COURSE UNIT TITLE

: MATHEMATICS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MIM 1015 MATHEMATICS COMPULSORY 3 0 0 3

Offered By

Architecture

Level of Course Unit

First Cycle Programmes (Bachelor's Degree)

Course Coordinator

PROFESSOR DOCTOR TANER UÇAR

Offered to

Architecture

Course Objective

The aim of this course is to introduce the definitions, the theorems and the applications on the basic mathematical concepts, limit, continuity, differential and integration. Matrices, determinants, solution of homogenous and non-homogenous systems of linear equations, numerical solutions of non-linear equations.

Learning Outcomes of the Course Unit

1   Evaluating limits of functions and examining continuity
2   Finding the derivative of functions and understanding applications of derivatives
3   Learning the integration methods and integral applications
4   Understanding matrix operations and evaluating determinants
5   Solving homogeneous and non-homogeneous systems of linear equations

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Limits, Right and left limits, Theorems on limits, Limits of trigonometric functions, Indeterminate forms, / type, 0/0 type, 0. type, - type, Continuity, Theorems on continuity, Right and left continuity, Supplementary examples.
2 The derivative, Derivative rules, Differentiation of a function of a function, Higher derivatives, Parametric differentiation, Implicit differentiation, Supplementary examples.
3 Differentiation of inverse functions, Differentiation of trigonometric functions, Differentiation of inverse trigonometric functions, Differentiation of exponential and logarithmic functions, Supplementary examples.
4 Using of derivatives to evaluate limits, L'Hospital Rule, 1. , 00, .0 indeterminate forms, Geometric interpretation of differentiation, Tangents and normals, Increasing and decreasing functions, Relative maximum and minimum values of a function, Supplementary examples.
5 Series expansion of functions, Taylor's and Maclaurin's series, Partial derivatives, Partial derivatives of higher orders, Indefinite integrals, Fundamental integration formulas, Integration methods, Integration by substitution (change of variables), Supplementary examples.
6 Trigonometric integrals, Integration by parts, Integration by partial franctions, Supplementary examples.
7 Trigonometric substitutions, Miscellaneous substitutions, Supplementary examples.
8 The definite integral, Properties of definite integral, Geometric interpretation of definite integrals, Areas by integration, Supplementary examples.
9 Mid-term exam.
10 Matrices, Matrix operations, Power of matrices, Properties of matrix operations, Square matrices, Determinants, Supplementary examples.
11 Minors and cofactors, Evaluatiing determinants, Rule of Sarrus, Properties and theorems for determinants, Supplementary examples.
12 Inverse of a square matrix: using the definition, using adjoint matrix, using elementary row operations, using the Cayley-Hamilton theorem, Rank of a matrix, Supplementary examples.
13 Systems of linear equations, Solution of non-homogeneous systems of linear equations using matrices, Gaussian elimination, Inverse matrix method, Supplementary examples.
14 Inverse matrix method, Solution of homogeneous systems of linear equations, Solution of homogeneous systems of linear equations using determinants, Cramer's rule, Supplementary examples.

Recomended or Required Reading

- Lecture notes
- Tin, A.T., Badem, N. (2011). Matematik I, Cilt 1-2. Dokuz Eylül Üniversitesi, Mühendislik Fakültesi Basım Ünitesi, Izmir.
- Aydın, S. (1980). Analize Giriş. Başarı Yayınları, Ankara.
- Speigel, M.R. (1978). Advanced Calculus. Mc-Graw-Hill Book Company, New York.
- Stein, S.K., Barcellos, A. (1996). Calculus ve Analitik Geometri, Cilt 1-2. Mc-Graw-Hill-Literatür, Istanbul.
- Ayres, F. (1980). Matrices. Schaums Outline Series, Mc-Graw-Hill Book Company, New York.
- Lipschutz, S. (1974). Linear Algebra. Schaums Outline Series, Mc-Graw-Hill Book Company, New York.
- Çatal, (Alku) S. (2003). Sayısal Çözümleme ve Örnekler. Dokuz Eylül Üniversitesi Müh.Fak. Basım Ünitesi, Izmir.
- Oturanç, G. Kurnaz, A. Kiriş, M.E. (2003). Sayısal Analiz. Dizgi Ofset Yayınları, Konya.
- Uzun, I. (2000). Nümerik Analiz. Beta Yayınları, Istanbul.
- Gündoğdu Ö., Kopmaz O., Ceviz M.A., (2004). Matlab Mühendislik ve Fen Uygulamalarıyla. Nobel Yayın Dağıtım, Istanbul.

Planned Learning Activities and Teaching Methods

Theoretical lectures, supplementary examples, midterm exam and final exam.

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE MIDTERM EXAM
2 FINS FINAL EXAM
3 FCG FINAL COURSE GRADE MTE * 0.50 + FINS * 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

50% Mid-term exam (LO1, LO2, LO3)
50% Final exam (LO1, LO2, LO3, LO4, LO5)

Language of Instruction

Turkish

Course Policies and Rules

Attendance to the 70% of the lectures is compulsory in order to be accepted to the final exam.

Contact Details for the Lecturer(s)

taner.ucar@deu.edu.tr

Office Hours

Any suitable time.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 13 3 39
Tutorials 0 0 0
Student Presentations 0 0 0
Preparation about subject 0 0 0
Preparations before/after weekly lectures 12 1 12
Preparation for midterm exam 1 10 10
Preparation for final exam 1 15 15
Preparations before/after weekly lectures 0 0 0
Preparing presentations 0 0 0
Midterm 1 2 2
Final 1 2 2
Quiz etc. 0 0 0
TOTAL WORKLOAD (hours) 80

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15
LO.122
LO.222
LO.322
LO.422
LO.522

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

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