Numerical Analysis
Explore differential equations, numerical integration, and root-finding methods using software tools. Learn practical techniques for solving complex mathematical problems in engineering and science.
Power System Dynamics and Control
This course first introduces a student to power stability problems and the basic concepts of modeling and analysis of dynamical systems. Modeling of power system components - generators, transmission lines, excitation and prime mover controllers - is cov…
Numerical Analysis With Matlab
Learn iterative methods, interpolation, and numerical integration techniques with Matlab implementations for solving complex mathematical problems.
Numerical Integration - Discrete Riemann Integrals and Trapezoid Rule
Explore numerical integration techniques including Riemann integrals, trapezoidal rule, and Simpson's rule. Learn to approximate definite integrals with Python and MATLAB implementations.
Chaotic Dynamical Systems
Explore chaotic dynamical systems, their sensitive dependence on initial conditions, and applications in nature and engineering. Learn to recognize chaos and numerically integrate these complex systems.
Introduction to the Finite Element Method: 1D Basis Functions
Explore 1D basis functions in finite element method. Learn key concepts and applications for numerical analysis and engineering problem-solving.
2D Finite Element Method - Summary of FEM Procedure
Explore the 2D Finite Element Method procedure, covering key steps and applications in engineering analysis. Gain insights into this powerful numerical technique for solving complex problems.
Why Does the RMS Voltage Have a Square Root of 2?
Explore the concept of RMS voltage, its relationship to the square root of 2, and the average of sin^2 using Python code examples.
Chaos in ODEs - Lorenz and the Double Pendulum
Explore chaos in ordinary differential equations through Lorenz systems and double pendulum examples, examining numerical integration challenges and chaotic dynamics in engineering mathematics.
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.
Numerical Integration With Trapezoidal and Simpson's Rule
Learn to approximate definite integrals using the Trapezoidal and Simpson's Rules, powerful numerical methods for solving complex integration problems.
Numerical Methods
Comprehensive exploration of numerical methods covering error analysis, linear systems, interpolation, differentiation, integration, and solving algebraic equations using various techniques.
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.
Runge-Kutta Integrator Overview - All Purpose Numerical Integration of Differential Equations
Comprehensive introduction to Runge-Kutta schemes for numerical integration of differential equations, covering RK2 and RK4 methods with intuitive explanations and visual representations.
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.
Deriving Forward Euler and Backward-Implicit Euler Integration Schemes for Differential Equations
Explore Forward and Backward Euler integration methods for ODEs, including derivations, error sources, and stability analysis. Gain insights into numerical integration techniques for solving differential equations.
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.
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 and Numerical Integration
Explore numerical differentiation and integration techniques in engineering mathematics, covering key concepts and practical applications for solving complex problems.
Quadrature Rules on Manifolds - Useful Results - Lecture 3
Explore advanced quadrature techniques for manifolds, focusing on key results and applications in harmonic analysis. Gain insights into cutting-edge mathematical approaches.
Quadrature Rules on Manifolds - Designs - Lecture 1
Explore quadrature rules on manifolds and designs in harmonic analysis. Learn about cutting-edge mathematical techniques for solving complex problems in geometry and analysis.