Mathematics 1a (Polytechnical foundation)

• 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

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.

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