MIDDLE EAST TECHNICAL UNIVERSITY
9060528 - 1
COURSE SYLLABUS
Course Information
Course Code
Course Section
Course Title
Course Credit
Course ECTS
Course Catalog Description
Prerequisites
Schedule
9060528
1
FUNDAMENTALS OF MATHEMATICS FOR INFORMATION SYSTEMS
3
8.0
The aim of the course is to acquaint the non-technical background graduate students with the
fundamental theory and techniques of engineering mathematics. This will be achieved by teaching
fundamental theory as well as application based homework using MATLAB tool. The course covers
subjects like Basic Calculus (Functions, Continuity, Integrals, Derivatives, Sequences, Series, Differential
equations and their numerical implementations); Linear Algebra; Optimization; Fourier Transformation;
Fundamentals of Signal processing and Filtering.
No prerequisites
Tuesday , 13:40 - 16:30, II-04
Instructor Information
Name/Title
Prof.Dr. ÜNAL ERKAN MUMCUOĞLU
Office Address
Email
Office Phone
merkan@metu.edu.tr
210 3753
Office Hours
Course Objectives
Upon completion of the course, students should have:
solid understanding of the basic calculus concepts such as functions, limits, continuity, derivatives and integration
basic understanding of the fundamental linear algebra concepts like system of linear equations, matrices, spaces, vectors, least
squares solution, Eigenvalues/Eigenvectors of matrices, quadratic optimization and its iterative solution methods
basic knowledge of differential equations
hands on practice with the analytic manipulation of basic mathematical expressions and the solution of basic calculus, linear
algebra and differential equation related problems
experience to implement all the numerical techniques studied using MATLAB scientific software
Course Learning Outcomes
By the end of the course, the students will be able to
implement all the numerical methods studied using MATLAB
In Calculus:
identify whether a given formula is a function or not
determine the inverse of a function if exists
draw a function of a single or more variables and common graphs
draw and solve basic trigonometric, exponential and logarithmic functions
evaluate basic limits
define the formal meaning of continuity and differentiability
calculate the derivatives of a function by analytic and numerical methods
solve implicit differentiation problems
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9060528 - 1
MIDDLE EAST TECHNICAL UNIVERSITY
COURSE SYLLABUS
find the roots and critical points (minimum and maximum points) of a function by using analytical and numerical techniques
find the linear or higher order approximation of a function
evaluate basic single and double integrals
In Linear algebra:
translate a verbal statement of variables in the form of a linear equations
formulate and solve a system of linear equations
calculate the determinant and inverse of a matrix
define a vector and a subspaces
prove basic linear algebra properties and equations
find the Eigenvalues and Eigenvectors of a square matrix
formulate and solve basic least square problems (quadratic optimization)
solve a quadratic optimization problem using basic iterative methods (steepest descent, conjugate gradient, etc)
In Differential Equations:
classify and interpret differential equations
solve first order linear, separable and exact differential equations analytically
Instructional Methods
Lectures
Written and MATLAB application homeworks
Tentative Weekly Outline
Week
Topic
1
Functions, Common Graphs
Relevant Reading
Assignments
Paul's Online Math
Notes, Calculus I,
related sections
Paul's Online Math
2
Limits, Continuity
Notes, Calculus I,
related sections
Paul's Online Math
3
Derivative, Application of Derivatives
4
Integrals, Applications of Integrals
5
Systems of Equations
6
Matrices, Matrix Arithmetic & Operations
Notes, Calculus I,
related sections
Paul's Online Math
Notes, Calculus I,
Homework 1
related sections
Paul's Online Math
Notes, Algebra,
related sections
Paul's Online Math
Notes, Algebra,
related sections
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9060528 - 1
MIDDLE EAST TECHNICAL UNIVERSITY
COURSE SYLLABUS
Week
Topic
Relevant Reading
Assignments
Paul's Online Math
7
Inverse Matrices and Elementary Matrices, LU-Decomposition
8
Midterm Exam
9
Determinants, Vectors, Dot Product, Euclidean n-Space
Notes, Algebra,
related sections
Paul's Online Math
Notes, Algebra,
Homework 2
related sections
Paul's Online Math
Vector Spaces, Linear Independence, Fundamental Subspaces
10
Notes, Algebra,
related sections
Paul's Online Math
11
Least Squares, Eigenvalues and Eigenvectors, Diagonalization
12
Quadratic optimization, Iterative Solution Methods
Notes, Algebra,
related sections
Handouts
Paul's Online Math
Differential Equations - I
13
Notes, Differential
Equations, related
Homework 3
sections
Paul's Online Math
Differential Equations - II
14
Notes, Differential
Equations, related
sections
Course Textbook(s)
Paul's Online Math Notes:
http://tutorial.math.lamar.edu/download.aspx
(for Calculus, Linear Algebra and Differential Equations)
Course Material(s) and Reading(s)
Material(s)
Additional lecture notes will be provided by the instructor.
Reading(s)
Additional lecture notes will be provided by the instructor.
Supplementary Readings / Resources / E-Resources
Resources
FR Giordano, MD Weir, WP Fox, A first Course in Mathematical Modeling, Intern Thomson Publishing Company, 2nd Edition, 1997.
N Gerhenfeld, The Nature of Mathematical Modeling, Cambridge University Press, 1999.
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9060528 - 1
MIDDLE EAST TECHNICAL UNIVERSITY
COURSE SYLLABUS
PV O?Neil, Advanced Engineering Mathematics. Brooks/Cole Publishing Company, 4th Edition, 1995.
G Strang, Introduction to Linear Algebra, Wellesley-Cambridge Press, 4th Edition, 2009.
DG Luenberger, Linear and Nonlinear Programming, Springer, 2nd Edition, 2003.
Course Grading
Deliverable
Grade Points
Midterm exam
25
Final exam
25
Three homework
50
Total
100
Course Policies
Class Attendance
Student should attend at least 50% of the lectures to get a valid grade.
Class Participation
Students are encouraged to participate in-class and online discussions.
Your participation level may change your grades.
Late Submission of Assignments
Late policy is as follows: -10% will be deducted from your homework grade for each day after the deadline is past. Homework will not be
accepted after 5 days delay.
Final Exam Entrance Conditions
If student misses any of the in-class exams, the grade will be N/A outomatically.
Information for Students with Disabilities
To obtain disability related academic adjustments and/or auxiliary aids, students with disabilities must contact the course instructor and the
ODTÜ Disability Support Office as soon as possible. If you need any accommodation for this course because of your disabling condition,
please contact me. For detailed information, please visit the websie of Disability Support Office: http://engelsiz.metu.edu.tr/
Academic Honesty
The METU Honour Code is as follows: "Every member of METU community adopts the following honour code as one of the core principles of
academic life and strives to develop an academic environment where continuous adherence to this code is promoted. The members of the METU
community are reliable, responsible and honourable people who embrace only the success and recognition they deserve, and act with integrity in their
use, evaluation and presentation of facts, data and documents."
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