Full course description
In this course, we will discuss, among others, the following topics: limits and continuity, integration and differentiation, inverse and transcendental functions, mean value theorem, sequences and series. In addition to the main facts and concepts, problem solving strategies will be discussed as well. Both the intuition behind the concepts and their rigorous definitions will be presented along with a number of examples and formal mathematical proofs so to better understand the concepts. Furthermore, these objectives will be reinforced through short digital interactive sessions organized during the lectures.
Knowledge and understanding: Calculus offers an indispensable basis, in the contents as well as in the methodologies, for studying and applying exact sciences, which will be built on during the rest of the curriculum.
Applying knowledge: The skills and facts which are taught in this course are of use for most of modern engineering or scientific problems. After the completion of the course, the students should be able to solve simple problems in the areas mentioned above and to judge the validity of a mathematical argument, which is related to the material of the course.
Skills: After having passed the exam, the student will be able to tackle not only the standard type of problems (graph-drawing, calculation of maxima and minima of functions, computing limits, summing infinite series etc.), but also apply his knowledge to considerably more relevant problems.
- To become familiar with functions and limits.
- To become familiar with differentiation and integration.
- To understand how to use differentiation and limits/continuity of a function to sketch the graph of a function.
- To become familiar with sequences and series.
- To understand the basic of differential equations and Taylor series.
Hand-outs will be distributed during the course.
- Calculus, A Complete Course by A. Adams and C. Essex, 8th Edition – Pearson 2014
- Thomas’ Calculus' by M. Weir, J. Hass, and C. Heil, 12th Ed. Or newer - Pearson