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Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS CME 2207 DIFFERENTIAL EQUATIONS AND LINEAR ALGEBRA COMPULSORY 4 0 0 5

Offered By

Computer Engineering (English)

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR BURCU SILINDIR YANTIR

Offered to

Computer Engineering (English)

Course Objective

The goal of this course is to establish the mathematical background about the fundamental concepts, solution methodologies and technical applications of linear algebra and differential equations.

Learning Outcomes of the Course Unit

1   Understand solution methods of first order ordinary differential equations. 2   Understand the theory and the solutions of higher order linear differential equations with homogeneous and inhomogeneous terms. 3   Understand matrix algebra. 4   Analyze linear transformations. 5   Compute eigenvalues and eigenvectors of a matrix. 6   Solve systems of linear differential equations by matrix exponential function.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description 1 Introduction to differential equations, solution curves. First order ordinary differential equations: Seperable differential equations. 2 Homogeneous differential equations, linear differential equations. 3 Bernoulli type nonlinear differential equations, exact differential equations. 4 Integrating factors and non-exact differential equations. 5 Existence and uniqueness theorems of first order differential equations. Applications of first order differential equations. 6 Matrix Calculus: Matrix operations, transpose of a matrix, Symmetric and skew-symmetric matrices. 7 Elementary row operations, inverse of a matrix. Solutions of systems of linear equations by elementary row operations. 8 Determinant, properties of determinant. Cramers rule. 9 Linear Transformations, image, kernel and associated properties. 10 Matrix representations of linear transformations. 11 Higher order linear differential equations, linear dependence and independence of solutions, representation of solution spaces. 12 Method of Variation of Parameters. 13 Eigenvalues and eigenvectors. Diagonalization. 14 Matrix formulation of systems of linear differential equations and the solutions of systems of linear differential equations by matrix exponential function.

Recomended or Required Reading

1. Lectures on Differential equations, E.Akyıldız, et all, 2012, METU Press. 2. Differential Equations and Linear Algebra, C.H. Edwards, D.E. Penney, Third Edition, 2010, Pearson. 3. Linear algebra with applications, S. J. Leon, Eight edition, 2010, Pearson.

Planned Learning Activities and Teaching Methods

Lecture presentation, application

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA 1 MTE MIDTERM EXAM 2 FIN FINAL EXAM 3 FCG FINAL COURSE GRADE MTE * 0.50 + FIN * 0.50 4 RST RESIT 5 FCGR FINAL COURSE GRADE (RESIT) MTE * 0.50 + RST * 0.50

Further Notes About Assessment Methods

None

Assessment Criteria

MIDTERM(%50) + FINAL EXAM (%50)

Language of Instruction

English

Course Policies and Rules

Participation is mandatory.

Contact Details for the Lecturer(s)

Assoc.Prof.Dr. BURCU SILINDIR YANTIR burcu.silindir@deu.edu.tr DEÜ Eng. Fak. Computer Engineering. Tınaztepe Campus Buca-Izmir

Office Hours

TBA

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours) Lectures 14 3 42 Preparations before/after weekly lectures 14 3 42 Preparation for midterm exam 1 17 17 Preparation for final exam 1 20 20 Final 1 2 2 Midterm 1 2 2 TOTAL WORKLOAD (hours) 125

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 LO.1 5 3 3 LO.2 5 3 3 LO.3 5 3 4 LO.4 5 3 4 3 3 3 LO.5 5 3 4 3 LO.6 5 3 3 3 3