
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 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 radius of convergence of a power series
 calculate Taylor series and Taylor polynomials
3. solve first and secondorder ordinary differential equations
 solve firstorder separable differential equations using separation of variables
 solve firstorder linear differential equations using the integrating factor
 solve first and secondorder linear homogeneous differential equations with constant coefficients using the characteristic equation
 solve first and secondorder 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 followup 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 firstorder separable differential equations and firstorder linear differential equations are presented in detail. A method for solving secondorder linear differential equations with constant coefficients is also presented, but several details are left out.
Before secondorder 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.




 Assumed previous knowledgeIntroduction to Mathematics + Calculus 1A 
  Required materialsBookThomas' Calculus, Early Transcendentals. ISBN: 9781781344170 

 Recommended materialsInstructional modesAssessmentPresence duty   Yes 
 Lecture
 Self study with assistance
 Self study without assistance
 Tutorial

 TestsCalculus 1B
 Case study


 