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Course Details

Course Department: Department of Mathematics and Statistics
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):
Semester/Trimester when the Course Unit is Delivered: Fall Semester 
Spring Semester
Name of Lecturer(s): Evangelides Pavlos 
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: Lectures  
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 and Final exam 
Language of Instruction: Greek
Delivery Mode: Face-To-Face 
Work Placement(s): Not Applicable