Heuristic Algorithms: A Case Study
The objectives for any research is that we want to build a mathematical model to formulate the given problem. The...
Non-Linear Programming: Gradient Descent and Newton’s Method
Non-Linear Programs When visualizing a linear program, its feasible region looks like a polygon. Because the objective function...
Stern-Gerlach Experiments & Dirac Bra-ket Notation
Electron Spin Electron has intrinsic angular momentum called spin that is not associated with its orbital motion. And...
My #81 course certificate from Coursera
Vector Calculus for Engineers The Hong Kong University of Science and Technology We can’t emphasize enough the importance...
Special Relativity: Space and Time
For hundreds years, space and time were absolute in the concept of Newton, they are something that can...
Quantum Mechanics: 1-Dimensional Finite Potential Problems
Finite Potential Well Finite potential well problem is more realistic compared to the infinite potential well. It is...
Time-Independent Schrödinger Equation
Wave-particle Duality The double-slit experiments show us: particle source P1 : probability pattern when slit 1 is openP2...
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Differential Equations for EngineersThe Hong Kong University of Science and Technology By highlighting both theories and applications in...
Vector Calculus: Fundamental Theorems
Gradient Theorem The fundamental theorem of single variable calculus was the one that told you “the integral of the...
Line and Surface Integrals
Line Integrals Scalar Fields We have a curve C in the x-y plane, we can represent a point...
My #79 course certificate from Coursera
Logic for EconomistsUniversity of Amsterdam The logo of University of Amsterdam is cool, so is this succinct course....
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...
Systems of Differential Equations
Systems of Homogeneous Linear First-order ODEs The system of linear first order homogeneous equations can be written in matrix...
My #78 course certificate from Coursera
Corporate & Commercial Law II: Business Forms, Financing & Governmental RegulationUniversity of Illinois at Urbana-Champaign University of Illinois...
Polar, Cylindrical, Spherical Coordinates
Multidimensional Integration In Vector Calculus, we have to worry about integrating over two or three variables: double integrals...