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Course Details

Course Department: Department of Mathematics and Statistics
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):
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: 
  • Solve linear equations. 
  • Understand simple concepts of analytical geometry. 
  • Understand the concept of the function and the basic functions. 
  • Calculate basic limits and understand the notion of continuity of a function. 
  • Understand the notion of differentiation, be able to differentiate basic functions and to apply the knowledge of the notion of differentiation to real problems. 
  • Understand the notion of the integral, know the methods of integration and be able to apply integration to solve physical problems. 
  • Address problems involving applications of definite integrals. 
  • Understand the notion of the sequence. 
  • Determine the sum of simple series and test for convergence.
  • Determine power series for basic functions.
 
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:
  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
  5. Calculus with analytic geometry, 2nd ed., by D. G. Zill, PWS-KENT Publishing Company, 1998
 
Assessment: Mid-term exams (40%) and Final exam (60%) 
Language of Instruction: Greek
Delivery Mode: Face-To-Face 
Work Placement(s): Not Applicable