Numerical Differentiation - Second Derivatives and Differentiating Data
Explore numerical computation of second derivatives and data differentiation with Python and Matlab examples, covering finite difference schemes and practical applications.
Numerical Differentiation with Finite Difference Derivatives
Learn techniques for approximating derivatives numerically using finite difference schemes. Explore error analysis with Taylor series and see practical implementations in MATLAB and Python.
Linear Systems of Differential Equations with Forcing - Convolution and the Dirac Delta Function
Explores linear differential equations with forcing, covering impulse response, Dirac delta function, and convolution integral. Essential for control theory and linear systems analysis.
Systems of Differential Equations - Diagonalization and Jordan Canonical Form
Explore diagonalization and Jordan Canonical Form for systems of differential equations, covering eigenvectors, complex conjugates, repeated eigenvalues, and general matrix applications.
Non-Normal Linear Systems and Transient Energy Growth - Bypass Transition to Turbulence
Explore non-normal linear systems and their role in turbulence, including examples, code demonstrations, and applications in fluid dynamics and bypass transition.
Drawing Phase Portraits for Nonlinear Systems
Learn to analyze nonlinear systems by drawing phase portraits, identifying fixed points, linearizing, and inferring global dynamics. Gain practical skills in stability analysis using eigenvalues and eigenvectors.
Systems of ODEs: Imaginary Eigenvalues and Center Fixed Points
Explore imaginary eigenvalues and center fixed points in 2D ODE systems. Learn to compute eigenvectors, write solutions, and understand geometric intuition behind rotational dynamics.
Systems of ODEs - Saddle Points and Instability
Explore unstable saddle points in 2D linear ODEs, their applications in energy-efficient transport, and analysis using eigenvalues, eigenvectors, and phase portraits.
Systems of ODEs - Sources and Sinks
Explore 2D linear ODEs with real eigenvalues, analyzing unstable sources and stable sinks through eigenvalues, eigenvectors, and phase portraits. Gain insights into solution methods and visualizations.
Eigenvalues and Eigenvectors
Explore eigenvalues and eigenvectors, key concepts in linear algebra. Learn to compute them for any matrix, understand their significance in transformations, and apply them to solve complex linear systems.
More Examples of Second Order Differential Equations
Explore advanced examples of second-order ODEs, including characteristic polynomials, initial conditions, and matrix systems. Learn to solve, plot, and interpret results using MATLAB.
Engineering Math Pre-Req - Quick and Dirty Introduction to Python
High-level introduction to essential Python commands for engineering math, covering arithmetic, loops, arrays, plotting, and solving equations and differential equations.
Engineering Math Pre-Req - Quick and Dirty Introduction to Matlab
High-level introduction to essential Matlab commands for engineering math, covering arithmetic, loops, matrices, plotting, and solving equations and differential equations.
Second-Order ODE: Spring-Mass-Damper
Comprehensive tutorial on solving second-order ODEs for damped harmonic oscillators, covering derivation, solution methods, and practical implementation in Matlab and Python.
Second-Order Ordinary Differential Equations - Solving the Harmonic Oscillator Four Ways
Explore four methods to solve second-order ODEs for harmonic oscillators: guessing, Taylor series, alternative guessing, and matrix systems. Gain practical problem-solving skills in differential equations.
The Simplest Ordinary Differential Equation and Its Exponential Solution
Explore exponential solutions to simple ODEs through real-world examples like population growth, compound interest, and radioactive decay. Gain intuitive understanding of Euler's number and its applications.
Gentle Introduction to Modeling with Matrices and Vectors - A Probabilistic Weather Model
Explore probabilistic weather modeling using matrices and vectors, with practical examples in Python and MATLAB. Learn to represent and update weather states mathematically.
Differential Equations and Dynamical Systems - Overview
Explore dynamical systems and their applications in various fields. Learn classic and modern techniques for modeling real-world phenomena, from fluid dynamics to epidemiology.
Python Machine Learning & AI Mega Course - Learn 4 Different Areas of ML & AI
Comprehensive exploration of machine learning and AI in Python, covering algorithms, neural networks, chatbots, and game AI. Hands-on projects and in-depth explanations for practical skills development.
TensorFlow 2 Beginner Course
Comprehensive introduction to TensorFlow 2.0 and Keras, covering key concepts and practical applications in deep learning through hands-on projects and real-world examples.
Learn NumPy in 30 Minutes
Master essential NumPy functions for efficient array operations, data manipulation, and numerical computing in Python. Covers basics to advanced topics like multidimensional arrays, broadcasting, and linear algebra.