Analysis and an Introduction to Mathematical Software

12 ECTS credits
300 h study time

Offer 1 with catalog number 1017092ANR 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

Mid-term

Yes

Faculty

Faculty of Sciences and Bioengineering Sciences

Department

Mathematics-TW

Educational team

Andreas Debrouwere (course titular)

Activities and contact hours

68 contact hours Lecture
72 contact hours Seminar, Exercises or Practicals

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). Ordinary differential equations; systems of differential equations: integration methods; differential equations with constant coefficients.

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 Publications no. 154)
S. Caenepeel, Analyse II (1ste Bachelor Wiskunde) (VUB Publications no. 117)
S. Caenepeel, Oefeningen bij Analyse I (VUB Publications no. 129)
S. Caenepeel, Oefeningen bij Analyse II (1ste Bachelor Wiskunde) (VUB Publications no. 118)

Learning Outcomes

General competencies

Many disciplines that are important for Scientists and Engineers 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 external 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.

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 99 which comprises 99% of the final mark.
Tentamen with a relative weight of 1 which comprises 1% of the final mark. This is a mid-term test.

Note: during week 6; counts only if the result is better than that of the exam

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, 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 - 22,5 %) + written exam on exercises (the standard formularium may be used - 22,5 %).

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 %).

Second session:

oral exam on the theoretical part (closed book - 45 %).

written exam on exercises (the standard formularium may be used - 55 %).

The following additional minimal requirement has to be satisfied. An average grade of 7/20 must be achieved on the Analysis II part. 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.

Academic context