Bøger af Mohamed Ismail Mohamed Hessein

The contents are divided into ten chapters. It deals with Mathematical Induction, Partial Fractions, Finite Series, Binomial Theorems, Matrices and their applications, Determinants in a brief manner, eigenvalues and eigenvectors, settles the digitalization problem for symmetric matrices, theory of equations, (specially Horner¿s Method), Bi-quadratic equations, Cubic Equations (Cardan's method), Quartic Equations, Ferrari's Solution and Reciprocal Equations, Linear programming, fundamentals of sets, the fundamentals of logic. We will discuss "deductive logic" or deductive reasoning. We will show how sets and logic are so interrelated that the techniques of one can be used to solve problems in the other. Through these techniques, we will discuss and solve many classical word problems and puzzles. In chapter 10, we show that the Boolean algebra of sets and logic can also be applied to a third system, namely, the electrical system called "switching theory".

Numerical Analysis is very important subject in Mathematics, Physics, and Engineering. Every success in computer technology makes us in sure with success in Numerical Analysis. Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century also the life sciences and even the arts have adopted elements of scientific computations. Ordinary differential equations appear in celestial mechanics (planets, stars and galaxies); numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology. The contents are divided into six chapters. The Calculus Of Finite Differences numerical differentiation, Numerical Integration, Numerical Solution of Ordinary Differential Equations of First Order, Curve Fitting, Solution Of Nonlinear Equations and System of Linear Equations.

This book is Real analysis, consists of five chapters. Chapter 1 contains the fundamental concepts of Sets. Chapter 2 contains the fundamentals of Measurable Sets. In chapter 3 we will discuss Measurable functions. Chapter 4 presents The Lebesgue Integral. Chapter 5 contains the Fourier Series and Orthogonal Systems. In writing the book the author has injected his experience and expertise of teaching. In fact, the book closely follows the lectures given by the author to some classes at the Faculty of Science, Cairo University.

The title of this book is solved examples on Advanced Engineering Mathematics. It consists of several topics from Advanced Engineering Mathematics. In it, we collect a lot of examples with their solutions. Our goal in this book how to learn, not only to solve, in that sense in each problem, we discuss more than one method, but in solving, it is sufficient to use one of them. These topics are Linear Dependence and independence, second order differential equations, Fourier series, Fourier integrals, Laplace transforms, Special functions (gamma and Beta functions), Partial differential equations and solution of differential equations in series. The book can be of use to readers of various professions dealing with applications of mathematics in their current work. The subject matter is presented in a very systematic and logical manner.