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Week
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Topics
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Study Metarials
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1
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Algebra of sets, Transformations, Some algebraic structures, Permutation, polynomials
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R1-Chapter 1
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2
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Definitions and some basic concepts, equation of matrixs, sum of matrixs, multiplication of matrix by a scalar, matrix multiplication, application of matrix multiplication, multiplication of matrixs
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R1-Chapter 2
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3
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Multiplication of matrixs, Transposition of a matrix, Some special matrixs, Some relations with special matrixs, Trace and properties of a square matrix, Inverse matrixs, Zero dividing matrixs
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R1-Chapter 2
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4
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Elementary operations, Elementary matrixs
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R1-Chapter 3
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5
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calculate of inverse of an inverse matrix with elementary row operations, equivalent matrixs and applications
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R1-Chapter 3
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6
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Elementary properties of determinants, Calculation of determinants with minors, Permutations and determinants, Determinant of a product
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R1-Chapter 4
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7
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Sarrus rule, adjoint of a square matrix, the existence of inverse matrix by the block separation method, Permanents and their properties
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R1-Chapter 4
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8
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Definitions, systems of linear equations and matrixs, rank of a matrix
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R1-Chapter 5
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9
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Finding the rank of a matrix with elementary row operations, Criteria related to the existence of the solution of systems of linear equations, Solution of systems of linear equations, Solution of systems of homogeneous equations
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R1-Chapter 5
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10
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Definition of vector spaces and some elementary properties, Sub-vector spaces, Linear dependence and Linear independence, Base and dimension
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R1-Chapter 6
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11
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Coordinates of a vector according to a base, Row and column rank, The relation between the rank and determinant of a square matrix
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R1-Chapter 6
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12
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Inner product, vector norms, distance between two vectors, angle between two vectors, orthogonal vectors
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R1-Chapter 7
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13
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Characteristic polynomial, eigenvalue and eigenvector, eigenspace, finding the inverse of a square matrix with the help of Cayley-Hamilton theorem, estimation of the eigenvalues of a square matrix with the help of the matrix norm, singular values
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R1-Chapter 9
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14
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Similar matrixs, Diagonalization, Some applications of diagonalization, Diagonalization of symmetric matrixs
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R1-Chapter 10
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Prerequisites
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-
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Language of Instruction
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Turkish
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Responsible
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Assoc. Prof. Dr. İlyas İNCİ
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Instructors
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-
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Assistants
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Resources
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R1.Lineer Cebir, Prof. Dr. Dursun Taşçı, Gazi Kitabevi.
R2.Lineer Cebir Çözümlü Problemleri, Mehmet Ali Karaca, İTÜ vakfı yayınları, İstanbul.
R3.Çözümlü Lineer Cebir Problemleri, Prof. Dr. Fethi ÇALLIALP, İstanbul.
R4.Uygulamalı Lineer Cebir, Bernard Kolman, David r. Hill, Çeviri Editörü; Prof. Dr. Ömer AKIN, Palme yayıncılık.
R5.Lineer Cebir, Seymour Lipschutz, Schaums Outlines Çeviren: H. Hilmi Hacısalihoğlu, Nobel Yayın-Dağıtım.
R6.Elementary Linear Algebra: Applications Version, H. Anton, C. Rorres, Wiley, New York.
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Supplementary Book
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Goals
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The aim of this course is to develop awareness of the importance of matrix, determinant, linear equation systems and properties in civil engineering courses and to gain the ability of solution of related problems.
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Content
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Matrixs, Determinants, Linear Equation Systems, Vector Spaces, Eigenvalues and Eigenvectors.
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Program Learning Outcomes |
Level of Contribution |
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1
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To own sufficient background in mathematics, sciences and related engineering subjects; use the theoretical and practical knowledge in these fields together for Civil Engineering solutions.
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5
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2
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Identify, define, formulate and solve civil engineering problems; selects and applies modeling techniques with appropriate analytical methods to this aim.
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4
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3
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Analyze a system, system component or process and design under realistic constraints to meet the desired requirements; apply modern design methods in this aim.
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4
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4
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Designs and conducts experiments, collects data, analyzes and interprets results.
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-
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5
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Selects and uses the modern techniques and tools required for engineering applications; effectively use information technologies and at least one computer software (European Computer Using License Advanced Level).
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2
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6
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Accesses information and conducts resource research for this purpose, uses databases and other information sources.
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2
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7
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Work effectively in individual and multi-disciplinary teams, take responsibilityi.
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-
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8
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Aware of the necessity of lifelong learning; follows developments in science and technology and renews itself continuously.
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-
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9
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It manages the project, is aware of workplace practices, employee health, environment and occupational safety; is aware of the legal consequences of engineering applications,
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-
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10
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Communicates effectively in oral and written Turkish; Have at least one foreign language knowledge at the general level of European Language Portfolio B1,
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-
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11
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It is aware of the universal and social effects of engineering solutions and applications; is aware of the issues of entrepreneurship and innovation and has knowledge about the problems of the time.
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12
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To have the awareness of professional and ethical responsibility.
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