#### Course Description

Advance Mathematics is a course designed only for electrical engineering students. It is a 3 credit single semester course with three contact hours a week. This course introduces the students to vector calculus concepts, some special functions, complex numbers and complex functions. It focuses mainly on line integrals, surface integrals and on some applications of these integrals, Gamma functions, Beta functions and Bessel functions. The prerequisite of this course is Calculus III.

• Introduction and review of the vector calculus concepts div, curl, grad, Directional Derivative, Laplacian, and Vector Calculus Identities (e.g. div[curl V] = 0, div[grad V] = Laplacian …etc.).

• Line integrals: Parameterized Curves. Line Integrals of Vector and Scalar Fields. Applications. Green’s Theorem. Independence of Path.

• Surface integrals: Parameterized Surfaces, Surface Integrals, Oriented Surfaces. Applications.

• The Divergence Theorem and Stoke’s Theorem.

• Some special functions: Gamma Function. Beta Function. Bessel Function. Error Function. Applications.

• Complex variables and functions: Algebra of Complex Numbers. Modulus and Argument. Trigonometric Form. Exponential Form.

Roots. De Moivre’s Theorem. Functions of Complex Variables, Elementary Functions.

#### Course Objectives

1. The course aims at:

2. Developing the notion of vectors and their properties in the three-dimensional space and the plane. Acquainting students with the concepts of vector calculus and vector fields.

3. Acquainting students with the necessary theories and methods in both line integrals and surface integrals.

4. Equipping students with a number of methods for computing line integrals and surface integrals, concentrating on those which are of practical importance.

5. Introducing Gamma, Beta, Error functions, and Bessel functions, and providing skills to use them for evaluation of some integrals.

6. Introducing Bessel functions, and providing skills to simplify the work with such functions along with using them to solve some differential equations.

7. Introducing complex numbers, variables, and their properties, and providing skills to manipulate them.

#### Learning Outcomes

By the end of the course, the students should be able to:

1. Identify different types of line integrals and surface integrals.

2. Learn the methods of computing line integrals and surface integrals.

3. Recognize Green’s Theorem and its importance.

4. Identify the importance and relations between line integrals and surface integrals.

5. Demonstrate the ability to use the Divergence Theorem and the Stokes’ Theorem in evaluating many surface integrals.

6. Introduce complex numbers and their properties.

7. Visualize different forms of complex numbers.

8. Recognize complex functions and certain elementary functions.

9. Evaluate several integrals by using Beta and Gamma functions.

10.Identify Bessel functions, their importance and their properties.