Papers by Mohamed Ismail Mohamed Hessein
Journal of Biological Chemistry, Dec 1, 2014
Authors are urged to introduce these corrections into any reprints they distribute. Secondary (ab... more Authors are urged to introduce these corrections into any reprints they distribute. Secondary (abstract) services are urged to carry notice of these corrections as prominently as they carried the original abstracts.
Journal of Mathematical Analysis and Applications, Feb 1, 1993
These points make up the line of intersection of the cylinder r = 5 (circular cylinder of radius ... more These points make up the line of intersection of the cylinder r = 5 (circular cylinder of radius 5 about the z-axis) and the half-plane = /3, r > 0 (half-plane containing the z-axis and making an angle of /3 radians with the positive x-axis). Thus we have the line that passes through the point (5, /3, 0) parallel to the Z-axis. C. Spherical Coordinates: The spherical coordinates of a point p are (, , ) where (rho) is the distance to the origin, (phi) is the angle between the positive z-axis and a line joining p to the origin 0 , and the angle is the second polar coordinate of the projection p' of p onto (Figure 9
These points make up the line of intersection of the cylinder r = 5 (circular cylinder of radius ... more These points make up the line of intersection of the cylinder r = 5 (circular cylinder of radius 5 about the z-axis) and the half-plane = /3, r > 0 (half-plane containing the z-axis and making an angle of /3 radians with the positive x-axis). Thus we have the line that passes through the point (5, /3, 0) parallel to the Z-axis. C. Spherical Coordinates: The spherical coordinates of a point p are (, , ) where (rho) is the distance to the origin, (phi) is the angle between the positive z-axis and a line joining p to the origin 0 , and the angle is the second polar coordinate of the projection p' of p onto (Figure 9
This Book consists of six chapters. Chapter 1 contains the fundamental
concepts of vectors in thr... more This Book consists of six chapters. Chapter 1 contains the fundamental
concepts of vectors in three dimensions. Chapter 2, contains the calculus of vector
functions. In chapter 3 we will discuss partial differentiation. Chapter 4 deals with
Gradients. Chapter 5 presents multiple integrals (Double, triple, line, and surface
integrals). In chapter 6, we will discuss vector calculus (Gauss divergence theorem -
stoke,s theorem)
The contents are divided into six chapters. Chapter 1 deals with Calculus
Of Finite Differences n... more The contents are divided into six chapters. Chapter 1 deals with Calculus
Of Finite Differences numerical differentiation and Chapter 2 devoted to Numerical
Integration. Chapter 3, deals with the Numerical Solution of Ordinary Differential
Equations of First Order. Chapter 4, is devoted to the Curve Fitting. Chapter 5 deals with
Solution Of Nonlinear Equations Chapter 6 deals with the System of Linear Equations This book presents brief introductions to some selected topics in Numerical analysis. The emphasis is on the computational aspects of the subject keeping the abstractions down to a minimum.
Noor Publishing eBooks, Apr 25, 2017
Geometry, at its start, was largely arithmetical in nature. It dealt with lengths from the survey... more Geometry, at its start, was largely arithmetical in nature. It dealt with lengths from the surveyor's point of view, according to which every length is expressible as an exact multiple of some one length selected as the unit, or of certain subdivisions of this selected length such that it contains one subdivision as exact integral number of times. The Greeks, however, soon saw that there existed lengths which could not be expressed as exact integral or fractiona1 multiples of the unit of 1ength. Pythagorus, for example, showed that if the side of a square was one unit of length, then no subdivision of that unit could be found which would enable the diagonal to be expressed in terms of the side by means of a finite ratio. Algebra of a sort was, however, known to the ancient Egyptians, and Ahmes, a scribe who lived more than 1000 years before Christ, used a method similar to that of the solution of simple equations. The Arabs rule is found generally in algebraic works, particularly, the first systematic treatise on Algebra is the important book of Mohamed Ben Musa Alkorismi about 830 AD. Once the geometrical magnitudes represented by algebraic numbers, the road lay open to the applications of algebra to geometry. The chief feature of analytic geometry, which distinguishes it from the geometry, is its extensive use of algebraic methods in the solution of geometric problems. Just as the use of symbols in algebra makes possible the ready solution of many problems, which would be difficult if not impossible by the processes of arithmetic, so the use of algebraic reason simplifies
The present book is based on lectures given by the author to students of various colleges studyin... more The present book is based on lectures given by the author to students of various colleges studying mathematics. In designing this course, the author tried to select the most important mathematical facts and present them so that the reader could acquire the necessary mathematical conception and apply mathematics to other branches. Therefore, in most cases we did not give rigorous formal proofs of the theorem. The rigorousness of a proof often fails to be fruitful and therefore it is usually ignored in practical applications. 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. It contains material which you will find of great use, not only in the technical courses you have yet to take, but also in your profession after graduation, as long as you deal with the analytical aspects of your field. In writing, the book the actual mathematical background of working engineers is taken for granted. The author has injected in this book his experience and expertise of teaching.
