Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Second Order Differential Equations: Solving Examples and Conditions

In course

MATH-207(d): Analysis IV

The course studies the fundamental concepts of complex analysis and Laplace analysis with a view to their use to solve multidisciplinary scientific engineering problems. ...

Description

This lecture covers the solution of second order differential equations, focusing on examples and conditions. The instructor explains the process step by step, clarifying the use of different examples and the importance of specific conditions in the solutions. The lecture also touches on Fourier series calculations and the application of Sturm-Liouville theory. Students are guided through various exercises and examples to deepen their understanding of the topic.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Instructors (2)

David Valentin Strütt

Sébastien Basterrechea

Official source

Related concepts (21)

Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .

Partial differential equation

In mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.

Differential-algebraic system of equations

In electrical engineering, a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. In mathematics these are examples of differential algebraic varieties and correspond to ideals in differential polynomial rings (see the article on differential algebra for the algebraic setup).

Linear differential equation

In mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).

Differential equation

In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.

Related lectures (35)

Mathematical Methods for Physicists: Differential Equations and Special Functions

Covers solving differential equations and special functions essential for physicists, emphasizing practical problem-solving skills.

General Solution of Homogeneous Second Order Linear Differential Equations

Covers the general solution of homogeneous second-order linear differential equations with constant coefficients and the concept of linear independence of solutions.

Boundary Conditions and Basis Decomposition

Explores boundary conditions, basis functions, and PDE solutions using Fourier and Bessel series.

Differential Equations: Solution Methods MOOC: Electrical engineering II

Explores the resolution of differential equations and the properties of exponential functions in electrical engineering.

Canonical Transformations: Existence and Equations