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Course Details
| Course Department: | Department of Mathematics and Statistics |
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| Course Code: | MAS 018 |
| Course Title: | Introductory of 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 |
| Name of Lecturer(s): | Alekos Vidras, Christos Grigoriadis |
| Lectures/Week: | 2 (1.5 hours per lecture) |
| Laboratories/week: | 1 (1 hours per lecture) |
| Tutorials/Week: | -- |
| Course Purpose and Objectives: | This is the first out of two introductory Mathematics courses offered to Chemistry students. It aims to enable students understand calculus and to use basic methods to solve physical problems, which will be useful to them in the course of their studies for addressing analogous problems in Chemistry. This is a mandatory course, reflecting its importance for other courses in the Chemistry degree, especially those of the Physical Chemistry sector, which routinely use the language of Mathematics. This course is prerequisite for Introductory Mathematics II for Chemistry (MAS020), as well as for Quantum Chemistry (CHE241). |
| Learning Outcomes: |
After successful completion of this course, students will be expected to:
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| 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 Applications of integrals Area between two curves – volumes by slicing- volumes by cylindrical shells – length of a plane curve – area of surface revolution Improper integrals L’ Hopital rules Sequences Infinite series Convergence tests – alternating series Power series Maclaurin and Taylor series – convergence – differentiation and integration of power series |
| Teaching Methodology: | Lectures and problem-solving tutorials |
| Bibliography: |
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| Assessment: | Mid-term exams (40%) and Final exam (60%) |
| Language of Instruction: | Greek |
| Delivery Mode: | Face-To-Face |
| Work Placement(s): | Not Applicable |