LAP LAMBERT Academic Publishing eBooks, Jan 30, 2018
The contents are divided into ten chapters. It deals with Mathematical Induction, Partial Fractio... more 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".
The present book is based on lectures given by the author to students of various colleges studyin... more The present book is based on lectures given by the author to students of various colleges studying mathematics. In designing this course the author tried to select the most important mathematical facts and present them so that the reader could acquire the necessary mathematical conception and apply mathematics to other branches. Therefore in most cases we did not give rigorous formal proofs of the theorems. The rigorousness of a proof often fails to be fruitful and therefore it is usually ignored in practical applications. 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. It contains material which you will find of great use, not only in the technica1 courses you have yet to take, but also in your profession after graduation, as long as you deal with the analytical aspects of your field. This book consists of eight chapters. Vector Analysis. Multiple Integrals. We will discuss Functions of a Complex Variable. presents Complex Integration. Calculus Of Finite Differences. Numerical Integration. Curve Fitting.Solution of Nonlinear equations
Noor Publishing, Apr 25, 2017
Geometry, at its start, was largely arithmetical in nature. It
dealt with lengths from the surve... more Geometry, at its start, was largely arithmetical in nature. It
dealt with lengths from the surveyor's point of view, according to
which every length is expressible as an exact multiple of some one
length selected as the unit, or of certain subdivisions of this
selected length such that it contains one subdivision as exact
integral number of times. The Greeks, however, soon saw that
there existed lengths which could not be expressed as exact
integral or fractiona1 multiples of the unit of 1ength. Pythagorus,
for example, showed that if the side of a square was one unit of
length, then no subdivision of that unit could be found which
would enable the diagonal to be expressed in terms of the side by
means of a finite ratio.
Algebra of a sort was, however, known to the ancient
Egyptians, and Ahmes, a scribe who lived more than 1000 years
before Christ, used a method similar to that of the solution of
simple equations. The Arabs rule is found generally in algebraic
works, particularly, the first systematic treatise on Algebra is the
important book of Mohamed Ben Musa Alkorismi about 830 AD.
Once the geometrical magnitudes represented by algebraic
numbers, the road lay open to the applications of algebra to
geometry. The chief feature of analytic geometry, which
distinguishes it from the geometry, is its extensive use of algebraic
methods in the solution of geometric problems. Just as the use of
symbols in algebra makes possible the ready solution of many
problems, which would be difficult if not impossible by the
processes of arithmetic, so the use of algebraic reason simplifies
A non-empty subset W of a vector space V is a subspace of V if and only if it is closed under add... more A non-empty subset W of a vector space V is a subspace of V if and only if it is closed under addition and scalar multiplication; that is, x 1 , x 2 W implies x 1 + x 2 W, and c F, implies c x 1 W. Proof: Closure under scalar multiplication does the trick for us. For any x W, we have 0 = 0 w W and −x = (−1)x W, by the properties proved in the last section.É Theorem 1.2: Second subspace test: A non-empty subset W of the vector space V over F is a subspace if and only if, for any a, b F and x, y W, we have a x + b y W. Proof: If W is a subspace, and a, b, x, y are given, then the closure laws show that a x + b y W. Conversely, suppose that this condition holds. Then, choosing b = 0, we see that a x W for all a F and x W; that is, W is closed under scalar multiplication. Similarly, choosing a = b = 1 shows that it is closed under additionÉ.
