Lectures related to Nonlinear Systems: Equations and Solutions

Linear Algebra Basics

Covers the basics of linear algebra, including solving equations and understanding systems of linear equations graphically.

Absolute Values: Equations and Inequalities

Explores absolute values in equations and inequalities, focusing on solving |f(x)| = g(x).

Implicit Functions Theorem

Covers the Implicit Functions Theorem, explaining how equations can define functions implicitly.

Vectorization in Python: Efficient Computation with Numpy

Covers vectorization in Python using Numpy for efficient scientific computing, emphasizing the benefits of avoiding for loops and demonstrating practical applications.

Linear Independence: The Wronskian Concept

Explains the Wronskian and its role in determining linear independence of solutions to differential equations.

Advanced Analysis II: Cauchy Problem and Differential Equations

Covers the Cauchy problem in differential equations, focusing on initial conditions and their impact on solution uniqueness.

Cosmological Puzzles: Dark Matter and Energy

Explores fundamental cosmological puzzles related to dark matter and energy.

Riemann Sphere: Correlations and Conditions

Covers the Riemann sphere, focusing on its conditions and correlation functions in mathematical and physical contexts.

Nonlinear Systems: Seeking Solutions

Explores the search for solutions in nonlinear systems through various methods and techniques.

Monstrous Moonshine

Explores Monstrous Moonshine, focusing on the 1979 discovery and its mathematical connections.

Nonlinear Equations: Methods and Applications

Covers methods for solving nonlinear equations, including bisection and Newton-Raphson methods, with a focus on convergence and error criteria.

Cauchy Problem: Differential Equations and Initial Conditions

Covers the Cauchy problem, focusing on differential equations and the role of initial conditions in determining unique solutions.

Optimization Methods: Convergence and Trade-offs

Covers optimization methods, convergence guarantees, trade-offs, and variance reduction techniques in numerical optimization.

Primal-dual Optimization: Extra-Gradient Method

Explores the Extra-Gradient method for Primal-dual optimization, covering nonconvex-concave problems, convergence rates, and practical performance.

Diffusion Equations: Green's Function Approach

Covers the analysis and solution of diffusion equations using Green's function approach and discusses boundary conditions and dimensional analysis.

Nonlinear Equations: Fixed Point Method

Covers the topic of nonlinear equations and the fixed point method.

Linear Algebra: Systems of Linear Equations

Introduces linear algebra concepts, focusing on solving systems of linear equations and their representations.

Mathematical Equation Rule

Covers the process of converting handwritten entries into text and sharing mathematical equation rules.

Systems and Linear Equations: Introduction

Introduces systems and linear equations, defining lines and planes in 2D and 3D spaces.

Differential Equations: Initial Conditions and Solutions

Discusses ordinary differential equations, focusing on initial conditions and methods for finding solutions.