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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS MEN 2031 MATHEMATICS III COMPULSORY 4 0 0 4

Offered By

Marine Engineering

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

ASSISTANT PROFESSOR HANDE TUNÇEL GÖLPEK

Offered to

Marine Engineering

Course Objective

Linear equations and matrices, Real vector spaces, Inner product spaces. Linear transformations and matrices, Determinants, Eigenvalues and Eigenvectors.

Learning Outcomes of the Course Unit

1   will be able to understand consistent linear systems and solve the system by Gauss elemination 2   will be able to apply the basic techniques of matrix algebra, including finding inverse using Gauss Jordan method 3   will be able to apply basic concept to various applications 4   will be able to find subspaces, dimension and basis vectors of linear vector spaces 5   will be able to find eigenvalues and eigenvectors and understand orthogonality.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 System of linear equations, row reduction and echolon forms Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 1.1, 1.2 2 Vector Equations, the matrix equations Ax=b Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 1.3, 1.4 3 Solution sets of linear systems, applications of linear system Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 1.5, 1.6 4 Linear independence, introduction to linear transformation Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 1.7, 1.8 5 The matrix of a Linear transformations, linear models in business, science and engineering Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 1.9, 1.10 6 Matrix Operations, the inverse of a matrix, characterization of invertible matrix Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 2.1, 2.2, 2.3 7 Matrix factorization, introduction to determinants, properties of determinants Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 2.5, 3.1, 3.2 8 properties of determinants, Cramer's Rule Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. 3.2, 3.3 9 Cramer's rule, linear transformation, vector spaces and subspaces Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 3.3, 4.1 10 Null spaces, column spaces and Linear Transformations, linearly independent sets and basis Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 4.2, 4.3 11 Dimension, Rank, Markov Chains, Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 4.5, 4.6, 4.9 12 Eigenvalue and Eigenvectors Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 5.1, 5.2 13 Inner Product, Length and Orthogonality, Orthogonal sets Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 6.1, 6.2 14 Orthogonal Projections, The Gram-Schimidth Process Linear Algebra and its applications, David C. Lay, Steven R. Lay, Judi j. Mcdonald, Pearson, 5th ed. section 6.3, 6.4

Recomended or Required Reading

1. David C. Lay, Linear Algebra and its Applications, Pearson, 2003. 5th ed. 2. Bernard Kolman, David R. Hill, Elemantary Linear Algebra, Prentice Hall, 8th ed. 2001.

Planned Learning Activities and Teaching Methods

Cooperative and active teaching and learning strategies

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 FINS FINAL EXAM 3 FCG FINAL COURSE GRADE MTE * 0.40 + FINS * 0.60 4 RST RESIT 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.40 + RST * 0.60 *** Resit Exam is Not Administered in Institutions Where Resit is not Applicable.

Further Notes About Assessment Methods

None

Assessment Criteria

To be announced.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

To be announced.

Office Hours

To be announced.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 13 4 52 Preparations before/after weekly lectures 13 1 13 Preparation for midterm exam 1 10 10 Preparation for final exam 1 10 10 Preparation for quiz etc. 0 0 0 Preparing assignments 0 0 0 Final 1 2 2 Midterm 1 2 2 Quiz etc. 0 0 0 TOTAL WORKLOAD (hours) 89

Contribution of Learning Outcomes to Programme Outcomes

PO/LO PO.1 PO.2 PO.3 PO.4 PO.5 PO.6 PO.7 PO.8 PO.9 PO.10 PO.11 PO.12 PO.13 PO.14 PO.15 PO.16 PO.17 PO.18 PO.19 PO.20 LO.1 5 5 5 LO.2 5 5 5 LO.3 5 5 5 LO.4 5 5 5 LO.5 5 5 5