Applied Analysis

5 ECTS credits
140 h study time

Offer 1 with catalog number 1018649ANR for all students in the 2nd semester at a (A) Bachelor - preliminary level.

Semester

2nd semester

Enrollment based on exam contract

Impossible

Grading method

Grading (scale from 0 to 20)

Can retake in second session

Yes

Taught in

Dutch

Faculty

Faculty of Engineering

Department

Industriële ingenieurswetenschappen

Educational team

Thibaut Vandervelden
An Braeken (course titular)

Activities and contact hours

28 contact hours Lecture
18 contact hours Seminar, Exercises or Practicals

Course Content

Lecture:
The course aims to learn students how to use methods from mathematical analysis,needed to treat scientific and technical issuesthat occur in the curriculum of Industrial Engineering.

Taylor and McLaurin series
Real functions of several variables
Vector Fields
Multiple integrals
Line integrals
Surface integrals and integration theorems

The courses will be organised following the flipped classroom principle:
1. All lectures are available as a video recording on Canvas.
2. The students watch the video recordings in advance, according to the instructions in the learning guide.
3. During joint sessions, the subject matter is discussed and, where necessary, further explained or expanded upon.

Practical exercises:
In the practical exercise sessions students solve problems under supervision. The selected problems are a direct application of knowledge and concepts gained in the lectures.

Course material

Handbook (Recommended) : Wiskunde voor het hoger technisch onderwijs, Deel 1, L. Papula, 2de druk, Academic Service, 9789039526477, 2011
Handbook (Recommended) : Wiskunde voor het hoger technisch onderwijs, Deel 2, L. Papula, 2de druk, Academic Service, 9789039526484, 2011
Handbook (Recommended) : Schaum's Outline of Advanced Mathematics for Engineers and Scientists, M.M. Spiegel, McGraw-Hill, 9780071635400, 2009
Handbook (Recommended) : Calculus, R. Larson, R.P. Hostetler and B.H. Edwards, 11de, Houghton Miffin Company, 9780137559855, 2017
Handbook (Required) : Thomas' Calculus with MyMathLab, 1. BOEK + TOEGANGSCODE: 9781292459707 - 2. TOEGANGSCODE MET ETEXT: 9781292459684, G.B. Thomas, M.D. Weir and J. Hass, 15th, Pearson, 9781292459707, 2023
Course text (Required) : Toegepaste analyse, Braeken - Runacres, VUB, 2220170006482, 2019

Additional info

Description tutoring: after class, by appointment or via e-mail. During weekly afternoon tutoring session (dates to be announced ad valvas at the beginning of the academic year).

Learning Outcomes

Objectives

D1: insight into the utility of Taylor, Mac Laurin and Fourier series (BaLO 1)
D2: can define Taylor, Mac Laurin and Fourier series, together with their convergence criteria (BaLO 1)
D3: understands the basic definitions of real functions of several variables (implicit functions , partial derivatives, total differential, extrema, tangent and normal vector, directional derivative, gradient) (BaLO 1)
D4: can apply the basic definitions of real functions of several variables (implicit functions, partial derivatives, total differential, extrema, tangent and normal vector, directional derivative, gradient) (BaLO 1)
D5: can apply the basic operations (rotation and divergence) for vector fields (BaLO 1)
D6: knows the properties of conservative vector fields and their applications (BaLO 1)
D7: can solve multiple integrals (BaLO 1)
D8: can solve line and surface integrals (BaLO 1)
D9: understands the theorems of Green, Gauss Ostrogradski and Stokes and their applications (BaLO 1)

AD1: reasons and acts in a structured and systematic manner (BaLO 9)

AD2: communicates in Dutch in a comprehensible and structured manner (BaLO 10, 11)

AD3: develops a professional attitude (BaLO 9, 10, 13)

....

Learning outcomes

BaLO_1 To possess in-depth, application-oriented knowledge, understanding and practical skills related to mathematics and science, directed towards engineering applications.
BaLO_9 To demonstrate an engineering attitude: attention to planning, to technical, economic and societal factors as well as managerial implications, assessment of the risks and feasibility of the proposed approach or solution, being result-driven and achieving effective solutions, innovative thinking.
BaLO_10 To correctly handle the scientific and discipline-specific terminology in language relevant to the programme.
BaLO_11 To present and communicate the results of technical and scientific work, in writing, orally and visually.
BaLO_13 To act in an ethical and socially responsible manner with attention to technical, economic, human and sustainability aspects.

Grading

The final grade is composed based on the following categories:
Other Exam determines 100% of the final mark.

Within the Other Exam category, the following assignments need to be completed:

Other Exam with a relative weight of 100 which comprises 100% of the final mark.

Note: Exam time 1st session:
Lecture: written exam: 30% (not transferred to 2nd session)
Practical exercises: written exam exercises: 50% (not transferred to 2nd session)
Evaluation of exercises/tasks performed: 20% (not transferred to 2nd session)
Exam time 2nd session:
Lecture: written exam: 30%
Practical exercises: written exam exercises: 70%

When achieving a result of less than 8 out of 20 on one of the parts, then the lowest number becomes the final result for this course.

Additional info regarding evaluation

An illegitimate absence of more than 25 % for the practical exercise sessions leads to a refusal to participate in the practical exercises exam. This leads to an absent quotation for the related exam. The sanctions taken in the first exam session are transferred to the second exam session.

Allowed unsatisfactory mark

The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.

Academic context