The present book is an English translation from my book with the same title in Arabic language wh... more The present book is an English translation from my book with the same title in Arabic language which are based on my lectures given to students of various colleges studying mathematics. In designing this course, the author tried to select the most important mathematical facts and present them so that the reader could acquire the necessary mathematical conception and apply mathematics to other branches. Therefore, in most cases we did not give rigorous formal proofs of the theorem. The rigorousness of a proof often fails to be fruitful and therefore it is usually ignored in practical applications. 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. It contains material which you will find of great use, not only in the technical courses you have yet to take, but also in your profession after graduation, as long as you deal with the analytical aspects of your field. In designing this book the author tried to select the most important mathematical facts and present them so that the reader could acquire the necessary mathematical conception and apply mathematics to other branches. This book consists of seven chapters. Chapter 1, "Sets-Relations-Functions" in abstract algebra, Chapter 2 contains the "Groups" as one of the main subjects. In Chapter 3 , we will discuss "Permutation Group" as a practical part and very useful in Linear Algebra. Chapter 4 presents "Isomorphism" which a fundamental part, and has many applications. Chapter 5, contains "The Natural Numbers" and how to extend the natural numbers up to real filed. Chapter 6 contains " Rings-Fields" as the second main subjects to abstract algebra. Chapter 7, which deal with "Continuation on Groups".
Plane passing through a given point and parallel to two given straight lines …………………. Plane passi... more Plane passing through a given point and parallel to two given straight lines …………………. Plane passing through a given straight line and parallel to another given straight line ……………... Plane passing through a given straight line and perpendicular to a given plane ……………………….. Skew lines ……………………………………………………. EXERCISES 8 ……………………………………………… 9 THE SPHERE ………………………………………………. § 9.1: General equation of the sphere ………………………. § 9.2: The sphere through four points ……………………… § 9.3: Extremities of the diameter are given ……………... Analytic Geometry Contents 9 § 9.4: Vector equations to the sphere ……………………….. § 9.5: Intersection of a sphere and a line ………………….. Length of the tangent …………………………………….. Diametral plane …………………………………………….. § 9.6: Intersection of a sphere and a plane ……………….. § 9.7: Equation of a circle ……………………………………….. § 9.8: Sphere through a given circle ………………………… § 9.9: The intersection of two spheres ……………………... Radical plane ………………………………………………... § 9.10 The equation of the tangent plane …………………... Condition of tangency …………………………………… § 9.11 Angle of intersection of two spheres ……………… Condition of orthogonality of two spheres ……… EXERCISES 9 ……………………………………………… 10 Surfaces ……………………………………………………….. § 10.1: The locus in solid geometry …………………………... § 10.2: Cylindrical surfaces ……………………………………….
2. The vectors u = (1, 2, 3), v = (4, 5, 6), and w = (7, 8, 9), in R 3 are linearly dependent, si... more 2. The vectors u = (1, 2, 3), v = (4, 5, 6), and w = (7, 8, 9), in R 3 are linearly dependent, since u-2v+ w = 0. How did we come up with this? Start with the equation in the definition of linear dependence au +bv +c w = (0, 0, 0), and solve this system for possible values of a, b , c. 2. We can write this system in matrix form as
These points make up the line of intersection of the cylinder r = 5 (circular cylinder of radius ... more These points make up the line of intersection of the cylinder r = 5 (circular cylinder of radius 5 about the z-axis) and the half-plane = /3, r > 0 (half-plane containing the z-axis and making an angle of /3 radians with the positive x-axis). Thus we have the line that passes through the point (5, /3, 0) parallel to the Z-axis. C. Spherical Coordinates: The spherical coordinates of a point p are (, , ) where (rho) is the distance to the origin, (phi) is the angle between the positive z-axis and a line joining p to the origin 0 , and the angle is the second polar coordinate of the projection p' of p onto (Figure 9
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Papers by Mohamed Ismail Mohamed Hessein
concepts of vectors in three dimensions. Chapter 2, contains the calculus of vector
functions. In chapter 3 we will discuss partial differentiation. Chapter 4 deals with
Gradients. Chapter 5 presents multiple integrals (Double, triple, line, and surface
integrals). In chapter 6, we will discuss vector calculus (Gauss divergence theorem -
stoke,s theorem)
Of Finite Differences numerical differentiation and Chapter 2 devoted to Numerical
Integration. Chapter 3, deals with the Numerical Solution of Ordinary Differential
Equations of First Order. Chapter 4, is devoted to the Curve Fitting. Chapter 5 deals with
Solution Of Nonlinear Equations Chapter 6 deals with the System of Linear Equations This book presents brief introductions to some selected topics in Numerical analysis. The emphasis is on the computational aspects of the subject keeping the abstractions down to a minimum.
