School of Chemical and Environmental Engineering
Now offering two distinct diplomas: Chemical Engineering and Environmental Engineering
1. COURSE INFORMATION:
|Course ID||MATH 201||Semester||2nd|
|Course Modules||Instruction Hours per Week||ECTS|
|Lectures and Laboratory Exercises||5|
Th=4, E=0, L=1
|Course Type||General Background|
|The course is offered to Erasmus students||No|
|Course URL||https//www.eclass.tuc.gr/courses/MHPER313/ (in Greek)|
2. LEARNING OUTCOMES
This course aims to introduce the basic ideas and techniques of linear algebra for use in many other lecture courses, as well as in solving linear systems that arise from the modeling of natural phenomena. Topics include systems of linear equations and their solutions, matrices and matrix algebra, inverse matrices, determinants; real n-dimensional vector spaces, abstract vector spaces and their axioms, linear transformations; inner products (dot products), orthogonality, cross products, and their geometric applications; subspaces, linear independence, bases for vector spaces, dimension, matrix rank; eigenvectors, eigenvalues, matrix diagonalization. Some applications of linear algebra will be discussed, such as linear regression (least squares), elementary Markov chains.
Upon successful completion of this course, the student will be able to
3. COURSE SYLLABUS
Contents: Introduction to linear algebra and the algebra of vectors and matrices. Direct methods of solving systems of linear equations. Determinants. Vector spaces, subspaces. Linear dependence, independence, basis of a vector space. Fundamental subspaces of a matrix. Eigenvector,eigenvalues. Diagonalization and applications. Gram-Schmidt process of orthonormalization, least square method. Iterative methods for solving linear systems.
Laboratories: Introduction to MATLAB software with emphasis on the problems and the theory of Linear Algebra as well as the linear systems solving algorithms. Supported Operations for Vectors and Matrices. Creating, Concatenating vectors and matrices,expanding matrices. Functions and Subfunctions.
4. INSTRUCTION and LEARNING METHODS - ASSESSMENT
|Lecture Method||Direct (face to face)|
|Use of Information and Communication Technology||Specialized software, E-class support|
|Instruction Organisation||Activity||Workload per Semester|
|- Lab assignments||13|
|- Autonomous study||85|
Ι. Written final examination (80%)
ΙΙ. Laboratory exercises (20%).
5. RECOMMENDED READING