Εκτύπωση     Κλείσιμο

Course Details

Course Department: Department of Mathematics and Statistics
Course Code: MAS 002
Course Title: Mathematics II
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: Spring Semester 
Name of Lecturer(s): Evangelides Pavlos
Gregoriades Christos
Maragkos Christos
 
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. Basic knowledge of Linear Algebra  
Learning Outcomes:

  • Applications of definite integrals
  • the concept of improper integral
  • evaluation of limits with the use of L’ Hopital rule
  • the concept of sequence and evaluation of sequence limits 
  • evaluation of basic series and knowledge of convergence tests for series. Similarly, for power series
  • solve simple first order differential equations
  • solve linear second order differential equations 
  • solve linear systems - the concept of matrix and determinant 
  • the definition of vector space 
  • the concept of linear independence 
  • to determine eigenvalues and eigenfunctions

 
Prerequisites: Not Applicable 
Co-requisites: Not Applicable 
Course Content: 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 

Sequencies 

Infinite series 
Convergence tests – alternating series 

Power series 
Maclaurin and Taylor series – convergence – differentiation and integration of power series 

Differential equations 
First order differential equations – Second order linear differential equations 

Linear Algebra 
Systems of linear systems – Matrices -Determinants – Vectors – Vector spaces – Eigenvalues and eigenfunctions
 
Teaching Methodology: Lectures and Laboratories   
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 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