Subject Area  Applications and Foundations of Computer Science 

Semester  Semester 2 – Spring 
Type  Required 
ECTS  6 
Recommended Courses 

Course Site  http://eclass.uth.gr 
Course Instructors 
Ioannis Hatzaras, Αdjunct Professor 
Vectors in the plane and polar coordinates. Line and plane in 3dimensions. Plane curves. Functions of two or more variables. Vector functions. The directional derivative and the gradient. Partial derivative. Chain’s rule. Tangent planes to surface. Extrema of a function of two variables. Constrained maxima and minima. Lagrange multipliers. Exact differentials. Divergence and rotation Double integral and its applications. Green’s Theorem. Double integrals in polar coordinates. Surface area. Triple integral and its applications. Stokes theorem.. Complex numbers. Operations. Trigonometric form of a comlex. Roots of a complex. Functions of a real or complex variable. Limit, continuity and derivative of a complex function. Analytic function. Cauchy Riemann equations. Harmonic functions. Smooth lines. Line Integrals. Cauchy Theorem. Sequences and series of complexes. Criteria of convergence. Power series. Taylor’s and Laurent’s series.
The course aims to teach beyond rules and theorems, the mathematical viewpoint and thinking , in order to develop combinatorial ability to solve problems.
Upon successful completion of this course, the student will be able to:
 know, calculate the equation of a line in space, the equation of a plane recognize basic forms of surfaces.
 Calculate partial derivative, calculate extrema of a function of two variables and constrained extrema .
 Calculate a double integral and to know its usage in applications (volume of a solid, surface of a plane area, center of mass, moment of inertia)
 Calculate an integral on a surface or any curve and to know their usages in finding an area of asurface, the work on a curve and also to use the Green and Stokes Theorems.
 To find the trigonometrical form a complex number and to calculate the roots of a complex number and also the logarithm of a complex number.
 Differentiate and to find an integral of a complex fuanction (Cauchy theorem)
 Know the Laurent series and the integral residues.