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.