Back

## Linear Algebra

PÎRÎ REİS UNIVERSITY

ENGINEERING FACULTY

Naval Architecture and Marine Engineering Programme

2017 - 2018 Fall Term Course catalogue Form

 Course Name : Linear Algebra Degree: Undergraduate Code Year/Semester Local Credits ECTS Credits Course Implementation, Hours/Week Course Tutorial Laboratory MATH 113 1/1 (Fall) 2,5 4 2 1 0 Department Naval Architecture and Marine Engineering Instructors Dr. Orhan Özgür AYBAR Contact Information oaybar@pirireis.edu.tr Office Hours TBA Web page www.pirireis.edu.tr Course Type Compulsory Course Language English Course Prerequisites MATH 121 Course Category by Content % Basic Sciences Engineering Science Engineering Design Humanities 90 10 - - Course Description Systems of linear equations, matrices, determinants, the Euclidean vector space, vector spaces and subspaces, eigen values and eigenvectors, diagonalization and quadratic forms, linear transformations Course Objectives To introduce the fundamental concepts and methods of Linear Algebra To provide an ability to apply knowledge of linear algebra to solve engineering problems Course Learning Outcomes Upon successful completion of the course students should be able to: Find and classify the types of solutions of linear system of equations Perform basic matrix operations Use the row reduction operations put a matrix in upper echelon form Find the inverse of a matrix Compute the determinants of square matrices Understand and apply the basic properties of vectors in Rn Understand the concepts of vector space, basis, dimension and subspace. Determine the matrix representation of a linear transformation Find Eigen values and eigenvectors of a matrix Diagonalize a matrix and understand the concept of similarity of matrices Instructional Methods and Techniques Lecture, problem solving Tutorial Place Class Co-term Condition - Textbook H. Anton, C. Rorres, Elementary Linear Algebra, 10 th Edition, Wiley, 2010 Other References B.Kolman, D.R.Hill, Elementary Linear Algebra with Applications, 9th Edition, Pearson, 2007 Homework & Projects Laboratory Work Computer Use Other Activities

 Assessment Criteria Activities Quantity Effects on Grading, % Attendance Midterm 1 30 Quiz 4 20 Homework Term Paper/Project Laboratory Work Practices Tutorial Seminar Presentation Field Study Final Exam 1 50 TOTAL 100 Effects of Midterm on Grading, % 50 Effects of Final on Grading, % 50 TOTAL 100

 ECTS/ WORKLOAD TABLE Activities Count Hours Total Workload Lecture 13 3 39 Midterm 1 20 20 Quiz 4 2 8 Homework Term Paper/Project Laboratory Practices Tutorial Seminar Presentation Field Study Final Exam 1 30 30 Total Workload 97 Total Workload/25 97/25 Course ECTS Credits 4

COURSE PLAN

 Week Topics Course Outcomes 1 Introduction to Systems of  Linear Equations, Gaussian Elimination I-II-III 2 Matrices and Matrix Operations, Inverses,  Algebraic Properties of Matrices I-II-III-IV 3 Elementary Matrices and a Method for Finding A-1, More on Linear Systems  and Invertible Matrices, Diagonal, Triangular, and Symmetric Matrices II-III-IV-V 4 Determinants by Cofactor Expansion, Evaluating Determinants by Row Reduction VI 5 Properties of  Determinants,  Cramer’s Rule VI-VII 6 Vectors in 2-Space, 3-Space, n-Space, Norm, Dot Product, and Distance in Rn, Orthogonality, The Geometry of Linear Systems, Cross Product II-III-VIII 7 Real Vector Spaces, Subspaces, Linear Independence, Coordinates and Basis, Dimension I-II-III 8 MIDTERM 9 Change of Basis, Row Space, Column Space, and Null Space, Rank, Nullity VI 10 Eigenvalues and Eigenvectors, Diagonalization II-III-IV 11 Orthogonal Matrices, Orthogonal Diagonalization, Quadratic Forms, Optimization Using Qudaratic Forms II 12 Hermitian, Unitary, and Normal Matrices,  Linear Transformations, Isomorphism II-IV-V 13 Compositions and Inverse Transformations II-IV-VIII 14 Matrices for General Linear Transformations II-IV-X

Relationship between the Course and the Naval Architecture and Marine Engineering Programme

Curriculum

 Program Outcomes Level of Contribution 1 2 3 a An ability to apply knowledge of mathematics, science, and engineering X b An  ability to design and conduct experiments, as well as to analyze and interpret data X c An ability to design a system, component or process to meet desired needs X d Ability to function on multi-disciplinary teams X e An ability to identify, formulate, and solve engineering problems X f An understanding of professional and ethical responsibility X g An ability to communicate effectively X h The broad education necessary to understand the impact of engineering solutions in a global and societal context X i A recognition of the need for, and an ability to engage in life-long learning X j A knowledge of contemporary issues X k An ability to use the techniques, skills and modern engineering tools necessary for engineering practice X l An ability to apply engineering knowledge in fluid mechanics, structural mechanics, material selection and energy/propulsion systems in the context of marine vehicles and offshore structures. X

1: Small, 2: Partial, 3: Full

Programme Outcomes & Course Outcomes Connectivity Matrix

 Course Outcomes I II III IV V VI VII VIII IX X Programme Outcomes a X X X X X X b X X X X c X d X X X e X X X X X X f X g X X h X X i X X X j X X X X X k X X l X X X X X

Prepared by

# Date

### Signature 