COURSE UNIT TITLE

: INTRODUCTION TO APPLIED MATHEMATICS

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MAT 5083 INTRODUCTION TO APPLIED MATHEMATICS ELECTIVE 3 0 0 9

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

ASSISTANT PROFESSOR CELAL CEM SARIOĞLU

Offered to

COASTAL ENGINEERING
Data Science
Biology
Ph.D. in Biology
MARINE LIVING RESOURCES
Data Science (Non-Thesis-Evening)
NAVAL ARCHITECTURE
COASTAL ENGINEERING
GEOPHYSICAL ENGINEERING
COASTAL ZONE MANAGEMENT

Course Objective

This course aims to remind and teach basic concepts of calculus and linear algebra to the students without strong mathematical background.

Learning Outcomes of the Course Unit

1   Will be able to express the continuity and limit concepts theoretically.
2   Will be able to use calculus in applied problems by interpreting derivatives and integral concept.
3   Will be able to find local or absolute maxima and minima of several variables using multivariable methods such as Second Derivative Test and Lagrange Multipliers.
4   Will be able to evaluate areas, volumes, line integrals and surface integrals.
5   Will be able to analyse linear system of equations.
6   Will be able to operate diagonalization.
7   Will be able to apply inner product operation to Gram-Schmidt s ortogonalization process.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Limit of a function and limit laws, precise definition of limits, continuity, limits involving infinity, asymptotes.
2 Tangent line, rate of convergence, derivative, linearization and differentials, differentiation rules.
3 Application of derivatives: Extreme values of a function, maximum and minimum problems, optimization and related rate problems.
4 Integration, Application of integration: work, moments and center of mass.
5 Sequences and series, convergence of series: integral test, comparision test, ratio and root test, alternating seires, absolute convergence.
6 Power series, Taylor and Maclaurin series, convergence of Taylor series.
7 Vector functions and their derivatives, integral of vector functions.
8 Functions of several variables, limit and continuity in higher dimensions
9 Partial derivatives and its applications, Lagrange Multipliers for constrained maxima and minima.
10 Multiple integrals and its applications, area by double integration, volume by tripple integration, double integrals in polar form.
11 System of linear equations, matrix, determinant, rank of a matrix, homogeneous and nonhomogeneous linear systems, Cramer's Rule.
12 Vector spaces, subspaces, bases and dimension, coordinates
13 Eigenvalues and Eigenvectors, Jordan canonical form.
14 Inner product spaces, Orthogonality, Gram-Schmidt s ortogonalization process.

Recomended or Required Reading

1) Stewart, J., Calculus: Concepts and Contexts, 2nd edition, Brooks/Cole.
2) Leon, S.J., Linear Algebra with Applications, 7th edition, Pearson Prentice Hall.

Planned Learning Activities and Teaching Methods

Lecture notes, presentation, problem solving, discussion.

Assessment Methods

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


Further Notes About Assessment Methods

Homework assignments/presentation (%50) + Final (%50)

Assessment Criteria

50% (Midterm examination) +50% (Final examination)

Language of Instruction

Turkish

Course Policies and Rules

Attending at least 70 percent of lectures is mandatory.

Contact Details for the Lecturer(s)

Asst. Prof. Dr. Celal Cem SARIOĞLU
E-mail: celalcem.sarioglu@deu.edu.tr
Phone: +90 232 301 8585
Office: B212 (Mathematics Department)

Office Hours

To be announced later.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 14 3 42
Preparations before/after weekly lectures 13 8 104
Preparation for midterm exam 1 35 35
Preparation for final exam 1 40 40
Final 1 3 3
TOTAL WORKLOAD (hours) 224

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10
LO.13211451215
LO.23211451215
LO.33211231213
LO.43211551215
LO.53211551215
LO.63211441214
LO.73211441214

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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