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)
supremum and infimum of sets of real numbers; limits of sequences; limits of functions and continuity (also of functions in several variables); derivatives of functions in one variable and applications: tangent line, velocity and accelaration; Rolle's theorem and applications: Lagrange's theorem, approximation by Taylor polynomials and L'Hospital's rule; extreme values of functions in one variable; partial derivatives and differentiable functions in several variables; extreme values of functions in several variables; the inverse and implicit function theorem's and applications; bounded extreme values; the integral of a continuous function on a closed interval and applications: area, work and distance; the fundamental theorem of integral calculus; integration techniques; improper integrals.

Analysis II (second semester)
advanced integral notions: line integral, double integral, surface integral and volume integral; applications of integral calculus: area, volume, work and distance; main theorems of integral calculus: Green, Stokes and Gauss-Ostrogradsky; series and convergence criteria; series of functions: power series and goniometric series; ordinary differential equations; elementary solution methods; differential equations with constant coefficients; systems of differential equations; solving linear differential equations using power series.

Course material

Course text (Required) : Analyse: afleiden, integreren, wiskundige software, Analyse I, A. Debrouwere, S. Caenepeel, VUB, 2220170009506, 2022
Course text (Required) : Analyse: afleiden, integreren, wiskundige software, Analyse II, A. Debrouwere, S. Caenepeel, VUB, 2220170009476, 2022
Course text (Required) : Analyse: afleiden, integreren, wiskundige software, Oefeningen Analyse I, A. Debrouwere, S. Caenepeel, VUB, 2220170009490, 2022
Course text (Required) : Analyse: afleiden, integreren, wiskundige software, Oefeningen Analyse II, A. Debrouwere, S. Caenepeel, VUB, 2220170009483, 2022
Course text (Required) : Analyse: afleiden, integreren, wiskundige software, Formularium analyse, A. Debrouwere, S. Caenepeel, VUB, 2220170009513, 2022

Additional info

Does not apply

Learning Outcomes

General competencies

In many branches of mathematics and other scientific disciplines concepts like derivatives, integrals and differential equations are frequently used. The aim is to deliver the students a profound knowledge of these and related subjects. During the lectures, the fundamental theoretical aspects are discussed, while during the problem sessions the computational tecniques are practiced. We have the following specific learning outcomes

1. The student is able to formulate the basic concepts (definitions and theorems) from mathematical analysis in his own words.

2. The student is able to reason about the basic concepts of mathematical analysis. More specifically, the student is able to construct (counter)examples and to answer insight questions about the basic concepts.

3. The student can formulate the proofs of the theorems in his own words.

4. The student has insight into the proofs of the theorems. More specifically, the student is able to explain steps in the proofs and answer insight questions about the proofs.

5. The student masters the learned computational techniques and can apply them to solve mathematical exercises.

6. The student is able to solve simple problems from physics and engineering sciences using the learned computational techniques.

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:

Examen 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: tijdens 6de week van het eerste semester; telt enkel mee indien resultaat beter dan resultaat examen

Additional info regarding evaluation

First session:
Analysis I (first semester): written exam
Analysis II (second semester): written and oral exam

Second sesion:
Analysis I and II: written and oral exam

Participation to all the partial tests is needed to obtain a final grade. The following additional requirement has to be satisfied to pass: an average grade of 7/20 must be achieved on Analysis II. 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