Euler Angle Simulation with MATLAB - Integrating the Rotational Kinematic Differential Equations
Simulate rigid body orientation using Euler angles and MATLAB. Learn to integrate kinematic differential equations, visualize results, and explore alternative attitude coordinates like quaternions.
Limit Cycles - Poincare-Bendixson Worked Examples: Glycolysis
Explore Poincaré-Bendixson theorem applications in limit cycle analysis, including a glycolysis model. Learn to construct trapping regions using nullclines and understand parameter spaces for stable limit cycles.
Advanced Math
Explore advanced mathematical concepts beyond calculus and linear algebra, including differential equations, vector fields, and complex theorems for a deeper understanding.
Linear Algebra
Comprehensive exploration of linear algebra concepts, including SVD, Fourier analysis, and compressed sensing, with practical applications and coding examples in MATLAB and Python.
Why Don't They Teach Newton's Calculus of What Comes Next?
Explore discrete calculus, Newton-Gregory interpolation, and sequence analysis. Uncover connections to Fibonacci, Pascal's triangle, and Maclaurin series in this alternate mathematical reality.
Euler’s Method - How to Use It
Comprehensive guide to Euler's method for approximating solutions to differential equations, covering its application, methodology, limitations, accuracy, and error analysis.
Differential Equations
Comprehensive coverage of ordinary and partial differential equations for CSIR NET, GATE, and JAM exams, including theory, methods, and solved examples.
Differential Equations
Comprehensive exploration of differential equations, covering theory, applications, and problem-solving techniques. Ideal for mastering this fundamental mathematical concept.
JuliaSim: Machine Learning Accelerated Modeling and Simulation
Explore JuliaSim: Accelerate modeling and simulation with machine learning. Learn about fast differential equation solvers, neural network integration, and surrogate models for enhanced computational efficiency.
Macroscopic Models of Epidemic Dynamics - Week 6
Explore macroscopic epidemic models, transitioning from stochastic to deterministic approaches. Learn about SIR models, continuous-time dynamics, and differential equations in epidemiology.
Adventures in Computing - From Punch Cards to Differential Equations
Prof Linda Petzold explores her journey in computational science, from punch cards to modern differential equations, highlighting key developments in numerical methods, stochastic simulations, and their applications in various fields.
Solving PDEs with the Laplace Transform - The Heat Equation
Learn to solve the heat equation using Laplace Transforms. Explore problem setup, transform application, ODE solutions, and boundary conditions. Gain insights into frequency and time domain solutions.
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.
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.