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Lecture series by Dr Kamran Khan on Complex Integration Kamran Khan is an assistant professor at the department of mathematics, Aligarh Muslim Universi…

Solve the equation $2\cosh{2x}+10\sinh{2x}=5$ ................. 🆔 This is a hyperbolic trigonometric function equation, in order to solve the given equation, we must re…

Find the integer solution $x^2+3x+9=9y^2$.............(1) This is a beautiful quadratic Diophantine's equation that requires an integer solution. So how …

Find the value of $x$ $\frac{x^{\sqrt{x}}} {\sqrt{x}}=\frac{{\sqrt{x}}^x}{\sqrt{x}}$ Since both sides of the equation have a common denominator, multiply through by $\sq…

Find the integer solution for $3^x+27^y+81^z=10935$ This is a rather thickish question so we have to be very careful in our simplifications. The left hand side of the eq…

olve the logarithmic equations $\log_3(x+1)=\log_4(x+8)$ The bases of this equation is different so Let $\log_3(x+1)=y$...............................(i) And Let $\log_4…

Solve the indicial equation $4^\frac{1}{x}-6^\frac{1}{x}=9^\frac{1}{x}$ To solve the equation, simply divide through by any of the term since the indices are all given i…

Solving quadratic equations using the Poh-Shen Log method. The Poh-Shen Loh method is another method for solving quadratic equations, the method was pioneered by Prof. P…

An object is thrown vertically upwards with an initial velocity, $u$ of $20m/s$. The motion of the object follows the differential equation $\frac{ds}{dt}=u-gt$, where $…

Below is a beautiful proposition on matrix eigenvalues. It says find the minimal eigenvalue of the matrix $A^{2021}$. We find the eigenvalue using the determinant for $|…

The question below was obtained from one of the past questions for the Skoltech institute entrance examination for admission into computational science masters program. …

Prove of the Cassini-Samson Identity The Cassini-Samson Identity is an identity that involves the Fibonnaci numbers, it states that $F_{n-1}F_{n+1}-F_{n}^2=(-1)^n$ for $…

Determine the value of the following series $\sum^{\infty}_{n=1}(\frac{4}{n^2+4n+3}-9^{-n+2}4^{n+1})$ Solution To determine their value, we must check if the series is a…