Lecture

Exam Problems: Nonlinear Equations & ODEs

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In course

ChE-312: Numerical methods

This course introduces students to modern computational and mathematical techniques for solving problems in chemistry and chemical engineering. The use of introduced numerical methods will be demonstrated using the Python programming language. ...

Description

This lecture covers exam-like problems related to nonlinear equations and ordinary differential equations (ODEs). It includes solving chemical reaction systems, Regula-Falsi and Newton-Raphson methods for nonlinear equations, and the predator-prey model for ecosystem dynamics. Additionally, it explores differentiation, integration, and numerical methods for solving complex mathematical problems.

Instructors (2)

Kevin Sivula

See webpage for more info limno.epfl.ch Teaching & PhD PhD Students Odile Louise Andres, Arthur Eliot Bouchez, Benjamin Goldman, Nicolas Johannes Diercks, Aurélie Fanny Marie Célérien, Jiajun Li, Louise Marie Foltzer-De Cian, Melanie Victoria Johanning, Nils William Laurent Golay Past EPFL PhD Students Andrea Gasperini, Pauline Bornoz, Xavier Adrian Jeanbourquin, Xiaoyun Yu, Mathieu Steven Prévot, Muhammad Aiman Bin Rahmanudin Hamdan, Nhât-Tân Vuong, Yongpeng Liu, Arvindh Sekar, Barbara Alexandra Primera

Ljubisa Miskovic

Ljubisa Miskovic earned his Ph.D. degree in Automatic Control from the Swiss Federal Institute of Technology (EPFL) under the co-supervision of Dominique Bonvin and Alireza Karimi, in 2006. He pursued his postdoctoral studies at the Centre for Systems Engineering and Applied Mechanics, Universite Catholique de Louvain with Michel Gevers before moving to the laboratory of Vassily Hatzimanikatis at the EPFL. In 2010, he became a research scientist. His research interests include systems biology, metabolic engineering, synthetic biology, data-driven control design, system identification, stochastic processes and estimation theory.

Official source

Ontological neighbourhood

Mathematics

Analysis: Numerical analysis

Related concepts (32)

Lotka–Volterra equations

The Lotka–Volterra equations, also known as the Lotka–Volterra predator–prey model, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.

Numerical integration

In analysis, numerical integration comprises a broad family of algorithms for calculating the numerical value of a definite integral, and by extension, the term is also sometimes used to describe the numerical solution of differential equations. This article focuses on calculation of definite integrals. The term numerical quadrature (often abbreviated to quadrature) is more or less a synonym for numerical integration, especially as applied to one-dimensional integrals.

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), .

Euler method

In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler, who first proposed it in his book Institutionum calculi integralis (published 1768–1870).

Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.

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