Calculus and Linear Algebra (2025/2026: Semester 1 – Fall)

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Cursusdoel

After completing this course students are able to:
  1. apply basic techniques of single-variable calculus, such as differentiation, integration and Taylor expansions,
  2. find solutions to simple ordinary differential equations,
  3. apply basic techniques of linear algebra, including matrix diagonalization,
  4. optimize functions of several variables, with and without constraint,
  5. understand and extend these techniques beyond the level of recipes so they can be applied to new problems in their future field of study,
  6. make basic use of the symbolic manipulation program Mathematica for the purpose of evaluating expressions and creating graphs.
Relationship between assessment and learning goals:
  1. mid-term exam: 1, 2, 3, 4
  2. final exam: 1, 2, 3, 4
  3. Take-home assignments: 1, 2, 3, 4, 5, 6

Vakinhoudelijk

This introductory course focuses on basic concepts of calculus starting with functions of a single variable. First you explore simple linear and nonlinear differential equations. Such equations are key in explaining the dynamic behavior of many different systems in a wide variety of fields. This serves as a motivation to learn about techniques, such as differentiation, integration, expansion in a small variable, and complex numbers.
Next you learn to use powerful tools to study systems of many variables: linear vector spaces, linear operators (matrices) in such spaces, and key properties of matrices. You also extend techniques such as differentiation to functions of several variables and learn about their geometrical representation. The course concludes with various approaches to optimization of functions of several variables.
The techniques you learn in this course have proven to be highly effective in a wealth of areas as will be illustrated by examples in various fields. Some attention is paid to underlying mathematical foundations, but the focus is on understanding the methods and on learning to apply the techniques.
Format
There are four class hours per week of lectures and guided tutorials. During the tutorials the students work on problems and give presentations. In addition to the lectures and tutorials, students are expected to work for ten hours a week on average on self-study reading and problem solving, doing take-home assignments to be handed in, preparing their student presentations and studying for the exams.

Werkvormen

UCU SCI 1 course

Toetsing

mid-term exam

Verplicht | Weging 25% | ECTS 1,88

final exam

Verplicht | Weging 25% | ECTS 1,88

Exercises

Verplicht | Weging 20% | ECTS 1,5

Assignment

Verplicht | Weging 20% | ECTS 1,5

Class participation

Verplicht | Weging 10% | ECTS 0,75

*midterm FEEDBACK*

Niet verplicht

Ingangseisen en voorkennis

Ingangseisen

Er is geen informatie over verplichte ingangseisen bekend.

Voorkennis

Secondary school knowledge of mathematics is required. Passed final high school exams in IB Analysis & Approaches Higher Level Mathematics, Dutch VWO “Wiskunde B”, or similar “Calculus and Algebra” courses from a foreign high school should be sufficient. Students who do not meet this math requirement should take UCACCMAT01 first.

Voertalen

  • Engels

Competenties

  • Presenteren

Cursusmomenten

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Tentamens

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Verplicht materiaal

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Aanbevolen materiaal

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Coördinator

dr. V.N.E. Blasjö v.n.e.blasjo@uu.nl

Docent

Inschrijving

Let op: deze cursus is niet toegankelijk voor studenten van andere faculteiten, bijvakkers mogen zich dus niet inschrijven.

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