Numerical Simulation of Ordinary Differential Equations - Integrating ODEs
Explore numerical integration of ODEs to analyze nonlinear systems and generate trajectories. Learn techniques for solving complex dynamics where analytic methods fall short.
Differential Equations with Forcing: Method of Variation of Parameters
Learn to solve forced linear differential equations using the powerful method of variation of parameters, replacing unknown coefficients with time-dependent functions based on external forcing.
Differential Equations with Forcing: Method of Undetermined Coefficients
Learn to solve linear differential equations with external forcing using the method of undetermined coefficients. Understand homogeneous solutions, particular solutions, and how to combine them for a complete solution.
Deriving the Heat Equation in 2D and 3D and in N Dimensions with Control Volumes and Vector Calculus
Explore the derivation of the heat equation in multiple dimensions using Gauss's theorem, control volumes, and vector calculus techniques for a comprehensive understanding of heat transfer.
Partial Differential Equations Overview
Explore the mathematical language of physical phenomena with an overview of partial differential equations, covering canonical PDEs, linear superposition, and nonlinear PDEs like Burgers Equation.
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.
Hankel Alternative View of Koopman - HAVOK Analysis
Decompose chaos into linear systems with intermittent forcing using HAVOK analysis. Learn to build linear regression models on eigen-time-delay coordinates for complex dynamical systems.
Laplace Transform Solutions to PDEs
Explore Laplace transform techniques for solving partial differential equations, enhancing your understanding of advanced mathematical methods in engineering applications.
Convolution Integrals, Impulse and Step Responses
Explore convolution integrals, impulse response, and step response in engineering mathematics, enhancing understanding of system behavior and analysis techniques.
The Laplace Transform
Explore the Laplace Transform in engineering mathematics, covering its applications and fundamental principles. Gain insights into this powerful tool for solving differential equations and analyzing systems.
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.
Heat Equation in 2D and 3D - 2D Laplace Equation on Rectangle
Explore multidimensional heat equations and the 2D Laplace equation on rectangles, advancing your understanding of engineering mathematics and partial differential equations.
Analytic Solution to Laplace's Equation in 2D - On Rectangle
Explore the analytic solution to Laplace's equation in 2D on a rectangle, enhancing your understanding of engineering mathematics and partial differential equations.
Inverse Laplace Transform and the Bromwich Integral
Explore the inverse Laplace transform and Bromwich integral in engineering mathematics, focusing on applications and problem-solving techniques for complex systems analysis.
ML Bounds and Examples of Complex Integration
Explore ML Bounds and complex integration techniques in engineering mathematics, enhancing problem-solving skills for advanced mathematical applications.
Cauchy Integral Formula
Explore the Cauchy Integral Formula in complex analysis, a fundamental tool for evaluating contour integrals and analyzing holomorphic functions in engineering mathematics.
Integration in the Complex Plane - Cauchy-Goursat Integral Theorem
Explore integration in the complex plane and the Cauchy-Goursat Integral Theorem, essential concepts in engineering mathematics for advanced problem-solving techniques.
Stokes' Theorem and Conservative Vector Fields
Explore Stokes' theorem and conservative vector fields in engineering mathematics, focusing on applications and theoretical foundations for advanced problem-solving in fluid dynamics and electromagnetics.
Div, Grad, and Curl
Explore fundamental vector calculus concepts: divergence, gradient, and curl. Learn their applications in engineering mathematics through clear explanations and examples.
Linear Algebra in 2D and 3D - Inner Product, Norm of a Vector, and Cross Product
Explore fundamental concepts of linear algebra in 2D and 3D spaces, including inner product, vector norms, and cross product, essential for engineering mathematics applications.
Gauss's Divergence Theorem
Explore Gauss's Divergence Theorem in engineering mathematics, understanding its applications and significance in vector calculus and fluid dynamics.