Calculus for Artificial Intelligence
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBAI04805 
Vaknaam  Calculus for Artificial Intelligence 
Niveau(s)  propedeuse 
Voertaal  Engels 
Periode  semester I 
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 firstorder differential equations and can calculate the general solution of a firstorder linear differential equation by means of variation of constants. 7. The student can solve homogeneous secondorder differential equations with constant coefficients and calculate a particular solution for nonhomogeneous 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 epower, 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 realvalued 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, computerassisted 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 


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 socalled ‘unofficial’ premaster’s – please use the official procedure through the Board of Examiners form. 

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