Integral Calculus of Many Variables
| Title | ΟΛΟΚΛΗΡΩΤΙΚΟΣ ΛΟΓΙΣΜΟΣ ΠΟΛΛΩΝ ΜΕΤΑΒΛΗΤΩΝ / Integral Calculus of Many Variables |
| Code | ΜΑΥ2206 |
| Faculty | Sciences |
| School | Physics |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Winter/Spring |
| Coordinator | Charalampos Moustakidis |
| Common | No |
| Status | Active |
| Course ID | 600021664 |
Programme of Study: PROGRAMMA SPOUDŌN 2022
Registered students: 175
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| KORMOS | Compulsory Course | 3 | 2 | 6 |
| Academic Year | 2025 – 2026 |
| Class Period | Winter |
| Faculty Instructors |
|
| Instructors from Other Categories |
|
| Weekly Hours | 4 |
| Total Hours | 52 |
| Class ID | 600280720
|
Course Type 2021
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600280720
- At the Website of the School: https://www.physics.auth.gr/courses/152
- eLearning (Moodle): https://elearning.auth.gr/course/view.php?id=6245
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
General Prerequisites
- Basic knowledge of differential and integral calculus of one variable.
- Understanding of fundamental concepts in linear algebra, such as vectors, matrices, and basic operations on them.
- Familiarity with vector calculus, including concepts of vector-valued functions, vector fields, partial derivatives, gradient, divergence, and curl.
Learning Outcomes
- Describe and analyzes curves and surfaces using parametric equations and geometric quantities.
- Compute double and triple integrals in various coordinate systems using appropriate transformations.
- Applie the theorems of Green, Gauss, and Stokes to solve physical field problems.
- Calculate line and surface integrals in physical applications such as work, flux, and mass.
General Competences
- Apply knowledge in practice
- Be critical and self-critical
- Advance free, creative and causative thinking
Course Content (Syllabus)
- Introduction to the theory of curves: parametric representation of a curve, arc length, tangent and normal plane, curvature and torsion, Frenet frame.
- Introduction to the theory of surfaces: parametric representation of a surface, first fundamental form, metric tensor, covariant and contravariant components, surface element.
- Curvilinear coordinates: coordinate surfaces and curves, area element, volume element, Cartesian, spherical and cylindrical coordinates, gradient, divergence, and curl.
- Double integrals: definition and properties of the double integral, geometric interpretation, calculation of area of a planar region.
- Double integrals: change of variables in integration, applications.
- Triple integrals: definition and properties, change of variables in integration, applications.
- Introduction to line integrals of the first and second kind: definitions and properties of line integrals, relationship between line integrals of the first and second kind, applications.
- Green’s theorem – potential function and irrotational fields in the plane – line integrals in multiply connected regions.
- Surface area – surface integrals of the first and second kind.
- Gauss’s and Stokes’s theorems.
- Applications of Gauss’s and Stokes’s theorems – potential function and irrotational fields, applications in multiply connected regions.
- Applications of double and triple integrals – computation of mass, moment of inertia, center of mass, gravitational potential, and Coulomb potential.
Educational Material Types
- Notes
- Book
Use of Information and Communication Technologies
Use of ICT
- Use of ICT in Course Teaching
- Use of ICT in Communication with Students
Description
- Use of Zoom platform for online teaching when necessary.
- Use of the e-learning platform for uploading exercises and lecture notes.
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 140 | 4.7 | ✓ | ||
| Tutorial | 40 | 1.3 | ✓ | ||
| Total | 180 | 6 |
Student Assessment
Description
- Class participation: Assessment of active participation, understanding, and ability to explain concepts.
- Problem-solving exercises: Evaluation of practical skills and applications through exercises during the semester.
- Written exams: The main method for assessing understanding of theory and application of mathematical concepts and techniques.
Student Assessment methods
- Written Exam with Extended Answer Questions (Formative)
- Written Assignment (Formative, Summative)
- Written Exam with Problem Solving (Formative, Summative)
Bibliography
Course Bibliography (Eudoxus)
-Απειροστικός λογισμός, Briggs W., Cochran L., Gillett B., Εκδόσεις Κριτική, 2018(Eύδοξος: 77109719)
-Διανυσματική Ανάλυση Β' Έκδοση, Μουστακίδης Χ.,Εκδόσεις Σοφία,2020( Εύδοξος: 94689294)
-Διανυσματικός Λογισμός, Λεοντάρης Γ., Εκδόσεις Θεοδωρίδη,2015(Εύδοξος: 50658616)
-Εφαρμοσμένη Ανάλυση και Θεωρία Fourier, Φιλιππάκης Μ., Εκδόσεις Τσότρας,2014(Εύδοξος: 68403139)
Last Update
21-07-2025
