Subject Area  Applications and Foundations of Computer Science 

Semester  Semester 1 – Fall 
Type  Required 
Teaching Hours  4 
ECTS  6 
Course Site  https://courses.ece.uth.gr/ECE113/ 
Course Director 
Panagiota Tsompanopoulou, Associate Professor 
Course Instructor 

 Function. Composition of functions. Inverse function. Limit, continuity and theorems.
 The derivative and formulas for differentiation. The differential. Applications of the derivative: Rolle;s Theorem, the mean value Theorem, L’ Hopital rules, Increasing and decreasing functions, local maxima and minima. Asymptotes.
 Antiderivative. The definite integral. Techniques of integration. Applications of the definite integral. Improper integrals.
 Polar coordinates. Conic sections.
 Sequences. Criteria of convergence.
 Infinite series. Criteria of convergence. Power series. Functions defined by power series. Taylor’s Theorem.
This course is taught to freshman students, therefore it connects the high school math with all the necessary stuff that will be taught at an Engineering School and especially in an electrical and computer engineering department. 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 ableto thoroughly understand the concept of continuity of a function based on the mathematicale – definition and to decide on the continuation of a function.
 Have indepth knowledge of the concept of the existence of the limit of a function to real number or divergence to infinity or not.
 Ownthe meaning of the derivative (with the mathematical definition of the limit of the ratio change) and will be able to calculate the derivatives first or higher order of any continuous function.
 Be able to study a function and decide for properties like differentiability, monotonicity, and total/ local extrema , asymptotes lines.
 Be capable to study at curves in 2D and calculate their derivative with implicit differentiation.
 Own the meaning of indefinite and definite Riemann integral, and will be able to use numerous integration techniques for various function groups.
 Be able to solve (analytically) first and second degree ordinary differential equations using antiderivatives.
 Be capable to calculate the area of 2Dshapes and the volume/surface of 3D shapes using appropriate integrals.
 Own the concept of sequence, and the criteria for the convergence of a sequence.
 Own the concept of the series, the convergence criteria and when they are applicable, the Taylorand McLaurin series.
 Have strong knowledge of the polar coordinates for both 2D and 3D space and the properties of the functions called conic sections.