Numerical Analysis

1. COURSE INFORMATION:

School	Chemical and Environmental Engineering
Course Level	Undergraduate
Direction	-
Course ID	ENVE 336	Semester	4^th
Course Category	Required
Course Modules	Instruction Hours per Week		ECTS
Lectures and laboratory exercises	6 T=4, E=0, L=2		4
Course Type	Scientific Area
Prerequisites
Instruction/Exam Language	Greek
The course is offered to Erasmus students	No
Course URL	https//www.eclass.tuc.gr/courses/MHPER322/ (in Greek)

2. LEARNING OUTCOMES

Learning Outcomes

Upon successful completion of the course, the student will be able to:
Recognize basic Numerical Analysis methods (approximation, errors, SDE problem solving, arithmetic derivation and integration, etc.)
Applie basic Numerical Analysis methods, using proper software, to problems of Environmental Engineering.
Process experimental and numerical data.
Use the numerical analysis approach to problem solving.
Distinguish the differences between the numerical and the analytical methods of problem solving.
Use the proper computer software in order to solve real life problems of Chemical and Environmental Engineering (scenarios).

General Competencies/Skills

3. COURSE SYLLABUS

Introduction to Numerical Methods- Algorithms – Number representation.
Errors
Equation solving Ι: interval methods (bisection, false position)
Equation solving ΙΙ: initial value methods (fixed point, Newton-Raphson, secant).
Newton-Raphson’s method for non-linear systems. Basic theorems of Mathematical Analysis. Horner’s rule.
Interpolation I: interpolation polynomials (Langrange, divided differences, Newton)
Interpolation II: splines
Regression – Least Squares Method (L.S.E.).. .
Differentiation (method of finite differences , method of coefficient determination, use of interpolation polynomials).
Integration (methods: trapezoid, Simpson e.t.c).
More integration methods.
Initial and Boundary Value Problems for Ordinary Differential Equations.
Applications in Environmental Engineering.

4. INSTRUCTION and LEARNING METHODS - ASSESSMENT

Lecture Method	Direct (face to face) and Lab exercises
Use of Information and Communication Technology	Specialized software; Power point presentations; E-class support
Instruction Organisation	Activity	Workload per Semester (hours)
	- Lectures	52
	- Review exercises/Lab exercises	26
	- Autonomous study	22
	Course Total	100
Assessment Method	I. Written final examination (80%). - Theoretical/applied problems to be solved. II. Laboratory Exercises (20%) OR I .Midterm and final exam (80%=40%+40%) II. Laboratory Exercises (20%)

5. RECOMMENDED READING

Tsanis I, Solved problems of computational hydraulic and environmental engineering, 2005, Ed Tziola.
Chapra S. - Canale R, Numerical methods for Engineers, 7th ed, 2014, Ed Tziola.
Sarris I., karakasidis Th., Numerical methods and Applications for Engineers, 2017, Ed Tziola.
E-class notes

6. INSTRUCTORS

Course Instructor:	Associate Professor T. Daras (Faculty - ChEnvEng)
Lectures:	Associate Professor T. Daras (Faculty - ChEnvEng)
Tutorial exercises:
Laboratory Exercises:	Associate Professor T. Daras (Faculty - ChEnvEng)

Technical University of Crete