Calculus I and Linear algebra
FACULTY | ENGINEERING | ||||
DEPARTMENT | CHEMICAL ENGINEERING | ||||
LEVEL OF STUDY | UNDERGRADUATE | ||||
SEMESTER OF STUDY | 1o | ||||
COURSE TITLE | Calculus I and Linear algebra | ||||
| COURSEWORK BREAKDOWN | TEACHING WEEKLY HOURS | ECTS Credits | |||
| Lectures | 3 | ||||
| Laboratory | 0 | ||||
| Projects | 1 | ||||
TOTAL | 5 | ||||
| COURSE TYPE | Compulsory | ||||
| PREREQUISITES | - | ||||
| LANGUAGE OF INSTRUCTION/EXAMS | Greek | ||||
| COURSE DELIVERED TO ERASMUS STUDENTS | - | ||||
MODULE WEB PAGE (URL) | https://eclass.uowm.gr/ | ||||
2. LEARNING OUTCOMES
Learning Outcomes | |
| Upon successful completion of the course, students will be able to solve problems that involve Plane analytical geometry, Complex numbers, Algebra of matrices, Systems of linear equations, Vector spaces, Linear representations, Inverse trigonometric and hyperbolic functions, Indefinites integrals, Integration techniques, etc. | |
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| The student will become familiar with all the mathematical processes that refer to the optimization of scientific processes and situations. Such a high-level course fosters creative and inductive thinking and becomes an essential tool for scientific completion. Other skills Search, analyze and synthesize data and information, using the necessary technologies Decision making Critical Thinking Autonomous work Teamwork |
3. COURSE CONTENTS
| 1. Plane Analytical geometry i) Lines in the plane, ii) Locus, Straight line, Quadratic curves (conic sections): Parabolas, Ellipses, Hyperbolas iii) Polar coordinates 2. Complex numbers i) Definition of Complex, Image, Vector Radius, Measure and Argument of Complex, Conjugate of Complex, Properties of Conjugate and Measure, Properties of Argument ii) Sum, Difference, Product and Quotient of complex numbers iii) Powers of imaginary unit i, Quadratic complex equation iv) Complex locus 3. Tables i) The concept of matrix, Definition, Degree of matrix ii) Matrix Operations, Addition, Subtraction, Multiplication, Properties iii) Matrix Types, Zero, Square, Symmetric, Antisymmetric, Inverse, Unit, Diagonal, Upper and Lower Triangular iv) Determinant, Dimension and expansion of determinant, Properties, Triangulation of determinant v) Inverse square matrix, Inverse vi) Matrices and linear systems, Cramers rule, Gausss method 4. Vector spaces - Linear representations i) The concept of real vector space, Linear dependence, Basis and dimension of vector space ii) Linear mappings in a vector space, Linear mapping matrix iii) Eigenvalues and eigenvectors 5. Inverse trigonometric and hyperbolic functions i) Definition of real function, 1-1 (one to one) function, Definition of inverse function, Basic Identities ii) Inverse trigonometric and hyperbolic functions (may be requested in combined exercises) 6. Indefinite integral i) Definition, Basic concepts, Original function or factor, Properties ii) Indefinite integral of trigonometric, hyperbolic, inverse trigonometric and inverse hyperbolic functions iii) Methods of integration: method of substitution with application to composite functions, method of factorial integration, calculation of the integral of an explicit function |
4. TEACHING METHODS – ASSESSMENT
| MODE OF DELIVERY | Lectures (Face to face), Tutorial Exercises | ||||||||||||||||||||||||
| USE OF INFORMATION AND COMMUNICATION TECHNOLOGY | Projectors, computers, e-class, lectures using power point, computing tools | ||||||||||||||||||||||||
TEACHING METHODS |
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| ASSESSMENT METHODS | Written final exam, Optional midterm exam. |
5. RESOURCES
Suggested bibliography : |
| 1. Calculus of Functions of One Variable and Linear Algebra, 2nd Edition, Mylonas Nikolaos, Schoinas Christos, Papaschoinopoulos G. 2. Analysis and Linear Algebra Courses, Kravbaritis D. |
Related academic journals: |