🧠Cloud AI for numerical analysis and code verification

This curriculum demonstrates the progression from fundamental, idealized 1D mechanical models (elastic strings and beams) to more complex 2D physical systems (elastic membranes, wave propagation, heat diffusion) and abstract mathematical/financial concepts (transport, Schrödinger, Black-Scholes), culminating in numerical methods (Finite Difference for Elliptic Problems). Through a blend of plotting, detailed analysis, and dynamic animations, it illustrates how increasing complexity in physical phenomena necessitates higher-order differential equations and sophisticated computational techniques to model their behavior, often with counter-intuitive results compared to simpler systems.

This curriculum demonstrates the progression from fundamental, idealized 1D mechanical models (elastic strings and beams) to more complex 2D physical systems (elastic membranes, wave propagation, heat diffusion) and abstract mathematical/financial concepts (transport, Schrödinger, Black-Scholes), culminating in numerical methods (Finite Difference for Elliptic Problems). Through a blend of plotting, detailed analysis, and dynamic animations, it illustrates how increasing complexity in physical phenomena necessitates higher-order differential equations and sophisticated computational techniques to model their behavior, often with counter-intuitive results compared to simpler systems.

🧠Exploring Elastic String Behavior: From Plotting to Problem Solving-1/10🧠The Elastic Beam: Plotting, Analysis, and Visualization-2/10🧠Understanding and Modeling the Elastic Membrane-3/10🧠The Transport Equation: Plotting and Modeling-4/10🧠Cloud-Based Analysis of the Vibrating String-5/10🧠From Strings to Membranes: Exploring the Wave Equation in 1D and 2D Cloud Environments-6/10🧠Solving the Heat Equation in the Cloud: From Fourier's Insights to Numerical Stability-7/10🧠Visualizing and Analyzing Quantum Wave Packet Dynamics with the Schrödinger Equation-8/10🧠Implementing the Black-Scholes Equation for European Call Options in the Cloud-9/10🧠Approximating Derivatives: The Finite Difference Method-10/10