Linear Mixed Model in R with lme
Learn to implement Linear Mixed Models in R using lme(). Understand statistical modeling concepts, fixed and random effects, and interpret results for complex data relationships.
Understanding Predictive Modeling with R
Learn to create predictive models using R, covering key concepts, training techniques, and practical demonstrations. Gain insights into model selection and explore various applications in data analysis.
Solving Systems of Differential Equations with Eigenvalues and Eigenvectors
Learn to solve systems of linear ODEs using eigenvalues and eigenvectors. Covers problem setup, solution methods, and intuitive interpretation, with code examples in Python and MATLAB.
Hankel Alternative View of Koopman Analysis
Decomposing chaos into linear systems with intermittent forcing using HAVOK analysis. Explores eigen-time-delay coordinates for regression models, offering new insights into complex dynamical systems.
Laplace Transform and ODEs with Forcing and Transfer Functions
Explore Laplace transforms, ODEs, and transfer functions in engineering mathematics, focusing on spring-mass-damper systems and frequency response analysis.
FFT and Image Compression
Explore FFT-based image compression techniques, including natural image analysis, compression algorithms, and practical examples for efficient data representation.
Fourier Series
Explore Fourier Series: representation of functions, L2 integral norm, and MATLAB examples. Gain practical insights into engineering mathematics with real-world applications.
Vectorized Integration and the Lorenz Equation
Explore vectorized integration and the Lorenz equation, focusing on chaos, turbulence, and uncertainty in engineering mathematics, with practical MATLAB implementations.
Runge-Kutta Integration of ODEs and the Lorenz Equation
Explore Runge-Kutta integration methods for ODEs and delve into the fascinating Lorenz equation, uncovering its chaotic behavior and applications in engineering mathematics.
Matrix Systems of First Order Equations Using Eigenvectors and Eigenvalues
Explore matrix systems of first-order equations, diagonalization techniques, and higher-order linear ODEs. Learn to solve complex differential equations using eigenvectors and eigenvalues.
Overview of Engineering Mathematics
Explore engineering mathematics through weather modeling, covering fluid dynamics, disease networks, and systems of equations using MATLAB.
Numerical Integration of Chaotic Dynamics - Uncertainty Propagation & Vectorized Integration
Explore chaos and uncertainty propagation in dynamical systems through numerical integration. Learn efficient vectorization techniques in Python and MATLAB for faster computations.
Coding a Fourth-Order Runge-Kutta Integrator in Python and Matlab
Learn to implement a 4th-order Runge-Kutta integrator in Python and Matlab, and apply it to simulate the chaotic Lorenz 1963 system. Gain practical coding skills for numerical integration.
Numerical Integration of ODEs with Forward Euler and Backward Euler in Python and Matlab
Explore Forward and Backward Euler integration methods for ODEs using Python and Matlab. Compare stability, error, and implementation on a spring-mass-damper system with analytic solutions.
Linearizing Around a Fixed Point - Control Bootcamp
Explore linearization of nonlinear systems around fixed points, demonstrated with a simple pendulum example using both manual calculations and MATLAB implementation.
Numerical Solution to Laplace's Equation in Matlab - Intro to Fourier Series
Explore numerical solutions to Laplace's Equation using MATLAB and get introduced to Fourier Series in this engineering mathematics lecture, with practical code examples and comprehensive notes provided.
Numerical Solutions to ODEs - Forward and Backward Euler
Explore numerical methods for solving ordinary differential equations, focusing on Forward and Backward Euler techniques in engineering mathematics applications.
Numerical Integration and Numerical Solutions to ODEs
Explore numerical methods for integration and solving ordinary differential equations, enhancing your computational skills in engineering mathematics.
Numerical Differentiation Using Finite Difference
Explore numerical differentiation techniques using finite difference methods, with practical applications in engineering mathematics and accompanying Matlab code examples.
Degenerate Systems of Equations and Non-Normal Energy Growth
Explore degenerate equation systems and non-normal energy growth in engineering mathematics, focusing on key concepts and practical applications in dynamic systems analysis.
Eigenvalues, Eigenvectors, and Dynamical Systems
Explore eigenvalues, eigenvectors, and dynamical systems in engineering mathematics, focusing on their applications and significance in solving complex problems.