3103.17 - Mathematics 1
Upper secondary school with mathematics on level A
The course content is the mathematical basis for a broad range of technical fields and also provides a starting point for further studies in mathematics and applied mathematics. The dominating theme of the course is linearity. The goal is to give students the ability to employ fundamental tools of mathematics in theoretical studies as well as in applied projects. The use of modern computer software supports both of these aspects.
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
Online activities and lecture, group work, individual work, exercise classes, written assignments with feedback, project work.
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.
There will be four sub grades (by the 7 step grading scale) based on: 1) Exams the first semester, 2) Exams for the second semester, 3) A 3-week project with a written report and an oral exam, 4) Written assignments. The final grade is the average of these four grades, but each sub grade has to be passed. If a sub grade is not passed, there will be one extra attempt to pass each nonpassed sub grade. If a student does not pass the course, then the final grade is '-3' if one of the final sub grades is '-3' (or the student did not participate), otherwise the grade is 00. The course is coordinated with DTU, and will follow any changes made there. Reexamination consists of two four hour exams.
Online teaching material and textbook from DTU.