Title  ΛΟΓΙΣΜΟΣ Ι (ΜΑΘΗΜΑΤΙΚΑ Ι) / CALCULUS I (MATHEMATICS I) 
Code  101 
Faculty  Engineering 
School  Mechanical Engineering 
Cycle / Level  1st / Undergraduate 
Teaching Period  Winter 
Coordinator  Vasileios Rothos 
Common  Yes 
Status  Active 
Course ID  20000473 
Programme of Study: UPS of School of Mechanical Engineering
Registered students: 348
Orientation  Attendance Type  Semester  Year  ECTS 

Core  Compulsory Course  1  1  4 
Academic Year  2019 – 2020 
Class Period  Winter 
Faculty Instructors 

Instructors from Other Categories  
Weekly Hours  3 
Class ID  600149850

Type of the Course
 Background
Course Category
General Foundation
Mode of Delivery
 Face to face
Digital Course Content
 eStudy Guide https://qa.auth.gr/en/class/1/600149850
 eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=6878
Language of Instruction
 Greek (Instruction, Examination)
Learning Outcomes
After completing this course, students should have developed a clear understanding of the fundamental concepts of single variable calculus and a range of skills allowing them to work effectively with the concepts.
The basic concepts are:
1. Derivatives as rates of change, computed as a limit of ratios
2. Integrals as a "sum," computed as a limit of Riemann sums
After completing this course, students should demonstrate competency in the following skills:
Use both the limit definition and rules of differentiation to differentiate functions.
Sketch the graph of a function using asymptotes, critical points, the derivative test for increasing/decreasing functions, and concavity.
Apply differentiation to solve applied max/min problems.
Apply differentiation to solve related rates problems.
Evaluate integrals both by using Riemann sums and by using the Fundamental Theorem of Calculus.
Apply integration to compute arc lengths, volumes of revolution and surface areas of revolution.
Evaluate integrals using advanced techniques of integration, such as inverse substitution, partial fractions and integration by parts.
Use L'Hospital's rule to evaluate certain indefinite forms.
Determine convergence/divergence of improper integrals and evaluate convergent improper integrals.
Determine the convergence/divergence of an infinite series and find the Taylor series expansion of a function near a point. Fourier series
General Competences
 Apply knowledge in practice
 Work autonomously
 Work in teams
Course Content (Syllabus)
Introduction to Trigonometry. Calculus of functions with one variable. Implicit differentiation. Inverse functions, inverse trigonometric functions and hyperbolic functions. The definition of indefinite integral and properties of indefinite integrals. Integration techniques. Application of integrals. Improper integrals. Parametric equations and polar coordinates. Sequences and Power Series. Taylor Series and Fourier Series. Applications
Keywords
functions, limits, derivatives, integration, power series
Educational Material Types
 Notes
 Slide presentations
 Book
Use of Information and Communication Technologies
Use of ICT
 Use of ICT in Course Teaching
 Use of ICT in Communication with Students
Description
projector PC
Course Organization
Activities  Workload  ECTS  Individual  Teamwork  Erasmus 

Lectures  72  2.4  
Tutorial  20  0.7  
Interactive Teaching in Information Center  20  0.7  
Written assigments  5  0.2  
Exams  3  0.1  
Total  120  4 
Student Assessment
Description
Final exam 3hrs
Student Assessment methods
 Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Βιβλίο [12638355]: ΛΟΓΙΣΜΟΣ ΜΙΑΣ ΜΕΤΑΒΛΗΤΗΣ (ΘεωρίαΕφαρμογές σε Maple)., Βασίλειος Ρόθος και Χρυσοβαλάντης Σφυράκης
Βιβλίο [25]: ΑΠΕΙΡΟΣΤΙΚΟΣ ΛΟΓΙΣΜΟΣ ΤΟΜΟΣ Ι, FINNEY R.L., WEIR M.D., GIORDANO F.R
Last Update
09062020