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Course Details
| Course Department: | Department of Mathematics and Statistics |
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| Course Code: | MAS 001 |
| Course Title: | Mathematics I |
| Number of ECTS: | 6 |
| 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): | Dr Christos Raent-Onti, Dr Michael Aristidou |
| Lectures/Week: | 2 (1.5 hours per lecture) |
| Laboratories/week: | -- |
| Tutorials/Week: | 1 (1 hours per lecture) |
| Course Purpose and Objectives: | To understand calculus and to use basic methods to solve real problems. |
| Learning Outcomes: |
- Solve linear equations - Knowledge of simple concepts of Analytical Geometry - Knowledge of the concept of the function and the basic functions - Calculate basic limits and understanding the notion of continuity of a function - Understanding the notion of differentiation and to differentiate basic functions - Apply the knowledge of the notion of differentiation to real problems - Understanding the notion of the integral - Knowledge of the methods of integration |
| Prerequisites: | Not Applicable |
| Co-requisites: | Not Applicable |
| Course Content: |
Introduction Real numbers – Inequalities – Absolute value – Equation of a straight line, circle and parabola Functions Kinds of functions – Graph of a function – Inverse function – inverse trigonometric functions – Exponential and Logarithmic functions - Limit and Continuity Limit of a function – Continuity of a function - Intermediate-Value Theorem – Limits and Continuity trigonometric, Exponential and Logarithmic functions The Derivative The derivative function – techniques of differentiation – Implicit differentiation- differentiation of inverse function – parametric equations Applications of the Derivative Increasing and decreasing functions – Relative extrema – Absolute extrema - Graphing of a function – Newton’s method – Rolle’s theorem – Mean value theorem Integration The indefinite integral – the definite integral – the fundamental theorem of calculus – Average value of a function Principles of integral evaluation Integration by parts – integration by substitution – integration of rational functions by partial fractions |
| Teaching Methodology: | Two lectures and one tutorial to solve exercises/problems per week. |
| Bibliography: |
1. CALCULUS (7th Edition), by H. Anton, I. Bivens, S. Davis, John Willey & Sons, 2003 2. Thomas’ Calculus (10th Edition), by G. B. Thomas, R. L. Finney, M. D. Weir, F. R. Giordano, Pearson Addison Wesley, 2000 3. Calculus with Analytic Geometry, by H. C. Edwards, D. E. Penney, Prentice Hall, 1997 4. Calculus with analytic geometry, 4th ed., by R. Ellis, D. Gulick, Harcourt Brace Jovanovich, 1990 Calculus with analytic geometry, 2nd ed., by D. G. Zill, PWS-KENT Publishing Company, 1998
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| Assessment: | Mid-term exams (50%) and Final exam (50%) |
| Language of Instruction: | Greek |
| Delivery Mode: | Face-To-Face |
| Work Placement(s): | Not Applicable |