# CALCULUS I (MATHEMATICS I)

 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: 277
OrientationAttendance TypeSemesterYearECTS
CoreCompulsory Course114

 Academic Year 2021 – 2022 Class Period Winter Faculty Instructors Vasileios Rothos 3hrs Instructors from Other Categories Weekly Hours 3 Class ID 600192482
Course Type 2016-2020
• Background
Course Type 2011-2015
General Foundation
Mode of Delivery
• Face to face
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
Lectures722.4
Tutorial200.7
Interactive Teaching in Information Center200.7
Written assigments50.2
Exams30.1
Total1204
Student Assessment
Description
Final exam 3hrs or final coursework and 2 mideterm courseworks
Student Assessment methods
• Written Exam with Multiple Choice Questions (Formative, Summative)
• Written Exam with Short Answer Questions (Formative, Summative)
• Written Exam with Extended Answer Questions (Formative, Summative)
• Written Assignment (Formative, Summative)
• Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
Βιβλίο [12638355]: ΛΟΓΙΣΜΟΣ ΜΙΑΣ ΜΕΤΑΒΛΗΤΗΣ (Θεωρία-Εφαρμογές σε Maple)., Βασίλειος Ρόθος και Χρυσοβαλάντης Σφυράκης Βιβλίο [25]: ΑΠΕΙΡΟΣΤΙΚΟΣ ΛΟΓΙΣΜΟΣ ΤΟΜΟΣ Ι, FINNEY R.L., WEIR M.D., GIORDANO F.R
Last Update
12-01-2022