Mathematics
(Course Code: 401Υ, Course outline)
| Semester: | 1 | Teaching Credits: | 4 | ECTS Credits: | 5 | Type: |
Compulsory |
|
| Prerequisite Courses: | – | Course type: | General background | Instructor: | Demetris F. Lekkas | |||
- Generalize key calculus concepts and develop deeper understanding.
- Functions (Functions and Their Graphs, Combining Functions)
- Limits and Continuity
- Differentiation
- Applications of Derivatives
- Integration
- Applications of Definite Integrals
- Basic skill in solving environmental design applications.
- Knowledge of quantitative and qualitative characteristics of environmental systems and ability to calculate pertinent parameters
- An ability to calculate and/or estimate basic design parameters
| Topics per Week: | PART A – Calculus
Lecture 1: Introduction to Calculus – Numbers, functions, graphs, inverse of a function Lecture 2: Limits and Derivatives – Definition and properties of limits and derivatives, physical and geometric meaning of derivatives, applications Lecture 3: Integrals – Indefinite integral, integration rules, definite integral, properties Lecture 4: Ordinary Differential Equations I – Introduction to differential equations, class and order of differential equations, solution methods of 1st order differential equations, separation of variables, linear and homogenous equations Lecture 5: Ordinary Differential Equations II – Applications of differential equations on problems in environmental science and engineering Lecture 6: Multivariable Functions – Examples of multivatiable functions in modeling environmental processes, partial differentiation multiply integrals, applications of partial derivatives and multiple integrals PART B – Linear Algebra Lecture 7: Introduction to Vectors and Matrices – Definition of vectors and matrices, operations with matrices and vectors (addition, multiplication) Lecture 8: Solutions of Systems of Linear Equations I – Matrix formulation of systems of linear equations, the inverse of a matrix and the solution of systems of linear equations Lecture 9: Solutions of Systems of Linear Equations II – Gauss and Cramer’s method Lecture 10: Eigenvalues and Eigenvectors (Definitions) – Definition and estimation of the eigenvalues and the eigenvectors of a matrix Lecture 11: Applications of Eigenvalue Analysis – Solution of systems of Differential Equations Lecture 12: Applications of Eigenvalue Analysis |
| Theory – Lectures (hours / week): |
3 |
| Exercises – Laboratories (hours / week): |
2 |
| Other Activities: | – |
| Grading: | Final exam (100%)
Weekly tests and homeworks (optional, max. 30% of the total grade) The final grade is estimated by the final exam (100%) increased by a factor proportional to the optional weekly tests and homeworks given throughout the course. The increase of the final exam mark cannot be higher than 30%, and cannot exceed the value of 10 (maximum grade). |
| Notes: | – |
| Basic Textbook: |
|
| Bibliography: |
– |
| Language: |
The course is taught in Greek. English literature, instructions, and examinations can be provided in English for exchange students. |
| Internet Links: |
Thomas Calculus http://occawlonline.pearsoned.com/bookbind/pubbooks/thomas_awl/ MIT open coursework: http://ocw.mit.edu/OcwWeb/Mathematics/18-01Fall-2006/CourseHome/index.htm http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/ http://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2006/ http://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ Math archives, Calculus resources on-line |
