3040.21 - 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 thematic exercises and 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 the algebraic and geometric representation of complex numbers as well as the complex exponential function. • Use matrix calculus and Gaussian elimination for solving systems of linear equations. • Analyze and explain the linear structure of solution sets in vector spaces. • Perform calculations with the elementary functions including their inverse functions. • Use Taylor's formulas for approximations and limits. • Solve elementary first and second order differential equations and systems of differential equations. • Calculate extrema for multivariate functions, especially on domains with boundary. • Parametrize elementary curves, surfaces and massive solids and calculate elementary curce, surface and space integrals. • Use Gauss' and Stoke's theorems in simple applications. • Use mathematical terminology and reasoning in oral and written presentation. • Coordinate joint work in groups around thematic exercises and applications. • Use computer algebraic systems – currently Maple – for solving and visualization 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.