Single-Course English 10 ECTS

# Mathematics 1a (Polytechnical foundation)

## Overall Course Objectives

The course content provides a part of 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 themes of the course are logic and linear algebra. The goal is to strengthen the ability of students to use mathematical reasoning on the one hand and an algorithmic, computational approach on the other hand, to understand and work with fundamental concepts from linear algebra. The theory is exemplified by thematic exercises. Further, computer software is used to integrate computational and theoretical aspects of the curriculum.

Learning Objectives

• use truth tables to investigate statements from propositional logic
• use the algebraic and the geometric representation of complex numbers including the complex exponential function
• perform computations with polynomials over the complex numbers
• apply inductive thinking in mathematical statements
• compute/execute a function/algorithm defined in a recursive way
• use matrix algebra and Gaussian elimination for solving systems of linear equations and describe their solution sets
• analyze linear maps between vector spaces
• analyze the eigenvalue problem in particular for square matrices
• solve systems of first order linear differential equations with constant coefficients
• describe the structure of solutions to a second order linear differential equation with constant coefficients
• use mathematical terminology and logical reasoning in written presentations
• use a computer to execute various algorithms from linear algebra

Course Content

Propositional logic. Complex numbers. Recursion and induction. Systems of linear equations. Matrix algebra. Vector spaces. Linear maps. Eigenvalue problems. Systems of first order linear differential equations with constant coefficients. Use of computer in linear algebra. Examples of applications in the engineering sciences.

Teaching Method

From week: 2 lectures, 3h tutorials and 4h planned self study. Moreover thematic exercises in some weeks.

Faculty

See course in the course database.

## Registration

Language English 13 weeks Compute DTU Lyngby Campus 01003 Bachelor Week 35 Week 48
Price 15.000,00 DKK