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Course Details

Course Department: Department of Mathematics and Statistics
Course Code: MAS 019
Course Title: Introductory of Mathematics ΙΙ
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: Spring Semester 
Name of Lecturer(s): Smyrlis Yiorgos 
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 physical
problems. To understand an introduction to Linear Algebra.  
Learning Outcomes: The students should:

  • Understand what is the concept of vector in the space
  • To calculate dot and cross product
  • To determine the equation of a straight line in the space and also the equation of a plane
  • The concept of vector functions
  • To determine unit tangent and normal vectors
  • The concept of curvature
  • To study the motion of a particle along a curve
  • The concept of a function of two variables
  • The concept of partial derivative
  • To use the chain rule
  • To determine tangent planes
  • To understand the concept of directional derivative
  • To determine maximum/minimum of functions of two variables solve linear systems
  • the concept of matrix and determinant
  • the definition of vector space
  • the concept of linear independence
  • the concept of a base of a vector space
  • to determine eigenvalues and eigenfunctions
  • to diagonize a matrix
  • what is inner vector space
  • the concept of orthogonality
  • the concept of linear transformation
 
Prerequisites: Introductory Mathematics I 
Co-requisites: Not Applicable 
Course Content: VECTORS
Rectangular coordinates in 3-space – Vectors – Dot product – Cross
product – parametric equations of a line – planes in 3-space -Cylindrical and spherical coordinates

VECTOR-VALUED FUNCTIONS
Calculus of vector-valued functions – change of parameter – Arc length –
Unit tangent and normal vectors – Curvature – Motion along a curve

FUNCTIONS OF TWO VARIABLES
Limits and continuity – partial derivatives – Differentiability – the chain rule – Directional derivative – Tangent planes – Maxima and minima of functions of two variables – Lagrange multipliers

LINEAR ALGEBRA
Systems of linear systems – Matrices -Determinants – Vectors – Vector
spaces – Inner product spaces - Eigenvalues and eigenfunctions – Linear
transformations
 
Teaching Methodology:  
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
  6. H. Anton and C. Rorres, Elementary Linear Algebra, 6th edition, Wiley, 1991
  7. S.F. Andrilli and D. Hecker, Elementary Linear Algebra, 3rd ed., Elsevier Academic Press, 2003
 
Assessment: Mid-term exams and Final exam 
Language of Instruction: Greek
Delivery Mode: Face-To-Face 
Work Placement(s): Not Applicable