Introductory Calculus - Oxford Mathematics 1st Year Student Lecture
Comprehensive introduction to calculus at Oxford, covering differential equations, integration techniques, and problem-solving methods for first-year mathematics students.
Modeling and Simulation of Dynamic Systems
Learn MATLAB techniques for solving ODEs, analyzing spring-mass-damper systems, and applying Laplace transforms in dynamic system modeling and simulation.
Ordinary Differential Equations
Comprehensive introduction to ordinary differential equations, covering key concepts, methods, and applications in physics and engineering.
Taylor Series and Power Series Made Easy - Review of Calculus
Comprehensive review of Taylor and Power Series with visual aids and coding examples in Python and Matlab. Covers definitions, expansions for sine and cosine, and practical implementations.
Engineering Mathematics: Linear Algebra and ODEs, Fall 2014
Explore linear algebra and ODEs, covering numerical solutions for equation systems. Learn first and second-order equations with renowned instructor Gilbert Strang.
Transform Calculus and Its Applications in Differential Equations
Comprehensive exploration of integral transforms, focusing on Laplace and Fourier transforms, their properties, and applications in solving differential equations and boundary value problems.
QSS: A Solver for Large Sparse Stiff Discontinuous Systems
Explore a conference talk on QSS (Quantized State System), a solver designed for large sparse stiff discontinuous systems. Delve into the fundamental differences between classic methods and QSS algorithms, focusing on the concept of quantum Δ and its rol…
Modelling Cancer Radiotherapy: Fractional vs Ordinary Differential Equations
Explore a 19-minute conference talk on modeling cancer radiotherapy, comparing fractional and ordinary differential equations. Delivered by Kathleen Wilkie from Toronto Metropolitan University on September 23, 2024, as part of the Frontiers in Computatio…
A Second Course in Differential Equations
Explore advanced topics in ordinary differential equations, including linear systems, eigenvalues, numerical methods, and Python implementations for solving complex ODEs.
Differential Equations - Vol 1
Explore fundamental concepts and applications of ordinary differential equations, including solving techniques, graphing, and real-world applications in mixing, cooling, and electrical circuits.
PDE 101 - Separation of Variables or How I Learned to Stop Worrying and Solve Laplace's Equation
Explore the powerful Separation of Variables technique for solving PDEs, focusing on Laplace's equation in 2D for steady-state heat distribution, with applications in physics and engineering.
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.
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.
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.
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.
Differential Equations, a Tourist's Guide
Explore ordinary differential equations through intuitive visualizations, covering concepts like vector fields, phase spaces, and real-world applications in physics and social dynamics.