3116.17 - Mathematics 1, topic specific exercises
Mathematics 1, topic specific exercises
Upper secondary school with mathematics on level A – and to follow Mathematics 1, couse number 3103
The course aims to present some simple applications of mathematical skills obtained in Mathematics 1. The exercises take place over 4-8 times during the year in different topics.
Linear equations and linear maps. Matrix algebra. Vector spaces. Eigenvalue problems. Symmetric and orthogonal matrices. Complex numbers. Linear differential equations. Standard functions. Functions of one and several real variables: linear approximations and partial derivatives, Taylor expansions and quadratic forms, extrema and level curves, line, surface and volume integrals. Vector fields, Gauss' and Stoke's theorems. Applications of MAPLE in the above areas. Examples of applications in the engineering sciences.
Learning and teaching approaches
Exercises in groups.
A student, that successfully has completed this course, should be able to: • Use algebraic and geometric representation of complex numbers as well as the complex exponential function. • Use matrix calculus and Gaussian elimination in the context of solving systems of linear equations. • Analyze and explain sets of solution in vector spaces using the structure theorem. • Carry out simple calculations with the elementary functions – among these their inverses as well. • Use the different variants of Taylor's formula for approximations and limits. • Solve simple first and second order differential equations and systems of differential equations. • Calculate extrema for functions of several variables – also for regions with boundaries. • Parametrize simple curves, surfaces and regions in 3-space, as well as calculate simple line-, surface- and spaceintegrals. • Use Gauss' and Stoke's theorems in simple settings. • Use mathematical terminology and reasoning in oral and written expositions. • Organizing collaboration in a project about mathematical concepts and methods in a larger application context. • Apply symbolic software tools – currently Maple – to solve and graphically display of mathematical problems.
Group work with small projects within diverse relevant topics. When this work is finished, some questions will be posted, that each participant answers individually (while the are allowed to discuss them within the group). A general, individual evaluation of each student decides whether a student passes. The course is coordinated with DTU, and any changes there will be adapted to the course. Reexamination can e.g. be organized as an oral exam, where one of the projects is drawn.