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This is a collection of my learning notes. I find it helpful to write everything down to confirm my understanding, but they are mostly pedantic and boring. If you feel sleepless, feel free to read through them.
2026
In common engineering problems, the optimization problem is to minimize the residual of a parametric model with respect ...
Besides state estimation or localization, which provide a robot with knowledge of where it is, it’s equally important fo...
This note covers some of the fundamental concepts in Lie group and Lie algebra, and their applications to representing r...
In robot state estimation, the Bayes filter is a probabilistic approach that estimates the state from a sequence of cont...
2024
Two fundamental equations in acoustics areContinuity EquationThe continuity equation states that the rate at which mass ...
2023
A partial differential equation (PDE) is a relation involving one or more functions of several variables, and their part...
Now, we consider a somehow more general case, where we want to solve a linear second-order homogeneous equation with coe...
A function f:C→C is complex differentiable, or holomorphic, at z∈C iff′(z):=h→0,h∈Climhf(z+h)−f(z)exists. The follow...
The Laplace transform was first introduced by Pierre-Simon Laplace in his work on probability theory. The transform turn...
An important kind of equation to learn is those linear equations, which are those can be written in the form of Ly=bfor ...
First order ODE is equations that has the highest derivative of order one. It takes the formM(x,y)+N(x,y)y′=0The gener...