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| '''Bold text'''MATHEMATICS FOR PHYSICS
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| '''Bold text'''Differentiation:
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| ''Italic text''Constant quantity:
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| If the value of a quantity remains the same in a mathematical operation, it is called a constant quantity.
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| Examples: Integers (4, 7, 13, ...), the fraction (1/2, 4/5), n, e, etc.,
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| ''Italic text''Variable quantity:
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| If the quantity takes different values in a mathematical operation, it is a variable quantity. Examples:
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| (i) In the equation y = 2x + 3, x and y are variables.
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| (ii) In the equation F = ma where F, m and a are variables.
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| Variable quantities are divided into two types
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| (a) Independent quantity.
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| (b) Dependent quantity.
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| In the equation y = 2x + 3, x is the independent quantity, and y is the dependent quantity.
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| ''Italic text''Function:
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| If corresponding to any given value of x, there exists a single definite value then y is called a function of x. This is represented as y = f(x). This equation means that corresponding to one value of x, there is a single definite value of the variable y.
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| Example: (i) Let y = 2x, when x = 1 then y = 2; when x = 2 then y = 4...
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| Thus corresponding to each value of x, there is a definite value of y.
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| ''Italic text'' Difference and Differential coefficient:
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| Let y be a function of x. This is denoted as y = f(x). Here x and y are the variables. Let the value of x change to x+△x and correspondingly the value of y changes to y+△y.
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| The change between the initial and final values of a variable quantity is called Difference.
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| Difference in x = (x+ △x) - x = △x; Difference in y =(y+△y)-y=△y
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| The ratio of △y/△x is called the quotient of the two increments.
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| When Difference in x (i.e., △x) is very small i.e., almost approaching to zero, then
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