Chemistry (English) | |||||
Bachelor | TR-NQF-HE: Level 6 | QF-EHEA: First Cycle | EQF-LLL: Level 6 |
Course Code: | MATH112 | ||||
Course Name: | Linear Algebra with Applications | ||||
Semester: | Spring | ||||
Course Credits: |
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Language of instruction: | English | ||||
Course Condition: | |||||
Does the Course Require Work Experience?: | No | ||||
Type of course: | Compulsory Courses | ||||
Course Level: |
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Mode of Delivery: | Face to face | ||||
Course Coordinator: | Prof. Dr. SELÇUK DEMİR | ||||
Course Lecturer(s): | Assist. Prof. Dr. FUNDA ÖZDEMIR | ||||
Course Assistants: |
Course Objectives: | To improve abstract thinking skills by equipping students with the fundamental concepts of linear algebra and to gain the ability to use these concepts in solving engineering problems. |
Course Content: | Systems of linear equations and their solution sets, linear transformations, matrices and matrix operations, determinants, vector spaces, subspaces, linear independence, dimension, bases, change of basis, eigenvalues and eigenvectors, inner product, orthogonality, singular value decomposition. |
The students who have succeeded in this course;
1) Solve a system of linear equations using matrix reduction (elimination). 2) Represent linear transformations as matrices and, conversely, interpret matrices as linear maps; do basic arithmetical operations with matrices and find the inverse of an invertible matrix. 3) Compute determinant of a matrix and comprehends the properties of determinants. 4) Find the dimension and basis of a vector space and its subspaces,analyze some fundamental subspaces. 5) Compute eigenvalues and eigenvectors of a matrix via characteristic equation, identify whether a matrix is diagonalizable or not, learn how to diagonalize the symmetric matrices and to learn singular value decomposition. 6) Knows the concepts of length, distance and orthogonality in inner product spaces, and produce an orthogonal basis for any of its subspaces. |
Week | Subject | Related Preparation |
1) | Systems of linear equations, row reduction and echelon forms | |
2) | Vector equations, the matrix equation Ax=b, solution sets of linear systems, linear independence | |
3) | Introduction to linear transformations;, the matrix of a linear transformation | |
4) | Matrix operations, the inverse of a matrix, characterization of invertible matrices | |
5) | Partitioned (block) matrices, LU decomposition | |
6) | Determinants, properties of determinants, Cramer’s rule, volume | |
7) | Vector spaces, subspaces, null spaces and column spaces, kernel and range of a linear transformation | |
8) | Midterm Exam | |
9) | Linearly independent sets, span, bases, coordinates | |
10) | Dimension, rank, change of basis | |
11) | Eigenvalues and eigenvectors, characteristic equation, diagonalization | |
12) | Inner product spaces, length, distance and orthogonality, orthogonal sets | |
13) | Orthogonal projections, Gram-Schmidt process and QR decomposition | |
14) | Diagonalization of symmetric matrices, singular value decomposition |
Course Notes / Textbooks: | Linear Algebra and Its Applications, David C. Lay, Steven R. Lay, Judi J. McDonald, Pearson. |
References: | Elementary Linear Algebra, Howard Anton, Chris Rorres, Wiley, 11th Edition. |
Course Learning Outcomes | 1 |
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Program Outcomes | |||||||||||
1) Knows the basic concepts related to the theory and applications of chemistry, uses theoretical and applied knowledge, can select, develop and design methods. | |||||||||||
2) Makes experimental planning and application for analysis, synthesis, separation and purification methods, provide solutions to the problems encountered and interpret the results. | |||||||||||
3) Expresses the basic principles of sample preparation techniques and instrumental analysis methods used in qualitative and quantitative analysis of items, discusses their application areas. | |||||||||||
4) Has knowledge about the sources, production, industrial applications and technologies of chemical substances. | |||||||||||
5) Makes structural analyzes of chemical substances and interprets the results. | |||||||||||
6) Work individually and in multidisciplinary groups, take responsibility, plan their tasks and use time effectively. | |||||||||||
7) Follows the information in the field and communicates with colleagues by using English at a professional level. | |||||||||||
8) Uses information and communication technologies along with computer software at the level required by the field. | |||||||||||
9) Follows the national and international chemistry literature, transfers the knowledge gained orally or in writing. | |||||||||||
10) Determines self-learning needs, manages/directs his/her learning. | |||||||||||
11) Takes responsibility and adheres to the ethical values required by these responsibilities. |
No Effect | 1 Lowest | 2 Average | 3 Highest |
Program Outcomes | Level of Contribution | |
1) | Knows the basic concepts related to the theory and applications of chemistry, uses theoretical and applied knowledge, can select, develop and design methods. | |
2) | Makes experimental planning and application for analysis, synthesis, separation and purification methods, provide solutions to the problems encountered and interpret the results. | |
3) | Expresses the basic principles of sample preparation techniques and instrumental analysis methods used in qualitative and quantitative analysis of items, discusses their application areas. | |
4) | Has knowledge about the sources, production, industrial applications and technologies of chemical substances. | |
5) | Makes structural analyzes of chemical substances and interprets the results. | |
6) | Work individually and in multidisciplinary groups, take responsibility, plan their tasks and use time effectively. | |
7) | Follows the information in the field and communicates with colleagues by using English at a professional level. | |
8) | Uses information and communication technologies along with computer software at the level required by the field. | |
9) | Follows the national and international chemistry literature, transfers the knowledge gained orally or in writing. | |
10) | Determines self-learning needs, manages/directs his/her learning. | |
11) | Takes responsibility and adheres to the ethical values required by these responsibilities. |
Semester Requirements | Number of Activities | Level of Contribution |
Midterms | 1 | % 40 |
Final | 1 | % 60 |
total | % 100 | |
PERCENTAGE OF SEMESTER WORK | % 40 | |
PERCENTAGE OF FINAL WORK | % 60 | |
total | % 100 |
Activities | Number of Activities | Preparation for the Activity | Spent for the Activity Itself | Completing the Activity Requirements | Workload | ||
Course Hours | 13 | 0 | 2 | 26 | |||
Application | 13 | 0 | 2 | 26 | |||
Study Hours Out of Class | 13 | 0 | 2 | 26 | |||
Midterms | 1 | 13 | 2 | 15 | |||
Final | 1 | 23 | 2 | 25 | |||
Total Workload | 118 |