
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 antiderivates
 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



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 wellknown 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 followup 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 knowledgeIntroduction to Mathematics + Calculus 1A 
Bachelor Technical Computer Science 
  Required materialsBookThomas' Calculus, Early Transcendentals. ISBN: 9781781344170 

 Recommended materialsInstructional modesAssessment
 Lecture
 Self study with assistance
 Self study without assistance
 Tutorial

 TestsCalculus 1B


 