On the Algebraic Geometry of Spaces of Persistence Modules
Explore algebraic geometry's application to persistence modules in topological data analysis, offering insights into data structure and shape analysis.
Introduction to Chromatic Homotopy Theory - Lecture 3
Explore chromatic homotopy theory's advanced concepts and applications in algebraic topology, building on previous lectures to deepen understanding of this complex mathematical field.
Investigating Transmission-Blocking Anti-malarial Drugs: A Mathematical Modelling Approach
Explore mathematical models assessing transmission-blocking antimalarial drugs' impact on disease control, focusing on treatment coverage, drug efficacy, and protective effects in malaria hotspots.
Pendulum Simulation: In Search of Chaos - Part 6
Explore chaos in double pendulum systems through simulation, analyzing different initial conditions and observing complex behavior patterns.
Why π Is in the Normal Distribution - Beyond Integral Tricks
Explore the mathematical origins of π in the normal distribution through geometric insights, classic proofs, and the Herschel-Maxwell derivation, offering a deeper understanding beyond integral tricks.
CSS Trigonometry
Explore CSS trigonometry functions sin() and cos() for creative layouts and animations. Learn practical applications and optimize with Sass loops and custom properties.
Introduction to Chromatic Homotopy Theory - Lecture 2
Explore chromatic homotopy theory's foundations, techniques, and applications in algebraic topology. Delve into advanced concepts and their significance in modern mathematical research.
Introduction to Chromatic Homotopy Theory - Lecture 4
Explore chromatic homotopy theory's advanced concepts and applications in algebraic topology, building on previous lectures to deepen understanding of this complex mathematical field.
Convolutions and Adding Random Variables, Visually Explained
Visual explanation of convolutions and adding random variables, exploring discrete and continuous cases, with connections to the central limit theorem and practical examples.
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.
Div, Grad, and Curl
Explore fundamental vector calculus concepts: divergence, gradient, and curl. Learn their applications in engineering mathematics through clear explanations and examples.
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.
Higher-Order ODEs, Characteristic Equation, Matrix Systems of First Order ODEs
Explore higher-order linear ODEs, characteristic equations, and matrix systems of first-order equations in engineering mathematics, with accompanying notes and MATLAB code.