## Calculus for Artificial Intelligence

 Faculteit Science and Engineering Jaar 2021/22 Vakcode WBAI048-05 Vaknaam Calculus for Artificial Intelligence Niveau(s) propedeuse Voertaal Engels Periode semester I b ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Calculus for Artificial Intelligence
Leerdoelen 1. The student can calculate derivatives by applying the product rule, quotient rule, and chain rule, and combinations thereof. In addition, the student can use these techniques to find the local and absolute extreme values of a given function.
2. The student can calculate Taylor expansions of concrete functions and use these expansions to compute limits and
approximations for definite integrals.
3. The student can calculate limits using the limit laws and l'Hopital's rule.
4. The student can calculate integrals using the standard techniques of integration (substitution rule, integration by
parts) and is able to recognize which technique is best used in a given situation.
5. The student can calculate with complex numbers, can plot them in the complex plane, is able to formulate and use De
Moivre's Theorem, can compute roots of a complex number and can solve equations in that way. The student can give
the definition of the complex exponential function and can use that in applications.
6. The student can solve separable first-order differential equations and can calculate the general solution of a first-order
linear differential equation by means of variation of constants.
7. The student can solve homogeneous second-order differential equations with constant coefficients and calculate a
particular solution for non-homogeneous equations using the method of undetermined coefficients.
Omschrijving In this course, basic concepts (and skills) in the area of calculus are discussed.

The course starts with refreshing and improving the basic mathematical skills (BMS) during period 1a. 'Extra' lectures are given to bridge the gap between Mathematics A and Mathematics B, since topics like e-power, natural logarithm, sin and cos are no longer official part of the Mathematics A curriculum at Dutch secondary schools. In the 3rd week a diagnostic test is held: students who score less than 14 out of 20 points are required to follow additional BMS practice sessions. In the 7th week of period 1a the second BMS test is taken. The highest score for the two BMS tests counts for the final grade (see below).

In the actual Calculus course in period 1b, real functions of one real variable are treated: standard and composed functions, models, limits, derivatives, extreme values, Taylor expansions, and integrals (applications and techniques). Subsequently complex numbers are introduced, an imaginary extension of the real numbers. Finally, differential equations are solved to describe processes in physics, economy, medical sciences, etc. This topic includes: initial value problems, directional fields, equilibrium solutions and stability, separation of variables, variation of constants, homogeneous and inhomogeneous equations, and conversion of complex solutions into real-valued solutions.

The material is illustrated through examples that focus on the applications of mathematical techniques.
Uren per week
Onderwijsvorm Hoorcollege (LC), Werkcollege (T)
(Lectures, tutorials, computer-assisted tutorials to improve basic mathematical skills.)
Toetsvorm Schriftelijk tentamen (WE), Tussentoets (IT)
(There are 3 midterm tests, the average grade of the 2 best results of these tests leads to the grade MT. The final exam yields the grade FE. The final grade for the course is computed from: grade=0.7*FE+0.3*MT. Basic Mathematical Skills (BMS, tested in per. 1A) make up 10% of FE.)
Vaksoort propedeuse
Coördinator dr. ir. R. Luppes
Docent(en) dr. ir. R. Luppes
Verplichte literatuur
Titel Auteur ISBN Prijs
Fully worked-out solutions of all homework sets and midterm exam are provided, as well as worked-out solutions for old exams.
Calculus. Early transcendentals. Newest (9th) Edition (International Student Edition), London: Thomson Learning
James Stewart 9780357113516 ca. €  75,00
Entreevoorwaarden The course unit assumes only prior knowledge acquired from Mathematics B (preferably) or Mathematics A as taught in preuniversity programmes (VWO) at Dutch secondary schools (or equivalent).
Opmerkingen The course unit is followed by, and prepares students for, various AI BSc. courses (e.g. Linear Algebra & Multivariable Calculus and Signals & Systems) in which the learning objectives attained are required as prior knowledge.

Artificial Intelligence (BSc) is a Fixed Quota (Numerus Fixus) programme. As a consequence, their courses (course code WBAI) are closed for students that are not registered under the AI BSc programme, unless the course is part of the mandatory curriculum of their programme. If you wish to take this course in your minor – or as part of a so-called ‘unofficial’ pre-master’s – please use the official procedure through the Board of Examiners form.
Opgenomen in
Opleiding Jaar Periode Type
BSc Artificial Intelligence 1 semester I a verplicht
BSc Artificial Intelligence 1 semester I b verplicht
BSc Courses for Exchange Students: AI - Computing Science - Mathematics - semester I b
Pre-master/Fast-track for MSc AI - CCS – CS - Math  (Artificial Intelligence) - semester I b -