This book includes three main chapters: 1. Functions & Their Derivatives. 2. Minimum, Maximum and Inflection points. 3. Partial Derivative. In addition to many examples and exercises for the purpose of acquiring the student's ability to think correctly in solving mathematical questions.

A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.

The integral transformations is a complicated function from a function space into a simple function in transformed space. Where the function being characterized easily and manipulated through integration in transformed function space. The two parametric form of SEE transformation and its basic characteristics have been demonstrated in this study. The transformed function of a few fundamental functions along with its time derivative rule is shown. It has been demonstrated how two parametric SEE transformations can be used to solve linear differential equations. This research provides a solution to population growth rate equation. One can contrast these outcomes with different Laplace type transformations

The main process, for the elimination of cholesterol from the human body, involves the alteration of cholesterol into bile acid (BA), by the liver. The farnesoid X receptor (FXR), a member of the nuclear receptor superfamily, is essential for the regulation of BA, glucose, and lipid metabolism. It is largely found in the liver, intestines, kidney, and adrenal glands, and to a smaller degree in the heart and adipose tissue. The binding locations, of the FXR, are in close proximity to formerly undisclosed target genes, with distinctive activities associated with transcriptional regulators, autophagy, apoptosis, hypoxia, inflammation, RNA processing, and a number of cellular signaling pathways. The preservation of BA homeostasis, by the FXR, e

The aim of present investigation was Litilizing cow, sheep and chicken bones that included both hollow and flat to produce fat. The extraction rat was increased propotionally with rising temperature and extraction time for both cow and sheep bones. The lowest extraction rat form hollow and flat bones for cow and sheep was 12.66, 6.55, 6.93 and 7% respectively at 60°C for 3 hours. The highest extraction rat for hollow cow bones was 21.90% at 90°C for 5 houers, values for flat cow bones, hollow and flat sheep bones was 15.04, 16.4 and 12.8% respectively at 100°C for 5 hours. While, hollow and flat chicken bones resulted lowest extraction rate, thus thermal treatment was conducted only at 90 °c and showed propotional increase with incre

Many strains of lactic bacteria produce antimicrobial peptides of bacteriocins that are antibiotics used against pathogenic strains. The present work aimed to use a banana peels medium in the fermentation process to replace the commercial MRS medium for decreasing the cost of bacteriocins LAB production. Based on the result, banana peel was a cost-effective and viable alternative carbon source for the production and development of bacteriocin-producing Lactobacilli. The growth of lactobacilli in commercial MRS medium and Banana Peel medium showed no differences, therefore banana peel waste can be used to produce Lactobacilli bacteriocins. Lactobacillus strains grew exceptionally well at 37 C and pH 6.0.

  In this paper, we introduce and discuss an algorithm for the numerical solution of two- dimensional fractional dispersion equation.  The algorithm for the numerical solution of this equation is based on explicit finite difference approximation. Consistency, conditional stability, and convergence of this numerical method are described. Finally, numerical example is presented to show the dispersion behavior according to the order of the fractional derivative and we demonstrate that our explicit finite difference approximation is a computationally efficient method for solving two-dimensional fractional dispersion equation

Residential complexes have witnessed a great demand in most countries worldwide, as they are one of the main infrastructure elements, in addition to achieving a developed urban landscape. However, complex residential projects in developing countries face various factors that could be improved in their implementation, especially in Iraq. Sixty-two experts in residential complex projects were interviewed and surveyed to verify these projects' failure factors,. Fifty-one factors were the main failure factors, divided into four main components (leadership, management system, external forces, and project resources). The Relatively Important Index (RII) is used to determine the relative importance factors and obtain the top tw

The aim of this article is to solve the Volterra-Fredholm integro-differential equations of fractional order numerically by using the shifted Jacobi polynomial collocation method. The Jacobi polynomial and collocation method properties are presented. This technique is used to convert the problem into the solution of linear algebraic equations. The fractional derivatives are considered in the Caputo sense. Numerical examples are given to show the accuracy and reliability of the proposed technique.