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 3-dimensional 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 second order 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.