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Advanced Mathematics
Cursusdoel
After completing this course students are able to:
Midterm exam: 1, 2, 3
Final exam: 1, 2, 3
Hand-in exercises: 1, 2, 3
- develop conceptual arguments and reasoning to provide formal mathematical proofs;
- summarize a variety of advanced mathematical methods including Taylors theorem in more than one variable and the implicit function theorem;
- understanding basic applications of the implicit function theorem.
Midterm exam: 1, 2, 3
Final exam: 1, 2, 3
Hand-in exercises: 1, 2, 3
Vakinhoudelijk
Content
The course consists of three parts. In the first part basic conceptual notions of mathematical analysis are developed, such as limits, continuity, differentiation, sequences and series, uniform convergence etc. In the second part these fundamental concepts are blended with linear algebra and extended to the multivariable case resulting in the main theorems of mathematical analysis: Taylors theorem and the implicit function theorem. In the third part we study various applications of the implicit function theorem.
The course consists of three parts. In the first part basic conceptual notions of mathematical analysis are developed, such as limits, continuity, differentiation, sequences and series, uniform convergence etc. In the second part these fundamental concepts are blended with linear algebra and extended to the multivariable case resulting in the main theorems of mathematical analysis: Taylors theorem and the implicit function theorem. In the third part we study various applications of the implicit function theorem.
Format
Syllabus and projects
Every week exercises and projects must be handed in. The instructor and his assistants correct and return these to the students for discussion. The exercises serve as an integrated component of the learning process.
In addition to the contact hours, each student is expected to work ten hours a week on the course.
This time should be devoted to:
- reviewing the material of the preceding lecture;
- finishing the exercises started in the preceding problem session;
- preparing exercises to hand in;
- studying the corrections of the previously returned hand-in problems, making sure everything is clear.
Software packages
In the course the computer package Mathematica and Matlab can be used as a tool for computations.
Syllabus and projects
Every week exercises and projects must be handed in. The instructor and his assistants correct and return these to the students for discussion. The exercises serve as an integrated component of the learning process.
In addition to the contact hours, each student is expected to work ten hours a week on the course.
This time should be devoted to:
- reviewing the material of the preceding lecture;
- finishing the exercises started in the preceding problem session;
- preparing exercises to hand in;
- studying the corrections of the previously returned hand-in problems, making sure everything is clear.
Software packages
In the course the computer package Mathematica and Matlab can be used as a tool for computations.
Werkvormen
UCU sci 3 course
Toetsing
Final exam
Verplicht | Weging 30% | ECTS 2,25
Hand-in exercise
Verplicht | Weging 40% | ECTS 3
*midterm FEEDBACK*
Niet verplicht
Midterm exam
Verplicht | Weging 30% | ECTS 2,25
Ingangseisen en voorkennis
Ingangseisen
Er moet voldaan zijn aan de cursus:
En er moet voldaan zijn aan minimaal één van de cursussen:
- [UCSCIMAT21] Mathematical Methods
- [UCSCIMAT22] Probability and Networks
- [UCSCIMAT23] Analysis and Algebra
Voorkennis
Er is geen informatie over benodigde voorkennis bekend.
Voertalen
- Engels
Cursusmomenten
Gerelateerde studies
Tentamens
Er is geen tentamenrooster beschikbaar voor deze cursus
Verplicht materiaal
| Materiaal | Omschrijving |
|---|---|
| DIVERSE | Lecture notes |
Aanbevolen materiaal
Er is geen informatie over de aanbevolen literatuur bekend
Coördinator
| Onbekend | - |
Docenten
| Onbekend | - |
Inschrijving
Let op: deze cursus is niet toegankelijk voor studenten van andere faculteiten, bijvakkers mogen zich dus niet inschrijven.
Naar OSIRIS-inschrijvingen
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