Full course description
Calculus introduces the students to a theoretical notion of the basic concepts in applied mathematics. The course will start with discussing complex numbers, followed by limits and formalizing these. Next derivatives are defined in terms of limits and the approach for computing derivatives is discussed. Derivatives are then used for approximating functions with Taylor series (including error bounds) and for numerical optimization with Newton’s method. After this we will discuss Riemann sums, the fundamental theorem of calculus, antiderivatives and differnts integration methods. Then we focus our attention on infinite series with special attention to geometric and Fourier series. Both the intuition behind the concepts and their formal definitions will be presented along with simple examples of formal mathematical proofs.
Nowadays calculus is a tool used almost everywhere in the modern world to describe change and motion. Calculus also provides important tools in understanding functions and has led to the development of new areas of mathematics. The objective of this course is to introduce the fundamental ideas of the differential and integral calculus of functions of one or more variables. Emphasis is on an understanding of the basic concepts and techniques, and on developing the practical skills to solve problems from a wide range of application areas. After completing this course the student will obtain a theoretical notion of the basic topics in applied mathematics, and will be able to validate all kinds of mathematical arguments.