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| TNG001 | Calculus in One Variable, 8 p (sw) /Envariabelanalys/ Advancement level: B | |
| Aim: The aim of this course is that the students will - become familiar with the mathematical concepts and methods which are basic to scientific and technical subjects - have the proficiency in calculating, problem solving and mathematical modelling, and the capability of analysing the results of these models - achieve a good ability in using computer facilities as a tool in mathematical problem solving.Supplementary courses: Calculus in several variablesCourse organization: The course is divided into a preparatory course, containing compulsory problem solving, and a main course. Teaching is done in lectures and problem classes, with feature of computer laboratory experiments. The examination consists of compulsary problem solving and one written examination.Course content: Preparatory course: Rational, real and complex numbers. Algebraic manipulations. Absolute value and inequalities. Equations and systems of equations. Ploynomials, exponential functions, logarithms and trigonometric functions. Main course: Concepts and symbols from logic and set theory. Number systems. Induction. Binomial theorem. Sets of real numbers. Supremum and infimum. Complex numbers. Polynomials and other elementary functions. Sequences. Limits, continuity and derivatives. Properties of continuous and differentiable functions. Function investigation with applications. Taylor's formula. Maclaurin expansion of elementary functions with applications. Numerical series. Primitive functions and Riemann integrals. Methods of integration. Geometrical applications, such as area, arc length, volume and area of revolution. Indefinite integrals. Ordinary differential equations. First order equations. Linear equations of arbitrary order, with constant coefficients. Some special equations, e. g. Bernoulli and Euler equations. Direction fields and orthogonal trajectories. Applications are given by mathematical models of phenomena in physics and technology.Course literature: Will be decided later. | ||
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