Homogeneous Differential Equation
A differential equation is said to be a homogeneous differential equation. If it is of the form where f and g are homogenous functions, in x and y of the same degre..
A differential equation is said to be a homogeneous differential equation. If it is of the form where f and g are homogenous functions, in x and y of the same degre..Molecular Basis of Differentiation
All the cells of an organism receive the complete set of genes (total information) present in the fertilized egg through mitotic divisions. However, cells of an early embryo lose the potential for the expression of all the genes through the processes of induction and repression, perhaps by mechanis..
Linear Differential Equation
A differential equation is said to be linear, if the unknown function and its derivatives occur only in the first degree and are not multiplied together. Example: Note that the degree of a linear differential equation is 1, but a differential equation whose degree ..
A differential equation is said to be linear, if the unknown function and its derivatives occur only in the first degree and are not multiplied together. Example: Note that the degree of a linear differential equation is 1, but a differential equation whose degree ..Definition of Implicit Differentiation
When a relation is expressed in the form f(x,y) = 0, that is, an equation involving both x and y ,then either variable is said to be an implicit function of the other. To differentiate the function is nothing but finding dy / d..
Derivability or Differentiability at a Point
Let f be a function and a be any point in its domain. Let h>0 be a small number. f(x) is said to be differentiable if exists and is denoted by f | (a), then f | (a) is called the derivative or differential coefficient of f(x) at x = a. That ..
Let f be a function and a be any point in its domain. Let h>0 be a small number. f(x) is said to be differentiable if exists and is denoted by f | (a), then f | (a) is called the derivative or differential coefficient of f(x) at x = a. That ..Comparison between differentiation and integration
1. Both are operations on functions. 2. Both are linear. This is because of the following: (i) (ii) The constant can be taken outside the differential as well as integral sign as shown below: 3. We heve already seen that not all functions are differentiable. Similarly, all funct..
1. Both are operations on functions. 2. Both are linear. This is because of the following: (i) (ii) The constant can be taken outside the differential as well as integral sign as shown below: 3. We heve already seen that not all functions are differentiable. Similarly, all funct..Developoment and Differentiation Summary
Summary - Every multicelluar organism begins its life as a single cell called zygote which by cleavage forms numerous identical cells. As development proceeds, these cells become specialised into components of various tissues and organs. The process of specialisation called differentiation..
Product Rule for Differentiation
Let y = u. v, where both u and v are differentiable functions of x.Let y = u. v, where both u and v are differentiable functions of x. or (u.v)' = u.v' + v..
Let y = u. v, where both u and v are differentiable functions of x.Let y = u. v, where both u and v are differentiable functions of x. or (u.v)' = u.v' + v..ApproxiMations by Differentials
Let y = f (x) be a differentiable function of x, errors in x and y are denoted by d x and d y, we have \ Error in y = f ' (x) d ..
Let y = f (x) be a differentiable function of x, errors in x and y are denoted by d x and d y, we have \ Error in y = f ' (x) d ..Molecular Basis of Differentiation
Development involves precisely coordinated series of events. Each gene is switched on in its turn, and then something resulting from the expression of that gene, or some environmental influence, switches on the next gene in the programm..
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