Numerical differentiationIn numerical analysis, numerical differentiation algorithms estimate the derivative of a mathematical function or function subroutine using values of the function and perhaps other knowledge about the function. The simplest method is to use finite difference approximations. A simple two-point estimation is to compute the slope of a nearby secant line through the points (x, f(x)) and (x + h, f(x + h)). Choosing a small number h, h represents a small change in x, and it can be either positive or negative.
Numerical analysisNumerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). It is the study of numerical methods that attempt at finding approximate solutions of problems rather than the exact ones. Numerical analysis finds application in all fields of engineering and the physical sciences, and in the 21st century also the life and social sciences, medicine, business and even the arts.
Numerical stabilityIn the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues.
Numerical integrationIn 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.
ApproximationAn approximation is anything that is intentionally similar but not exactly equal to something else. The word approximation is derived from Latin approximatus, from proximus meaning very near and the prefix ad- (ad- before p becomes ap- by assimilation) meaning to. Words like approximate, approximately and approximation are used especially in technical or scientific contexts. In everyday English, words such as roughly or around are used with a similar meaning. It is often found abbreviated as approx.
Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Computational scienceComputational science, also known as scientific computing, technical computing or scientific computation (SC), is a division of science that uses advanced computing capabilities to understand and solve complex physical problems. This includes Algorithms (numerical and non-numerical): mathematical models, computational models, and computer simulations developed to solve sciences (e.
Red blood cellRed blood cells (RBCs), also referred to as red cells, red blood corpuscles (in humans or other animals not having nucleus in red blood cells), haematids, erythroid cells or erythrocytes (from Greek erythros 'red' and kytos 'hollow vessel', with -cyte translated as 'cell' in modern usage), are the most common type of blood cell and the vertebrate's principal means of delivering oxygen (O2) to the body tissues—via blood flow through the circulatory system.
Finite differenceA finite difference is a mathematical expression of the form f (x + b) − f (x + a). If a finite difference is divided by b − a, one gets a difference quotient. The approximation of derivatives by finite differences plays a central role in finite difference methods for the numerical solution of differential equations, especially boundary value problems. The difference operator, commonly denoted is the operator that maps a function f to the function defined by A difference equation is a functional equation that involves the finite difference operator in the same way as a differential equation involves derivatives.
Lipid bilayerThe lipid bilayer (or phospholipid bilayer) is a thin polar membrane made of two layers of lipid molecules. These membranes are flat sheets that form a continuous barrier around all cells. The cell membranes of almost all organisms and many viruses are made of a lipid bilayer, as are the nuclear membrane surrounding the cell nucleus, and membranes of the membrane-bound organelles in the cell. The lipid bilayer is the barrier that keeps ions, proteins and other molecules where they are needed and prevents them from diffusing into areas where they should not be.
Packed red blood cellsPacked red blood cells, also known as packed cells, are red blood cells that have been separated for blood transfusion. The packed cells are typically used in anemia that is either causing symptoms or when the hemoglobin is less than usually 70–80 g/L (7–8 g/dL). In adults, one unit brings up hemoglobin levels by about 10 g/L (1 g/dL). Repeated transfusions may be required in people receiving cancer chemotherapy or who have hemoglobin disorders. Cross-matching is typically required before the blood is given.
Vesicle (biology and chemistry)In cell biology, a vesicle is a structure within or outside a cell, consisting of liquid or cytoplasm enclosed by a lipid bilayer. Vesicles form naturally during the processes of secretion (exocytosis), uptake (endocytosis), and the transport of materials within the plasma membrane. Alternatively, they may be prepared artificially, in which case they are called liposomes (not to be confused with lysosomes). If there is only one phospholipid bilayer, the vesicles are called unilamellar liposomes; otherwise they are called multilamellar liposomes.
Explicit and implicit methodsExplicit and implicit methods are approaches used in numerical analysis for obtaining numerical approximations to the solutions of time-dependent ordinary and partial differential equations, as is required in computer simulations of physical processes. Explicit methods calculate the state of a system at a later time from the state of the system at the current time, while implicit methods find a solution by solving an equation involving both the current state of the system and the later one.
Volume (thermodynamics)In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state. The specific volume, an intensive property, is the system's volume per unit of mass. Volume is a function of state and is interdependent with other thermodynamic properties such as pressure and temperature. For example, volume is related to the pressure and temperature of an ideal gas by the ideal gas law. The physical volume of a system may or may not coincide with a control volume used to analyze the system.
Protein–lipid interactionProtein–lipid interaction is the influence of membrane proteins on the lipid physical state or vice versa.
Computational chemistryComputational chemistry is a branch of chemistry that uses computer simulation to assist in solving chemical problems. It uses methods of theoretical chemistry, incorporated into computer programs, to calculate the structures and properties of molecules, groups of molecules, and solids. It is essential because, apart from relatively recent results concerning the hydrogen molecular ion (dihydrogen cation, see references therein for more details), the quantum many-body problem cannot be solved analytically, much less in closed form.
Lipid raftThe plasma membranes of cells contain combinations of glycosphingolipids, cholesterol and protein receptors organised in glycolipoprotein lipid microdomains termed lipid rafts. Their existence in cellular membranes remains somewhat controversial. It has been proposed that they are specialized membrane microdomains which compartmentalize cellular processes by serving as organising centers for the assembly of signaling molecules, allowing a closer interaction of protein receptors and their effectors to promote kinetically favorable interactions necessary for the signal transduction.
Biological membraneA biological membrane, biomembrane or cell membrane is a selectively permeable membrane that separates the interior of a cell from the external environment or creates intracellular compartments by serving as a boundary between one part of the cell and another. Biological membranes, in the form of eukaryotic cell membranes, consist of a phospholipid bilayer with embedded, integral and peripheral proteins used in communication and transportation of chemicals and ions.
Polynomial interpolationIn numerical analysis, polynomial interpolation is the interpolation of a given bivariate data set by the polynomial of lowest possible degree that passes through the points of the dataset. Given a set of n + 1 data points , with no two the same, a polynomial function is said to interpolate the data if for each . There is always a unique such polynomial, commonly given by two explicit formulas, the Lagrange polynomials and Newton polynomials.
Blood cellA blood cell, also called a hematopoietic cell, hemocyte, or hematocyte, is a cell produced through hematopoiesis and found mainly in the blood. Major types of blood cells include red blood cells (erythrocytes), white blood cells (leukocytes), and platelets (thrombocytes). Together, these three kinds of blood cells add up to a total 45% of the blood tissue by volume, with the remaining 55% of the volume composed of plasma, the liquid component of blood.
