Mathematical Tool

Mathematics is the language of physics. It becomes easier to describe, understand, and apply the physical principles if one has a good knowledge of mathematics.

For Example, Tools are required to do physical work easily and mathematical tools are required to solve numerical problems easily

TRIGONOMETRY

[Measurement of angle and relationship between degrees and radian]

 

Exercise

 

 

DIFFERENTIATION

[The purpose is to study of nature where some quantities vary ( increases or decreases)]

Constant:- whose value does not change

Variable:- Whose value changes.

For example, in relation \dpi{120} \fn_cm y=2x+5

2 and 5 are constant, \dpi{120} \fn_cm x is variable known as independent variable, and \dpi{120} \fn_cm y is a variable known as a dependent variable because their value depends upon \dpi{120} \fn_cm x

\dpi{120} \fn_cm \frac{\mathrm{d} y}{\mathrm{d} x}\rightarrowdifferentiation of y w.r.t. x

or, Rate of change of y w.r.t. x

or a slope of tangent on the curve at a point.

Formula

Rule

\dpi{120} \fn_cm (i)\; \frac{d(cu)}{dx}=c\frac{du}{dx}\; where \;c\;is\;constant\;\;\;\;\;\;\;\;\;\;(ii)\;\frac{d(u\pm v)}{dx}=\frac{du}{dx}\pm \frac{dv}{dx}

\dpi{120} \fn_cm (iii)\; \frac{d(uv)}{dx}=u\frac{dv}{dx}+v\frac{du}{dx}

 

Exercise

 

MAXIMA & MINIMA

 

Exercise

(1) Find the minimum and maximum values of the function \dpi{120} \fn_cm y=x^3-3x^2+6. And also find the value of \dpi{120} \fn_cm x for which \dpi{120} \fn_cm y is maximum and minimum. ( x=0,2/6,2)

 

INTEGRATION

 

 

Exercise

 

 

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