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Hydrodynamics, Electricity and Magnetism , Special Theory of Relativity , Electrodynamics , Analytical Dynamics , Theory of Elasticity , Quantum Mechanics , Dynamics of Particles and Rigid Bodies , Statistical Mechanics , Applied Mathematics(I and II) ,Vector Calculus ,Calculus and Analytical Geometry, Linear Algebra, Differential Equations, Differential Geometry, Complex Analysis , Special Functions, Boundary Value Problems, Introduction to Statistics, Business Math.

Boundary Value Problems-Advanced Hydrodynamics

- MATH 310 - Quantum Mechanics
- MATH 314 - Potential Theory
- MATH 244 - Ordinary Differential Equations
- MATH 342 - Vector Calculus
- MATH 111 - Int. to Calculus & Analytical Geometry II

**Quantum Mechanics - MATH 310**

**Class Meeting:** Monday 08:00 - 10:00

**Catalog Description:**

Failure of classical mechanics in dealing with some physical problems, the origin of the old quantum theory, Bohr’s model of the hydrogen atom, Wilson, Sommerfield quantization method, special quantization, Stark effect for hydrogen, the decline of the old quantum theory, algebra of operators, commutation relation, eigenvalue problems, expectation values, Hermitian operator, elements of wave mechanics, Schrodinger’s wave equation, time derivative operators, some simple one-dimensional quantum mechanica.

**Course Objectives:**

The course aims to provide students with the specialist knowledge necessary or basic concepts in quantum mechanics and to understand its applications in real physical problems l problems.

**Course Outcomes:**

1- Knowledge and Understanding: Students are able to understand the nature and operations of mathematics. Demonstrate familiarity with theories and concepts used throughout the course, deal with different applications related to quantum mechanics and identify the steps required to carry out a piece of research on a topic within mathematics.

2- Intellectual and practical Skills: By the end of the course the student is expected to learn the fundamental aspects of quantum mechanics and implement it in a lot of application and use the considered techniques for solving new problems

3- Transferable Skills: Within the lectures the student is able to transfer ideas and experience and work effectively as a part of a group and independently.

Student Outcomes:

K2-Knowledge of the implementation of theories in problem solving.

I1-Ability to understand the different math concepts and be able to implement them in our everyday problems.

P3- Efficient use of the techniques, skills, and tools of modern mathematics

S1-Functioning in multi-disciplinary teams

Download course syllabus as PDF

**Potential Theory - MATH 314**

**Class Meeting:** Tuesday 10:00 - 12:00

**Catalog Description:**

Electrostatics: the electric field, boundary conditions, uniqueness of solution, equipotential surfaces, energy and stresses in the field, system of conductors, solution of potential problems using electrical images and harmonic functions, magnetostatics. The magnetic field, magnetic dipoles and magnetic shells, scalar and vector magnetic potentials, induced magnetism, boundary conditions, ,energy and stresses in magnetic fields, steady electric currents in continuous media, Ohm’s law, equation satisfied by the electric potential of a steady current, boundary Conditions, uniqueness of solutions.

**Course Objectives:**

The course aims to provide students with the specialist knowledge necessary for basic concepts in Electrostatics, magnetostatics and to understand its applications in real physical problems.

**Course Outcomes:**

1- Knowledge and Understanding: Students are able to demonstrate familiarity with theories and concepts used throughout the course, deal with different applications related to potential theory and identify the steps required to carry out a piece of research on a topic within mathematics.

2- Intellectual and practical Skills: By the end of the course the student is expected to learn the fundamental aspects of potential theory and implement it in a lot of applications and use the considered techniques for solving new problems

3- Transferable Skills: Within the lectures the student is able to transfer ideas and experience and work effectively as a part of a group and independently.

**Student Outcomes:**

K2-Knowledge of the implementation of theories in problem solving.

I1-Ability to understand the different math concepts and be able to implement them in our everyday problems.

P3- Efficient use of the techniques, skills, and tools of modern mathematics

S1-Functioning in multi-disciplinary teams

Download course syllabus as PDF

**Ordinary Differential Equations - MATH 244**

**Class Meeting:** Tuesday 0800 - 0930

Thursday 0800 - 0930

**Catalog Description:**

First order ordinary differential equations and applications, linear higher order differential equations, systems of linear differential equations, series solutions of differential equations, Laplace transforms.

**Course Objectives:**

This course aims to introduce the student into the field of Differential Equations, classify the types of Differential Equations and introduce to him different techniques of solutions. The focus in this course is on determining the analytical solution.

**Course Outcomes:**

1- Knowledge and Understanding: The student is able to classify differential equations and derives some methods to solve them.

2- Intellectual Skills: By the end of the course the student is expected to choose the suitable technique for the differential equation and find its solution.

3- Practical Skills: By the end of the course the student will be able to classify the types of differential equations, use available techniques for solving differential equations and model some processes mathematically into differential equations.

4- Transferable Skills: Within the lectures the student is able to transfer ideas and experience, work effectively both in a team and independently, solve problems analytically and use computational packages such as MATLAB for solving differential equations.

**Student Outcomes:**

K1-Knowledge of basic theorems and concepts in the different areas of mathematics.

K2-Knowledge of the implementation of theories in problem solving.

I1-Ability to understand the different math concepts and be able to implement them in our everyday problems.