dealt with lengths from the surveyor's point of view, according to
which every length is expressible as an exact multiple of some one
length selected as the unit, or of certain subdivisions of this
selected length such that it contains one subdivision as exact
integral number of times. The Greeks, however, soon saw that
there existed lengths which could not be expressed as exact
integral or fractiona1 multiples of the unit of 1ength. Pythagorus,
for example, showed that if the side of a square was one unit of
length, then no subdivision of that unit could be found which
would enable the diagonal to be expressed in terms of the side by
means of a finite ratio.
Algebra of a sort was, however, known to the ancient
Egyptians, and Ahmes, a scribe who lived more than 1000 years
before Christ, used a method similar to that of the solution of
simple equations. The Arabs rule is found generally in algebraic
works, particularly, the first systematic treatise on Algebra is the
important book of Mohamed Ben Musa Alkorismi about 830 AD.
Once the geometrical magnitudes represented by algebraic
numbers, the road lay open to the applications of algebra to
geometry. The chief feature of analytic geometry, which
distinguishes it from the geometry, is its extensive use of algebraic
methods in the solution of geometric problems. Just as the use of
symbols in algebra makes possible the ready solution of many
problems, which would be difficult if not impossible by the
processes of arithmetic, so the use of algebraic reason simplifies
concepts of vectors in three dimensions. Chapter 2, contains the calculus of vector
functions. In chapter 3 we will discuss partial differentiation. Chapter 4 deals with
Gradients. Chapter 5 presents multiple integrals (Double, triple, line, and surface
integrals). In chapter 6, we will discuss vector calculus (Gauss divergence theorem -
stoke,s theorem)
Of Finite Differences numerical differentiation and Chapter 2 devoted to Numerical
Integration. Chapter 3, deals with the Numerical Solution of Ordinary Differential
Equations of First Order. Chapter 4, is devoted to the Curve Fitting. Chapter 5 deals with
Solution Of Nonlinear Equations Chapter 6 deals with the System of Linear Equations This book presents brief introductions to some selected topics in Numerical analysis. The emphasis is on the computational aspects of the subject keeping the abstractions down to a minimum.
dealt with lengths from the surveyor's point of view, according to
which every length is expressible as an exact multiple of some one
length selected as the unit, or of certain subdivisions of this
selected length such that it contains one subdivision as exact
integral number of times. The Greeks, however, soon saw that
there existed lengths which could not be expressed as exact
integral or fractiona1 multiples of the unit of 1ength. Pythagorus,
for example, showed that if the side of a square was one unit of
length, then no subdivision of that unit could be found which
would enable the diagonal to be expressed in terms of the side by
means of a finite ratio.
Algebra of a sort was, however, known to the ancient
Egyptians, and Ahmes, a scribe who lived more than 1000 years
before Christ, used a method similar to that of the solution of
simple equations. The Arabs rule is found generally in algebraic
works, particularly, the first systematic treatise on Algebra is the
important book of Mohamed Ben Musa Alkorismi about 830 AD.
Once the geometrical magnitudes represented by algebraic
numbers, the road lay open to the applications of algebra to
geometry. The chief feature of analytic geometry, which
distinguishes it from the geometry, is its extensive use of algebraic
methods in the solution of geometric problems. Just as the use of
symbols in algebra makes possible the ready solution of many
problems, which would be difficult if not impossible by the
processes of arithmetic, so the use of algebraic reason simplifies