Lectures related to Partial Differential Equations: Basics and Classification

Partial Differential Equations: Characteristics and Solutions

Explores characteristic curves and solutions in partial differential equations, emphasizing uniqueness and existence in various scenarios.

Classification of PDEs: Linear, Semi-linear, Quasi-linear

Explores the classification of PDEs into linear, semi-linear, and quasi-linear types, emphasizing the properties of their solutions.

Partial Derivatives and Differential Equations

Covers partial derivatives, differentiability, differential equations, sets properties, and local extrema verification.

Partial Differential Equations

Introduces partial differential equations, covering derivatives, special cases, transformations, and the Jacobian matrix.

Canonical Transformations: Hamilton-Jacobi Equation

Explores canonical transformations, the Hamilton-Jacobi equation, symplectic groups, and differential equations in physics.

Eigenvalues and Optimization: Numerical Analysis Techniques

Discusses eigenvalues, their calculation methods, and their applications in optimization and numerical analysis.

Laplacian in Polar and Spherical Coordinates: Derivatives

Covers the Laplacian operator in polar and spherical coordinates, focusing on derivatives and integral calculations.

Quantum Mechanics: Jacobi Identity and Gauge Invariance

Explores Jacobi identity, gauge invariance, and conservation laws in quantum mechanics and classical physics.

Differentiability: Partial Derivatives and Hessiennes

Explains partial derivatives, Hessienne matrix, and their properties.

Hamiltonian Formalism: Harmonic Oscillator

Explores the Hamiltonian formalism for the harmonic oscillator, focusing on deriving Lagrangian and Hamiltonian, isolating the system, and generating new conserved quantities.

Differential Calculus: Applications and Reminders

Covers differential calculus applications and reminders, emphasizing the importance of differentiability in mathematical analysis.

Partial Derivatives and Functions

Explores partial derivatives and functions in multivariable calculus, emphasizing their importance and practical applications.

Fundamental Solutions

Explores fundamental solutions in partial differential equations, highlighting their significance in mathematical applications.

Mathematical Complements: df or δf, Consequences

Explores the consequences of exact differential forms and necessary conditions for total exact differentials, using examples from mountain hiking.

Advanced Analysis 2: Linear Differential of Functions

Explores linear differential of functions, continuity, differentiability, and matrix representation.

Differential Equations: Solutions and Functions

Explores solutions of differential equations and properties of functions.

Derivatives and Continuity in Multivariable Functions

Covers derivatives and continuity in multivariable functions, emphasizing the importance of partial derivatives.

Mathematical Complements: df or δf

Explores mathematical tools for differentials of functions of multiple variables and their practical applications in thermodynamics and real-life scenarios.

Canonical Transformations: Existence and Equations

Explores canonical transformations, focusing on existence, equations, simplicity, and differential equations' theory.

Geometric Interpretation of Derivatives

Explores the geometric interpretation of derivatives and properties of derivable functions.