
The student will
 be proficient in techniques of solving integrals including improper integrals as well as be familiar with the Fundamental Theorem of Calculus.
 Have a thorough understanding of infinite series and tests for convergence, in particular power and Taylor series.
 Be able to parametrise space curves and find arc lengths and tangent lines.
 Be able to work effectively with functions of two variables including sketching, assessing for differentiability, determining directional derivatives and tangent planes, and finding extrema using methods including Lagrange multipliers.


This course code is only for repeat students who need to retake the exam from last year.
All others: please refer to the new course code 202200179 .
Sequences, series and summation: We shall define sequences and series and consider the convergence of infinite sequences and series. To do this we use a variety of different tests for convergence and also look at approximation errors. Series of particular interest are the pseries, geometric series, and Taylor and Maclaurin expansions. We shall consider summation techniques with particular interest in the relationship with Riemann sums.
Integration: We define integration in the context of areas under curves and use Riemann sums to determine definite integrals from first principles. We study the Fundamental Theorem of Calculus and use some integration techniques such as integration by substitution and integration by parts.
Threedimensional geometry: Our primary interest here is in space curves and surfaces. We parametrise space curves, find arc lengths, and determine the intersection of surfaces as curves. We see the graphs of functions of two variables as surfaces and consider what it means for limits of such functions to exist and how to define continuity. In the context of surfaces we consider families of level curves, tangent planes, directional derivatives and optima. We close off this section with Taylor series in two variables and using Lagrange multipliers to determine optima.




 VoorkennisSecondary school mathematics up to and including an introduction to calculus. Calculus 1 for AT & EE is preferred but not required. 
Bachelor Advanced Technology 
  Verplicht materiaalBookAdams, R.A. and Essex, C. (2018).Calculus: A Complete Course, 9th Edition. Pearson.
ISBN: 9780134154367 

 Aanbevolen materiaalWerkvormenAssessmentAanwezigheidsplicht   Ja 
 HoorcollegeAanwezigheidsplicht   Ja 
 WerkcollegeAanwezigheidsplicht   Ja 
 Zelfstudie geen begeleiding
 Zelfstudie met begeleidingAanwezigheidsplicht   Ja 

 ToetsenCalculus 2 OpmerkingClosed book, written test


 