Mathematics 1 - Single variable calculus

Limits, continuity, differentiation, and integration of functions of one variable. The intermediate value theorem, the mean-value theorem, extreme values, transcendental functions, implicit differentiation, related rates, indeterminate forms, Newton's method. Techniques of integration and numerical integration. Riemann sums, the definite integral, and the fundamental theorem of calculus. Area, volume, arclength, area of surfaces of revolution. Sequences, series, and power series. Taylor series, Taylor's formula. First order separable and linear differential equations. Euler's method. Examples of mathematical modelling and from applications to science, technology, and economy.

1. Knowledge. The student understands and is able to recognize and apply concepts, results, and methods from single-variable analysis which deals with limits, continuity, differentiation, integration, convergence of sequences and series, Taylor polynomials, and Taylor series. The student understands and is able to apply basic numerical methods for solution of nonlinear equations, differential equations, and integration, and is aware of the possibilities and limitations that lie in the use of mathematical software.
2. Skills. The student is able to apply his or her knowledge of single-variable mathematical analysis to formulate and solve simple problems in mathematics and the natural sciences/technology, if necessary with the additional aid of mathematical software.

Lectures and compulsory exercises. Information regarding the number of compulsory exercises that must be approved will be listed on the course website at the start of the course. The lectures may be given in English.