Mymathware Shafii's math academy

The question says evaluate the polynomial $\frac{x^2}{ax+b}$ using long division. Therefore, $f(x)=x^2=(ax+b)(\frac{x}{a}-\frac{b}{a^2})+\frac{b^2}{a^2}$.

Lucas number: another beautiful patterns of sequence Formula for obtaining the Lucas numbers The Lucas numbers are numbers that form Fibonacci integer sequence, each Luc…

The harmonic functions and construction of analytic functions.  In this video series Dr. Kamran Khan takes us through harmonic functions and construction of analytic fun…

How to curry and uncurry a function $\mathbb{R}\rightarrow\mathbb{R}^N$.  The functions $A\rightarrow{B}^C$ corresponds to functions of the form $A\times{C}\rightarrow{B…

How do you proof $\sqrt{\frac{a}{b}}=\frac{\sqrt{a}}{\sqrt{b}}$? It is not always true. To see the clear picture, we solve some clear examples. Remember, $\sqrt{\frac{a}…

Find $x$ if $\sec^2{x}+\tan^2{x}=3$ From our trigonometric identities $\sec^2{x}=\frac{1}{\cos^2{x}}$ $\tan^2{x}=\frac{\sin^2{x}}{\cos^2{x}}$ Now, $\frac{1}{\cos^2{x}}+\…

Verify that $(n!+1,(n+1)!+1)=1$ Let $(n!+1,(n+1)!+1)=d$ Then there exists $(h,k)=1$ such that $n!+1=dh$.....................(i) $n!=dh-1$ and $(n+1)!+1=dk$..............…

Polar form of Cauchy-Riemann equations In this lecture series, Dr. Kamran Khan takes us through polar forms of Cauchy-Riemann equation, how they are derived and example…

Example of a function that satisfies the Cauchy-Riemann equation. In this lecture Dr. Kamran Khan takes his time to solve a problem that satisfies the Cauchy-Riemann equ…

Analytic functions and the Cauchy-Riemann equation - Lecture II In this lesson Professor Kamran Khan takes us through the Cauchy Riemann equation which is an equation th…

Introduction to complex analysis by Dr. Kamran Khan. Kamran Khan is an assistant professor at the department of mathematics, Aligarh Muslim University, Aligarh India. Ka…

Homomorphism of Groups: properties and examples. In abstract mathematics (algebra), homomorphism can be defined as a map or relation between two algebraic structures of…

The finite and infinite groups, the Lagrange theorem, its proof and a corollary. Today i will be discussing about the finite and infinite groups, and just like the set t…