This course introduces basic methods, algorithms and programming techniques to solve mathematical problems. The course is designed for students to learn how to develop numerical methods and estimate numerical errors using basic calculus concepts and results.
Prerequisite(s)
MCB1002-TBD Calculus II, IE2002 Introduction to Programming
Corequisite(s)
-
Special Requisite(s)
The minimum qualifications that are expected from the students who want to attend the course.(Examples: Foreign language level, attendance, known theoretical pre-qualifications, etc.)
Instructor(s)
Lecturer Tuğçe Beldek
Course Assistant(s)
Arş. Gör. Abdullah Osman
Schedule
This course is not offered in this semester.
Office Hour(s)
This course is not offered in this semester.
Teaching Methods and Techniques
Principle Sources
1. Burden, R.L. and Faires, J.D. Numerical Analysis. Brooks/Cole. (2001)
2. Sauer, T. Numerical Analysis: Pearson 2/E. (2013)
3. Punch, W.F. and Enbody, R.M. The Practice of Computing Using Python, Pearson 3/E. (2018)
4. Gaddis,T. Starting Out with Python, Pearson 4/E. (2019)
Other Sources
Anaconda Python, Jupyter Notebook
Course Schedules
Week
Contents
Learning Methods
1. Week
Introduction to mathematical preliminaries; Review of Calculus; The Bisection Method
Oral Presentation
2. Week
Fixed-Point Iteration;
The Newton's Method
Oral Presentation
3. Week
The Secant Method
Oral Presentation
4. Week
The Method of False Position;
Error Analysis for Iterative Methods;
Accelerating Convergence
Oral Presentation
5. Week
Interpolation and the Lagrange Polynomial
Oral Presentation
6. Week
Data Approximation and Neville's Method
Oral Presentation
7. Week
Divided Differences: Forward, Backward and Centered Differences
Oral Presentation
8. Week
MIDTERM EXAM
9. Week
Numerical Differentiation: Three and Five-Point Formulas Numerical Integration
Oral Presentation
10. Week
Taylor Series Method Numerical Differentiation: Second Derivative Midpoint Formula;
Oral Presentation
11. Week
Numerical Integration: the Trapezoidal and Simpson's Rule
Oral Presentation
12. Week
Numerical Integration: Composite Numerical Integration and Round-Off Error Stability
Ability to apply theoretical and practical knowledge gained by Mathematics, Science and their engineering fields and ability to use their knowledge in solving complex engineering problems.
PO-2
Ability of determining, defining, formulating and solving complex engineering problems; for that purpose develop the ability of selecting and implementing suitable models and methods of analysis.
PO-3
Ability of designing a complex system, process, device or product under real world constraints and conditions serving certain needs; for this purpose ability of applying modern design techniques
PO-4
Ability of selecting and using the modern techniques and devices which are necessary for analyzing and solving complex problems in engineering implementations; ability of efficient usage of information technologies.
PO-5
Ability of designing experiments, conducting tests, collecting data and analyzing and interpreting the solutions to investigate of complex engineering problems or discipline-specific research topics.
PO-6
Ability of working efficiently in intra-disciplinary and multi-disciplinary teams; individual working ability and habits.
PO-7
Ability of verbal and written communication skills; and at least one foreign language skills, ability to write effective reports and understand written reports, ability to prepare design and production reports, ability to make impressive presentation, ability to give and receive clear and understandable instructions
PO-8
Awareness of importance of lifelong learning; ability to access data, to follow up the recent innovation in science and technology for continuous self-improvement.
PO-9
Conformity to ethical principles; knowledge about occupational and ethical responsibility, and standards used in engineering applications.
PO-10
Knowledge about work life implementations such as project management, risk management and change management; awareness about entrepreneurship and innovativeness; knowledge about sustainable development.
PO-11
Knowledge about effects of engineering applications on health, environment and security in global and social dimensions, and on the problems of the modern age in engineering; awareness about legal outcomes of engineering solutions.
Learning Outcomes
LO-1
Demonstrates factual knowledge including the mathematical notation and terminology used in this course
LO-2
Interprets, and uses the vocabulary, symbolism, and basic definitions used in numerical analysis including those related to topics learned in calculus and algebra
LO-3
Describe the fundamental principles including the laws and theorems arising from the concepts, Identify and apply the properties and theorems that result directly from the definitions as well as statements discovered in calculus
LO-4
Applies the facts, formulas, and techniques learned in this course to develop and use algorithms and theorems to find numerical solutions and bounds on their error to various types of problems including root finding, polynomial approximation, numerical differentiation, numerical integration
LO-5
Gains the ability to use MS Excel and Python to solve numerical problems and acquire a level of proficiency in the fundamental concepts and applications necessary for further study in academic areas requiring numerical analysis as a prerequisite for graduate work or for work in occupational fields
