Calculus for LST

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Faculteit Science and Engineering
Jaar 2022/23
Vakcode WBLT006-05
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 first-order differential equations and can calculate the general solution of a first-order linear differential equation by means of variation of constants.

5.solve homogeneous second-order differential equations with constant coefficients and calculate a particular
solution for non-homogeneous 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 high-school calculus, with topics like derivatives, extreme values, integration (applications and techniques), e-power, 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 real-valued solutions. As final topic, multi-variable 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
Titel Auteur ISBN Prijs
Calculus. Early transcendentals.- 9th Edition James Stewart, London: Thomson Learning 9780538498876
Entreevoorwaarden Topics like differentiation, integration, e-power, natural logarithm, sine and cosine functions are assumed to be known.
Opmerkingen
Opgenomen in
Opleiding Jaar Periode Type
BSc Courses for Exchange Students: Chemistry - Chemical Engineering - semester I b
BSc Life Science and Technology 1 semester I b verplicht