I2-Ability to consider problems that could be solved by implementing concepts from different areas in mathematics

I3-Ability to identify, formulate, and solve problems

P2-Understanding of professional and ethical responsibilities

S2-Communicate ideas effectively in graphical, oral, and written media

S3-Recognize and respond to the need for lifelong and self learning for a successful career

Download course syllabus as PDF

**Vector Calculus - MATH 342**

**Class Meeting:** Wednesday 0800 - 0930

Monday 1200 - 1330

**Catalog Description:**

Vector fields, differentiation of vector functions, the derivation as a linear transform, gradient of scalar function, inverse and implicit function theorem, directional derivative, divergence, curl, differential forms, linear integrals, Stokes theorem and Green’s Theorem with applications, orthogonal curvilinear coordinate systems, cylindrical, spherical and elliptic coordinate systems.

**Course Objectives:**

The aim is to provide the student with basic topics in Vector Analysis, where the focus on the notion of the Gradient, the Curl, and the Divergence of vectors. Study important theorems in Physics and applied Mathematics such as Gauss divergence theorem and its applications, Stocks theorem, Green’s theorems, and Green theorem in the plane. The course is ended by studying the curvilinear coordinate systems.

Intended Learning Outcomes (ILO’s)

Knowledge and understanding:

K1-Identify basic theorems and concepts of vector calculus.

K2-Classify mathematical problems and discuss them with appropriate theorems and concepts in problem solving.

K3-Define vector derivatives and vector field integration.

Intellectual abilities:

I1-Formulate problems using tools of Stokes and Green theorems.

I2-Evaluate integrals using different methods and techniques.

I3-Apply techniques of vector derivatives and vector integration to physical and mathematical problems.

I4-Apply theorems and rules of calculus to physical and mathematical problems.

Professional and Practical competencies:

P1-Solve many physical problems using tools of vector calculus manually.

P2-Operate and practice with problems in mathematics and physics using available techniques of vectors.

P3-Solve problems using skills, and tools of modern mathematics.

**General and Transferable Skills:**

S1-Communicate ideas effectively in graphical, oral, and written media

S2-Functioning in multi-disciplinary teams.

S3-Deal with Scientific material in English

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**Download course syllabus as PDF

**Introduction to Calculus & Analytical Geometry - MATH 111**

**Class Meeting:** Wednesday 1200 - 1330

Thursday 1000 - 1130

**Course description
**

This course will cover extreme values of a function, the mean value theorem, Rolle’s theorem and intermediate value theorem, curve sketching, linearization and differentials, Riemann sums and definite integrals with application to areas between curves, volume by slicing, lengths of plane curves, analytic geometry in space, parametric equations, vectors in the plane and in space, vector functions and their derivatives, dot and cross products,

This course provides a continuation in calculus and analytic geometry for students with a weak background, and reinforces traditional calculus and analytic geometry approaches to give the student a better understanding of the mathematical concepts underlying them. Its goal is to prepare students to go on to more advanced mathematics. More precisely, it aims to teach the students the following topics:

1. Continuous and differentiable functions.

2. Application to derivatives.

3. Riemann sums and definite integrals.

4. Analytic Geometry.

5. Vectors.

At the end of this course, the students should be able to:

1.Describe some concepts, definitions and theorems in calculus and analytic geometry.

2.Implement the theories in problem solving.

3.Identify, formulate and solve problems.

4.Consider problems that could be solved by applying appropriate theories, principles and concepts relevant to functions, continuity, derivatives, analytic geometry and vectors.

Magnetohydrodynamics, Non- Newtonian Power –Law Fluids, Wave Motion, Micropolar Fluids, Viscous Fluids, Boundary Layer Flow.

1. K. A. Helmy, H. F. Idriss and S. E. Kassem, “An integral Method for the solution of the boundary layer equation for power-law fluid”, Indian J. Pure appl. Math., 32(6), 859- 870,June 2001.

2. K. A. Helmy, H. F. Idriss and S. E. Kassem, “MHD free convection flow of a micropolar fluid past a vertical porous plate”, Canadian J phys. Vol. 80(2002), 1661-1673.

3. A.A. Mohamadein and H. Idriss, “Analytical and Numerical Solution for Chemical Reaction and Radiation in an Optically Thin Gray Gas Flowing Past a Verical Infinite Plate in the Presence of Induced Magnetic Field ” , International Journal of Applied Mathematics and PhysicsVol.2, No.1 (2010), 57-62 .

2. K. A. Helmy, H. F. Idriss and S. E. Kassem, “MHD free convection flow of a micropolar fluid past a vertical porous plate”, Canadian J phys. Vol. 80(2002), 1661-1673.

3. A.A. Mohamadein and H. Idriss, “Analytical and Numerical Solution for Chemical Reaction and Radiation in an Optically Thin Gray Gas Flowing Past a Verical Infinite Plate in the Presence of Induced Magnetic Field ” , International Journal of Applied Mathematics and PhysicsVol.2, No.1 (2010), 57-62 .

-Participated in the Mathematics Workshop at Beirut Arab University, March 26, 2009.

- Participated in the organization of the One day workshop at Beirut Arab University,

April 26, 2012.

-Participated in the Workshop on Mathematical Analysis, Beirut Arab University, March15,2016.

- Participated in the organization of the One day workshop at Beirut Arab University,

April 26, 2012.

-Participated in the Workshop on Mathematical Analysis, Beirut Arab University, March15,2016.