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Cursus: 202001195
Calculus 1B
Cursus informatie
Studiepunten (ECTS)3
VoertaalEngels P. van 't Hof
VorigeVolgende 3
S.C. Dummer
Examinator P. van 't Hof
Contactpersoon van de cursus P. van 't Hof
Docent P. van 't Hof
ir. F.A. de Kogel
OpmerkingPart of module 2 B-BMT
AanmeldingsprocedureZelf aanmelden via OSIRIS Student
Inschrijven via OSIRISJa
After successfully finishing this study unit a student is able to:

1. work with elementary properties of integrals and calculate integrals using different techniques, for functions of 1 variable
  • formulate Riemann sums
  • formulate and use the Fundamental Theorem of Calculus
  • calculate integrals using anti-derivates
  • calculate integrals using the substitution method
  • calculate integrals using the technique of integration by parts
  • calculate improper integrals using limits
2. work with power series and Taylor series, for functions of 1 variable
  • calculate the radius of convergence of a power series
  • calculate Taylor series and Taylor polynomials
3. solve first- and second-order ordinary differential equations
  • solve first-order separable differential equations using separation of variables
  • solve first-order linear differential equations using the integrating factor
  • solve first- and second-order linear homogeneous differential equations with constant coefficients using the characteristic equation
  • solve first- and second-order linear inhomogeneous differential equations with constant coefficients using the method of undetermined coefficients
  • solve initial / boundary value problems
4. work with complex numbers
  • plot (sets of) complex numbers in the plane
  • convert complex numbers from Cartesian form to polar form and vice versa
  • apply complex arithmetic operations
  • find roots of a complex number and solve binomial equations
Just like Calculus 1A, Calculus 1B is a course in the basic mathematics programme of the UT, called the Mathematics Line.

Calculus 1B starts with a topic many students are already familiar with: integration theory. The integral of a function of one variable is introduced. Integration techniques such as substitution and integration by parts are discussed, as well as the concept of improper integrals. The follow-up course Calculus 2 will continue with integral calculus for functions of two or three variables.

Next, a short introduction to power series is given, with Taylor series and Taylor polynomials as its main application.

Another new concept that is introduced is that of a differential equation. The idea behind a differential equation is discussed. Methods for solving first-order separable differential equations and first-order linear differential equations are presented in detail. A method for solving second-order linear differential equations with constant coefficients is also presented, but several details are left out.

Before second-order linear differential equations are discussed, the set of complex numbers is introduced. Different representations of complex numbers are presented, as well as algebraic operations on complex numbers and solving equations involving complex numbers.
Introduction to Mathematics + Calculus 1A
Participating study
Bachelor Biomedische Technologie
Module 2
Verplicht materiaal
Thomas' Calculus, Early Transcendentals. ISBN: 9781781344170
Aanbevolen materiaal



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Calculus 1B


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