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Course Details

Course Department: Department of Mathematics and Statistics
Course Code: MAS 025
Course Title: Engineering Mathematics I
Number of ECTS: 5
Level of Course: 1st Cycle (Bachelor's Degree) 
Year of Study (if applicable):
Semester/Trimester when the Course Unit is Delivered: Fall Semester 
Spring Semester
Name of Lecturer(s): Christos Gregoriades
Charalambos Evripidou
 
Lectures/Week: 2 (1.5 hours per lecture) 
Laboratories/week: 1 (1 hours per lecture) 
Tutorials/Week: -- 
Course Purpose and Objectives: Introduction to the basic concepts of single variable Calculus  
Learning Outcomes: Understand the notions of limits, continuity and differentiability of functions. Be able to calculate derivatives and use them in applications. Be able to calculate definite and indefinite integrals using various techniques as well as use integrals in applications (e.g. volume, arc-length).

Study series and power series of functions and be able to recognize geometric, telescopic and harmonic series. Decide their convergence using appropriate tests. Calculate a Taylor series of a function.
 
Prerequisites: Not Applicable 
Co-requisites: Not Applicable 
Course Content:

The real number system. Complex numbers (definition, elementary operations). Sequences of real numbers and limits. Real functions of one variable, limits, continuity. Hyperbolic, trigonometric functions. Derivatives of functions of one variable, tangent to a curve. Applications of derivatives. Mean value theorem, monotonicity, extrema, asymptotes. L’Hôpital’s rule. Riemannian integral. Fundamental Theorem of Calculus. Indefinite integrals. Integration techniques (substitution, integration by parts, partial fractions, trigonometric substitution, etc.). Applications of integrals, calculation of area, volume and length of a curve. Real number series. Convergence criteria. Power series. Series and Taylor’s theorem.

 
Teaching Methodology: Lectures and tutorials 
Bibliography:
  1. J. Stewart, Single variable calculus early transcendentals, 5th edition, 2003.
  2. H. Anton, I. Bivens, S. Davis, CALCULUS (7th Edition), John Wiley & Sons, 2003.
  3. R. A. Adams, Calculus a complete course, 1991.
 
Assessment: One midterm (40%) and one final exam (60%) 
Language of Instruction: Greek
Delivery Mode: Face-To-Face 
Work Placement(s): Not Applicable