Mathematics III

COURSE OBJECTIVES
The purpose of this course is to round out the student's preparation for more sophisticated applications with an introduction to linear algebra, a continuation of the study of ordinary differential equations and an introduction to vector calculus.

1. Matrices and determinants (8 hours)
1.1 Matrix and determinants.
1.2 Vector spaces
1.3 Linear transformations
1.4 System of linear equations, Gauss elimination.
1.5 Rank, matrix inversion.
1.6 Eigen values, eigen vectors.

2 Fourier series (4 hours)
2.1 Fourier series,
2.2 Periodic functions
2.3 Odd and even functions.
2.4 Fourier series for arbitrary range.
2.5 Half range Fourier series.

3. Laplace transforms (8 hours)
3.1 Laplace transforms.
3.2 Standard L- transforms.
3.3 Inverse laplace transforms.
3.4 Applications.

4 Vector Calculus (7 hours)
4.1 Vector Calculus.
4.2 Differentiation and Integration of Vectors.
4.3 Divergence.
4.4 Gradient curl.

5 Line, surface and volume integrals (18 hours)
5.1 Line integrals.
5.2 Surface and volume integrals.
5.3 Integral transformation theorems- Stoke's, Gauss and Green's theorems.


Textbook
1.0 E. Kreszig, "Advanced Engineering Mathematics", Fifth Edition, Wiley, New York.
2.0 M. M. Guterman and Z.N. Nitecki, "Differential Equations, a First Course", 2nd Edition, Saunders, New York