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Course Details
| Course Department: | Department of Mathematics and Statistics |
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| 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): | 1 |
| 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: |
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| Assessment: | One midterm (40%) and one final exam (60%) |
| Language of Instruction: | Greek |
| Delivery Mode: | Face-To-Face |
| Work Placement(s): | Not Applicable |