PDF for mathematics from the official Punjab Board website. Access chapter-wise details for mathematics with the link to ...

This paper presents a rigorous mathematical analysis of the higher-order serial differentiator (HOSD), originally proposed by the authors for estimating time derivatives of time-varying signals.

The third formulation is for the risk-taker with price expectations modeled by an exponential distribution and a pricing function with a Levy-Khintchine formula that has sharp gains. For 2) decaying ...

Transformations of graphs of exponential and logarithmic functions. Transformations of exponential and logarithmic function graphs involve dilating (also known as stretching or compressing), ...

Exponential functions are commonly used to model phenomena such as population growth, the spread of coronavirus, radioactive decay and compound interest. Logarithmic functions, the inverse of ...

A PHASE relation familiar to students of applied mathematics exists between a simple harmonic oscillation and its derivative. Similar relations exist between exponential functions and their ...

4. understand polynomial, hyperbolic, exponential and logarithmic functions* 5. understand circular functions* 6. use differential calculus in the study of functions* 7. use integral calculus in the ...

Euler’s number is one of the most important constants in mathematics. It's a non-repeating number that never ends, beginning with 2.71828. In finance, e is used to calculate growth via compound ...

Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function. The formula for exponential growth is V = S x (1+R) T, where ...

Khalouta transform of derivatives of the functions Let f(u) be the function, then n th derivative of the function is ... Atangana A. Mathematical modelling and analysis of fractional epidemic models ...