzhu.ai/wp-content/uploads/2021/12/Vector-Calculus-16-724x1024.jpg)
Polar, Cylindrical, Spherical Coordinates
Multidimensional Integration In Vector Calculus, we have to worry about integrating over two or three variables: double integrals...
![Laplace transform](https://kzhu.ai/wp-content/uploads/2021/12/Differential-Equations-For-Engineers-33-793x1024.jpg)
Laplace Transform and Series Solution Method
Laplace transform Laplace transform is a technique for solving differential equations. By using the Laplace transform you can...