6 ECTS credits
150 h study time
Offer 1 with catalog number 1015393ANR for all students in the 2nd semester at a (A) Bachelor - preliminary level.
1 Series
1.1 Convergence of series
1.2 Convergence testst for series
1.3 Taylor series
2. Derivatives of functions of several variables
2.1 Functions of several variables
2.2 Limits and continuity in higher dimensions
2.3 Partial derivatives
2.4 Differentiability, tangent plane and linearization
2.5 The chain rule
2.6 Directional derivatives and gradient
2.7 Taylor’s formula in two variables
2.8 Extreme values and saddle points
2.9 Lagrange multipliers
3. Multiple integrals
3.1 Double integrals
3.2 Applications of double integrals
3.3 Double integrals in polar coordinates
3.4 Triple integrals
3.5 Triple integrals in cylindrical coordinates
3.6 Substitutions in multiple integrals
4. Line integrals and surface integrals
4.1 Line integrals of scalar functions
4.2 Line integrals of vector functions
4.3 Green’s theorem
4.4 Conservative vector fields
4.5 Surfaces
4.6 Surface integrals of scalar functions
4.7 Surface integrals of vector functions
4.8 Stokes' theorem
4.9 Gauss' theorem
In case of a problem with the content or the organization of this course, students are urged to contact the lecturer or an assistant as soon as possible.
Attendance of the WPO classes is mandatory. Students with more than 25% unexusable absences are not allowed at the written exam. The student can bring an official testimonial to the lecturer to excuse for an absence or send an excuse e-mail to inform about exceptional circumstances.
Required material:
Course notes available at VUB bookshop, information on the course organization can be found on the course webpage in the VUB learning platform
The student knows different techniques to prove mathematical properties.
The student is accurate in the use of scientific notations and in the formulation of mathematical properties.
The student knows the basic properties of derivatives of functions of several variables and can use these to solve extreme value problems in several variables.
The student can find a polynomial approximation of a given order for a function of two variables and can find an error estimate.
The student knows the definitions and basic properties of double and triple integrals and can use these to calculate areas and volumes and fysical characteristics such as centre of mass and moments of inertia.
The student knows the substitution rule for double and triple integrals and can use it in transitions to polar coordinates, cylindrical coordinates and spherical coordinates.
The student knows the concepts of ‘line integral’ and ‘surface integral’ and can use these in fysical calculations of work and flux of vector fields.
The students knows the relation between conservative vector fields and potential functions and can use it in calculations of work done in a conservative vector field.
The student knows the theorems of Green, Stokes and Gauss and can use them to calculate work on a closed curve in two and three dimensions and flux through a surface.
The final grade is composed based on the following categories:
Oral Exam determines 50% of the final mark.
Written Exam determines 50% of the final mark.
Within the Oral Exam category, the following assignments need to be completed:
Within the Written Exam category, the following assignments need to be completed:
The final exam consists of a written exam and an oral exam. On the written exam the students have to do exercises of types that were solved during the semester. On the oral exam knowing and understanding of the theoretical part of the course is tested. Each of these two parts counts for 50% of the final score.
No partial scores can be transferred to later exam periods. To get a final score for this course, the student has to take part in all parts of the exam.
This offer is part of the following study plans:
Bachelor of Bioengineering Sciences: Profile Cell and Gene Biotechnology (only offered in Dutch)
Bachelor of Bioengineering Sciences: Profile Chemistry and Bioprocess Technology (only offered in Dutch)
Bachelor of Bioengineering Sciences: Initial track (only offered in Dutch)