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Course Details
| Course Department: | Department of Mathematics and Statistics |
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| 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): | Dr Stratos Vernadakis, Dr Michael Aristidou, Dr Spyros P. Pasias, Dr Christos Raent-Onti |
| 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
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| 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: |
It is recommended to successfully attend MAS001 before enrolling in MAS002 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: | Two lectures and one tutorial to solve exercises/problems per week. |
| 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
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| Assessment: | Mid-term exams (50%) and Final exam (50%) |
| Language of Instruction: | Greek |
| Delivery Mode: | Face-To-Face |
| Work Placement(s): | Not Applicable |