Concept

First-order partial differential equation

Related lectures (27)

Covers the Black-Scholes-Merton model, dynamics, self-financing strategies, and the PDE.

Covers relations, sequences, and posets, emphasizing properties like anti-symmetry and transitivity, and introduces arithmetic and geometric progressions.

Differentiability Theorems

Covers differentiability theorems and methods to check for differentiability in functions.

First Order Equations: Constant Variation

Explains the constant variation method for solving first-order linear differential equations with an illustrative example.

Cauchy Problem: General Solution

Covers the general solution of Cauchy problems in first-order differential equations.

Bernoulli Differential Equation

Explores the Bernoulli differential equation, historical context, solution methods, linear homogeneous equations, and examples.

Separable Differential Equations

Explores the theorem of existence and uniqueness for differential equations and the method to find the general solution.

Solving Differential Equations: Separable Equations

Covers the method of separation of variables to find the general solution of differential equations.

Differential Equations: Existence and Uniqueness Theorems

Covers the existence and uniqueness of solutions for differential equations.

Ordinary Differential Equations: Definitions and Examples

Covers ordinary differential equations, their orders, examples, and applications in various fields.

Diffusion: Macroscopic View

Explores diffusion from a macroscopic perspective, emphasizing the derivation of the diffusion equation through mass conservation and fixed flux law.

Untitled

Partial Differential Equations: Basics

Covers the basics of Partial Differential Equations, including well-posedness, operators, and classification of physical PDEs.

Numerical Approximation of PDEs

Covers the numerical approximation of PDEs, including Poisson and heat equations, transport phenomena, and incompressible limits.

Differential Equations: Implicit Function Theorem Applications

Discusses the reduction of higher-order differential equations to first-order systems using the implicit function theorem.

Basis Decomposition of PDEs: 1D and Multidimensional Problems

Explores solving PDEs using eigenmodes decomposition and Fourier series representation of solutions.

Numerical Methods: Differential Equations

Covers the application of numerical methods to solve differential equations using MATLAB.

Stress Components & Transformation of Tensors

Covers stress components, tensor transformation, and invariants in continuum mechanics.

Relations, Sequences and Summations

Covers topics on relations, sequences, and summations, including lattices, recurrence relations, and sigma notation.

Second Order Equations

Covers second-order differential equations, focusing on finding particular solutions and the general solution.