Solution of elementary calculus and other mathematical thought

Functional Analysis : Continuity in Norm Linear Spaces

What is the use of iota (i) in real life? Tanu Shyam Majumder's answer: It has some conceptual application in fluid Dynamics. Stream function and velocity potential can be calculated from single entity from complex valued function where we find iota(i) in expression of connection between two quantities.

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Study of number in different approach in mathematics Idea of math with the help of blogs spread phylosophy of math,share Mathematical concept and thought.

0 create natural number system Idea of math with the help of blogs spread phylosophy of math,share Mathematical concept and thought.

Is the sum of uncountably many 0 equal to 0? Tanu Shyam Majumder's answer: In single word answer is negative. If we consider 0+0+0+……. Up to ∞ as S(sum) i.e. S= 0+0+0+.. Up to ∞. It can also be reduced to S= Lim n->∞ n.0 = ∞.0= undefined. On the other hand if we take S=0+0+0+.. up to ∞.So m(S)=m(0)+m(0)+m(0)+.. up to ∞.So m(S)=...

How do you solve p^2+2pycot(x)-y^2=0 where p=dy/dx? Tanu Shyam Majumder's answer: p² + 2pycot(x) + y² cot²(x) —y²cot²(x)--y²=0=>(p+ycot(x))²=y²(1+cot²(x))=>p+ycot(x)=±ycosec(x) => either p= — y(cot(x)—cosec(x)) or p=--y(cot(x)+cosec(x)=> either dy/dx=--y(cot(x)--cosec(x)) or dy/dx=--y(cot(x)+cosec(x)) then either integration of dy/y =...

What is the relation between the differentiability and continuity of a function? Tanu Shyam Majumder's answer: Property of differentiability of any function always ensure continuity. If f(x) be any function differentiable at any point then f'(x), derivative of f(x) defined by f'(x) = lim ∆x->0 f(x+∆x) - f(x)/∆x which shows lim ∆x->0 f(x+∆x)-f(x)= lim ∆x->0 ∆xf’(x...

MCQ question of group theory for competitive exam like M.sc. entrance,Net,Gate Discussion of various questions about group theory of abstract Algeria

Concept of ∞ by definition approach in Mathematics : If we consider x->∞ that mean if we consider a very large number H, then x>H i.e. x is larger than large number which indicates as x->∞.

How are concepts like derivatives and integration useful in real life? How can I develop an interest in learning them? Tanu Shyam Majumder's answer: Derivative is nothing but calculation of rate of change of any instantaneous parameter. Suppose if we calculate velocity,it will be rate of change of displacement. Similarly if we calculate acceleration ,it will be rate of change of velocity. Derivation is a concept....