Calculus for LST
Faculteit  Science and Engineering 
Jaar  2022/23 
Vakcode  WBLT00605 
Vaknaam  Calculus for LST 
Niveau(s)  bachelor 
Voertaal  Engels 
Periode  semester I b 
ECTS  5 
Rooster  rooster.rug.nl 
Uitgebreide vaknaam  Calculus for LST  
Leerdoelen  At the end of the course, the student is able to: 1.apply differentiation to find local and absolute extreme values of a given function, and can calculate integrals using standard techniques (substitution rule, integration by parts) to compute areas and average function values. 2.calculate Taylor expansions of concrete functions and use these to compute integrals and solve equations approximately. 3. calculate with complex numbers, can plot them in the complex plane, is able to formulate and use De Moivre's Theorem, can compute powers and 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. 4.solve separable firstorder differential equations and can calculate the general solution of a firstorder linear differential equation by means of variation of constants. 5.solve homogeneous secondorder differential equations with constant coefficients and calculate a particular solution for nonhomogeneous equations using the method of undetermined coefficients. 6.use partial differentiation to find extreme values and approximations of functions of 2 (or 3) variables. 7.set up and evaluate 2D and 3D integrals to compute volumes. 8.use partial differentiation to find extreme values and approximations of functions of 2 (or 3) variables. 9.set up and evaluate 2D and 3D integrals to compute volumes. 

Omschrijving  In this course, basic concepts (and skills) in the area of calculus are discussed, to prepare for and support other courses in the curriculum. The course starts with a quick refresher regarding highschool calculus, with topics like derivatives, extreme values, integration (applications and techniques), epower, natural logarithm, (co)sine functions, etc. Then Taylor expansions are used to solve problems approximately. Subsequently, complex numbers and functions are introduced, an imaginary extension of the real numbers. Differential equations are solved to describe processes in physics, life sciences, etc. This topic includes: initial value problems, separation of variables, variation of constants, homogeneous and inhomogeneous equations, and conversion of complex solutions into realvalued solutions. As final topic, multivariable calculus is introduced, where partial differentiation is used for extreme values and approximations of functions of 2 (or more) variables. Elementary 2D/3D integration is used for e.g. computing volumes and simple applications in physics. The material is illustrated through examples that focus on the applications of mathematical techniques. 

Uren per week  
Onderwijsvorm  Hoorcollege (LC), Werkcollege (T)  
Toetsvorm 
Opdracht (AST), Schriftelijk tentamen (WE), Tussentoets (IT)
(The average of the 3 best results of the 4 homeworksets leads to the grade HW. The midterm and final exam lead to the grades MT and ET. The final grade is computed from: 1) When HW en MT both higher than ET: grade = (3*ET + MT + HW)/5 (2) When only HW higher than ET: grade = (4*ET + HW)/5 (3) When only MT higher than ET: grade = (4*ET + MT)/5 4)) 

Vaksoort  bachelor  
Coördinator  Dr. T.K. Gebretekle  
Docent(en)  Dr. T.K. Gebretekle ,Dr. T.F. Görbe ,dr. ir. R. Luppes  
Verplichte literatuur 


Entreevoorwaarden  Topics like differentiation, integration, epower, natural logarithm, sine and cosine functions are assumed to be known.  
Opmerkingen  
Opgenomen in 
