Lectures related to Implicit Functions: Analysis II

Implicit Differentiation: Solving Equations Locally

Explores implicit differentiation and the Implicit Function Theorem for finding unique functions locally.

Implicit Functions Theorem

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

Block Pulled by a Spring

Explores the dynamics of a block pulled by a spring under various conditions.

Implicit Functions Theorem

Discusses the uniqueness of implicit functions solutions and surfaces described by equations.

Mechanics of Continuous Media

Covers potential energy, balance solutions, and the Ritz method in mechanics.

Implicit Functions Theorem

Explores the Implicit Functions Theorem, demonstrating how to find solutions to equations like x²+y²=1 through implicit differentiation and function properties.

Equations of Heat and Fourier Transform

Covers heat equations, Fourier transforms, and variable separation methods.

Exact Differential Equations

Revisits exact differential equations, discussing implicit function theorem and factors integrants.

Nonlinear Systems: Equations and Solutions

Explores solving nonlinear systems of equations using Newton's method.

Dynamical Theory: Nanoparticle Systems

Covers constructing a dynamical theory for nanoparticle systems, conservation equations, and transport phenomena.

Implicit Differentiation

Explores implicit differentiation and the Implicit Function Theorem for finding unique local functions.

Capstan Effect Study

Explores the capstan effect and presents experiments to validate related equations.

Numerical Analysis: Stability in ODEs

Covers the stability analysis of ODEs using numerical methods and discusses stability conditions.

Lorentz Covariant Formulation: Maxwell Equations

Covers Lorentz transformations, Maxwell equations, and charge conservation in Lorentz invariant physics.

Cosmological Puzzles: Dark Matter and Energy

Explores fundamental cosmological puzzles related to dark matter and energy.

Displacement Field by Point Forces

Explores solving displacement field by point forces using Green's functions and integration process to obtain total solution.

The Finite Volume Method

Covers the Finite Volume Method for numerical flow simulation, including conservation equations, discretization methods, and boundary conditions.

Implicit Function Theorem: Tangent Planes and Derivatives

Discusses the Implicit Function Theorem and its application to tangent planes and derivatives.

Duffour and Soret Effects in Thermophoresis

Explores the Duffour effect, the Soret effect, and thermophoresis under various experimental conditions.

Implicit Functions Theorem: n=2 and n=3

Explains the Implicit Functions Theorem for n=2 and n=3 cases.