1. COURSE INFORMATION:
School  Environmental Engineering  
Course Level  Undergraduate  
Course ID  MATH 102  Semester  2^{nd} 
Course Category  Required  
Course Modules  Instruction Hours per Week  ECTS  
Lectures and Tutorial Exercises  4 Th=3, E=1, L=0  5  
Course Type  General Background  
Prerequisites  
Instruction/Exam Language  Greek  
The course is offered to Erasmus students  No  
Course URL  https//www.eclass.tuc.gr/courses/MHPER295 (in Greek) 
2. LEARNING OUTCOMES
Learning Outcomes 
This course is continuation of Math 101 and aims to provides the essential mathematical techniques that an engineer needs in the theoretical part of his training as well as what he/she shall need in the computational part of his work. On completion of this course students will be expected to

General Competencies/Skills 

3. COURSE SYLLABUS
Vectors in Two and three Dimensional space. Inner, Cross, triple product. Lines and planes in Space. Polar, Cylindrical and Spherical Coordinates. Curves in the space and their Tangents. Integrals and derivatives of Vector Functions. Velocity, Tangential and Normal components of Acceleration. Functions of two and more variables. Partial Derivatives of functions of several variables, div, grad, Curl. The Chain rule. Directional Derivatives and Gradient vectors. Tangent Planes and differentials. Extreme values and Saddle points. Lagrange multipliers. Line Integrals. Path independence, Conservative Fields. Double and Triple integrals. Applications in Physics and Geometry :Moments and Centers of Mass, Volumes of Solids. Green’s theorem in the plane. Surface Integrals. Stoke’s Theorem. The divergence (Gauss’s) Theorem. 
4. INSTRUCTION and LEARNING METHODS  ASSESSMENT
Lecture Method  Direct (face to face)  
Use of Information and Communication Technology  Eclass support  
Instruction Organisation  Activity  Workload per Semester (hours)  
 Lectures  39  
 Tutorial Exercises  13  
 Autonomous study  73  
Course Total  125  
Assessment Method  Ι. Written final examination (100%) 
5. RECOMMENDED READING

6. INSTRUCTORS
Course Instructor:  Associate Professor A. Manoussakis (Faculty  EnvEng)  
Lectures:  Associate Professor A. Manoussakis (Faculty  EnvEng)  
Tutorial exercises:  Associate Professor A. Manoussakis (Faculty  EnvEng)  
Laboratory Exercises: 