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Kies de Nederlandse taal
Course module: 202001198
202001198
Calculus 1B
Course info
Course module202001198
Credits (ECTS)3
Course typeStudy Unit
Language of instructionEnglish
Contact persondr. T. Akkaya
E-mailt.akkaya@utwente.nl
Lecturer(s)
PreviousNext 3
Contactperson for the course
dr. T. Akkaya
Lecturer
dr. T. Akkaya
Lecturer
prof.dr.ir. N.E. Benes
Lecturer
ir. F.W. Hoeksema
Lecturer
dr.ir. P. van 't Hof
Academic year2020
Starting block
1B
Application procedureYou apply via OSIRIS Student
Registration using OSIRISYes
Aims
After successfully finishing this module a student is capable of:
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 convergence radius by the ratio test
  • calculate Taylor series and polynomials

3. solve linear differential equations
  • solve first order equations using integrating factor
  • solve second order homogeneous equations with constant coefficients using the characteristic equation
  • solve first and second order 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
  • calculate absolute value and argument of a complex number to express the complex number in polar form
  • apply the complex arithmetic operations
  • find roots of a complex number and solve binomial equations
Content
Like Cal1A, the course Cal1B is also a course in the line of basic Mathematics. But Cal1B will treat more new concepts as Cal1A did. Cal1B starts with a well-known topic: integration theory. The integral of a function of one variable is introduced and integration techniques such as substitution and integration by parts are discussed. Some applications are presented. The follow-up course Cal2 will extend the integral calculus for functions of two or three variables.

Next, a short introduction into power series is given, with the Taylor series as its main example.

Another new concept is the notion of differential equation. The idea behind a differential equation is discussed. A method to solve first order linear differential equations is presented in more detail. Also a basic method to solve second order linear differential equations is presented, but details are left out. In this method we will make use of the system of complex numbers. This system is an extension of the real number system and gives solutions to all algebraic equations. In this number system the equation [endif]--> has a solution. Attention is paid to the geometric representation of a complex number and to algebraic operations on complex numbers.
 
Assumed previous knowledge
Introduction to Mathematics + Calculus 1A
Module
Module 2
Participating study
Bachelor Chemical Science & Engineering
Required materials
Book
Thomas' Calculus, Early Transcendentals. ISBN: 9781781344170
Recommended materials
-
Instructional modes
Assessment

Lecture

Self study with assistance

Self study without assistance

Tutorial

Tests
Calculus 1B

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Kies de Nederlandse taal