
Upon completion of this course the student is able to:
 work with vectors in 2 and 3 dimensional spaces, complex numbers and complex exponential functions,
 formulate a first and second order differential equation, find a solution for a differential equation, and solve some of the differential equations involving complex numbers,
 understand the principles of logic, set theory and proof techniques,
 work with limits and the definitions of continuity and differentiability and applications.
 focus on writing complete and mathematically coherent solutions to exercises.
 critically read and understand a new mathematical concept,
 verbally communicate mathematical concepts to each other in a team of 4 or 5 students,
 write solutions to problems and in teams of two exchange their solutions to evaluate each other's written solutions. (Focusing on the importance of writing mathematical concepts properly.)


Calculus 1 is part of the mathematics track at the University of Twente. In this course students learn the geometric and algebraic properties of 2 and 3dimensional vectors. The next topic is complex numbers. This will be followed by a brief introduction to differential equations. The focus will be on solving first and secondorder differential equations. Next, set theory, logic and proof techniques are studied. Finally, limits (formal definition), continuity and differentiability of a function are introduced. Various applications of derivatives are discussed.
Two of the calculus lectures are devoted to Prooflab. The concepts that students cover during these two prooflabs are: complex numbers, set theory, logic and proof techniques.




  Required materialsBookMathematical Proofs; A Transition to Advanced Mathematics, van Gary Chartrand; Albert D. Polimeni; Ping Zhang, 3rd edition. ISBN: 9781292040646 
 BookCalculus: A Complete Course, R.A. Adams & C. Essex, 9th edition. ISBN: 9780134154367 

 Recommended materialsInstructional modesLecture
 OtherPresence duty   Yes 
 Self study with assistance
 Self study without assistance
 Tutorial
 WorkgroupPresence duty   Yes 

 TestsCalculus 1


 