Offer 1 with catalog number 1008037ANR for all students in the 1st and 2nd semester
at
a (A) Bachelor - preliminary level.
- Semester
- 1st and 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
- Faculteit Ingenieurswetenschappen
- Department
- Mathematics-TW
- Educational team
- Andreas Debrouwere
(course titular)
- Activities and contact hours
-
78 contact hours Lecture
68 contact hours Seminar, Exercises or Practicals
33 contact hours Independent or External Form of Study
- Course Content
Analysis I (First semester)
Limits and continuity (also of vector functions and functions in several variables); limits of sequences; derivatives and their applications: tangent line, velocity and accelaration; Rolle's Theorem and its applications (Cauchy, Lagrange, Taylor, L'Hospital); extreme values in one variable. Partial derivatives and differentiability; extreme values in several variables. The inverse function Theorem, the implicit function Theorem, and their applications; bounded extreme values. Integrals of continuous functions on closed intervals; the fundamental theorem of integral calculus; integration techniques; improper integrals; arc length.
Analysis II (Second semester)
Generalizations of the integral: line integrals, multiple integrals; applications of integrals: (surface) area, volume, work, travelled distance; differential operators and integral theorems (Green's, Stokes' and Gauss' formulas). Series; convergence of series; series of functions; power series; ordinary differential equations; systems of differential equations: integrations method; differential equations with constant coefficients. Integrating linear differential equations using power series. Introduction to MATLAB.
- Course material
- Course text (Required) : Analyse: afleiden, integreren, wiskundige software, Analyse I, S. Caenepeel, VUB, 2220170008653, 2021
Course text (Required) : Analyse: afleiden, integreren, wiskundige software, Analyse II, S. Caenepeel, VUB, 2220170008592, 2021
Course text (Required) : Analyse: afleiden, integreren, wiskundige software, Oefeningen Analyse I, S. Caenepeel, VUB, 2220170008608, 2021
Course text (Required) : Analyse: afleiden, integreren, wiskundige software, Oefeningen Analyse II, S. Caenepeel, VUB, 2220170008585, 2021
Course text (Required) : Analyse: afleiden, integreren, wiskundige software, Formularium analyse, S. Caenepeel, VUB, 2220170008660, 2021
- Additional info
S. Caenepeel, Analyse I (VUB Uitgaven nr. 154).
S. Caenepeel, Analyse II (VUB Uitgaven nr. 128).
S. Caenepeel, Oefeningen bij Analyse I (VUB Uitgaven nr. 129).
S. Caenepeel, Oefeningen bij Analyse II (VUB Uitgaven nr. 127).
- Learning Outcomes
-
General competencies
Many disciplines that are important for engineers or physicists today frequently use concepts like derivatives, integrals, differential equations. Therefore our aim is to deliver the student a profound knowledge of these and related subjects. We stress the internal coherence (the fundaments, definitions and proofs), as well as the internal links (applications in other disciplines, natural sciences, but also economy). During class, the more fundamental aspects are discussed, and, during the problem sessions, we practice computational skills, and apply them to problems.
The course contributes to the realisation of the following Programme Outcomes of the Bachelor in Engineering Sciences:
The Bachelor in Engineering Sciences has a broad fundamental knowledge and understanding of
1. scientific principles and methodology of exact sciences with the specificity of their application to engineering;
4. fundamental, basic methods and theories to schematize and model problems or processes.
The Bachelor in Engineering Sciences can
7. apply quantitative methods and computer software relevant to the engineering discipline in order to solve engineering problems;
12. reason in a logical, abstract and critical way.
- 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:
- Exam
with a relative weight of 1
which comprises 100% of the final mark.
Note: Inclusief tentamen. Voor details raadpleeg de rubriek ‘Aanvullende info m.b.t. examinering’.
- Additional info regarding evaluation
The students should understand the introduced concepts, and be able to handle and apply them. During an oral exam, the level of understanding will be examined. During the written exams and quizzes, more practical skills will be tested: computational skills, and application to solving problems. Active participation during the problem session is taken into account when the final grade is determined. Participation to all the partial exams is needed to obtain a final grade.
First session:
Analysis I (first semester): quizzes (5 %); written exam on the theoretical part (closed book - 20%) + written exam on exercises (the standard formularium may be used - 20 %).
Analysis II (second semester): quizzes (5 %); oral exam on the theoretical part (closed book - 22,5 %) + written exam on exercises (the standard formularium may be used - 22,5 %) + test on matlab (5 %).
Second session:
oral exam on the theoretical part (closed book - 42,5 %).
written exam on exercises (the standard formularium may be used - 52,5 %).
test on matlab (5 %).
A number of additional minimal requirements have to be satisfied. An average grade of 7/20 must be achieved on Analysis II part (with exclusion of matlab). If this requirement is not satisfied, then the maximal final grade that can be obtained is 7/20.
- Allowed unsatisfactory mark
- The supplementary Teaching and Examination Regulations of your faculty stipulate whether an allowed unsatisfactory mark for this programme unit is permitted.