11110 - Mathematics of Engineering I Modulübersicht

Module Number: 11110
Module Title:Mathematics of Engineering I
  Mathematik für Ingenieure I
Department: Faculty 1 - Mathematics, Computer Science, Physics, Electrical Engineering and Information Technology
Responsible Staff Member:
  • Prof. Dr. rer. nat. habil. Fügenschuh, Armin
Language of Teaching / Examination:English
Duration:1 semester
Frequency of Offer: Every winter semester
Credits: 6
Learning Outcome:The course provides an introduction into mathematical reasoning and into the basic principles and techniques of analytic geometry and linear algebra. The presentation of the material is accompanied by problem sessions in which the students are taught to apply the learned topics. Objectives of the course are to enable the students to perform simple mathematical arguments, to verify the validity of simple mathematical relations, and to deal with and get routine with some fundamental tools of advanced mathematics in the areas of analytic geometry and linear algebra.
Contents:Fundamentals:
Kinds of mathematical statements and reasoning (direct proof, indirect proof, proof by complete induction), essential statements of combinatorics and sum formulas, set theory (relations and operations), definition and examples of mappings and functions, real numbers (working with inequalities and absolute values, infimum and supremum), b-adic expansions, complex numbers (Cartesian, polar, and Euler representation, number operations in these presentations, determination of roots).
 
Analytic Geometry:
Vectors in the plane and in space (representation, operations, scalar product, vector product, triple product), representation of lines (point-direction and two-point equation, distance formulas), planes (point-directions equation, three-points equation, Hesse normal form).
 
Linear Algebra:
Vectors and matrices (representation and operations, systems of linear equations (representation and solvability), Gauss algorithm, rank of a matrix, linear dependence and independence of vectors, representation of the solution set of a homogeneous and inhomogeneous system of linear equations by linearly independent solutions of the homogeneous system, LU factorization by Gauss algorithm and solution of systems of linear equations by that, determinant of a matrix (definition, computation via Gauss algorithm and Laplace expansion), inverse matrix (existence and computation via Gauss algorithm), orthogonal vectors and matrices (definitions, properties, Gram-Schmidt procedure), QR factorization of a matrix and the solution of systems of linear equations by that, linear mappings (definition, orthogonal mappings and their geometrical properties), eigenvalues and eigenvectors (definition, computation, results on existence of linear independent eigenvectors), diagonalization of matrices (principal axes transformation and its application to quadratic equations), definiteness properties of matrices (definition and verification via computation of eigenvalues).
Recommended Prerequisites:None
Mandatory Prerequisites:None
Forms of Teaching and Proportion:
  • Lecture / 4 Hours per Week per Semester
  • Exercise / 2 Hours per Week per Semester
  • Self organised studies / 90 Hours
Teaching Materials and Literature:
  • Leon, S.: Linear Algebra with Applications, 5th ed., Yourdon Press, Englewood Cliffs, 1998
Module Examination:Prerequisite + Final Module Examination (MAP)
Assessment Mode for Module Examination:Prerequisite:
  • Successful completion of exercise sheets
Final module examination:
  • Written examination, 90 min.
Evaluation of Module Examination:Performance Verification – graded
Limited Number of Participants:None
Part of the Study Programme:
  • Abschluss im Ausland / Architektur / keine PO
  • Abschluss im Ausland / Environmental and Resource Management / keine PO
  • Bachelor (research-oriented) / Environmental and Resource Management / PO 2015
  • Abschluss im Ausland / Informatik / keine PO
  • Abschluss im Ausland / Informations- und Medientechnik / keine PO
  • Abschluss im Ausland / Maschinenbau / keine PO
  • Abschluss im Ausland / Mathematik / keine PO
Remarks:
  • Study programme Environmental and Resource Management B. Sc.: Mandatory module "B2".
Module Components:
  • Lecture Mathematics of Engineering I
  • Exercise Mathematics of Engineering I
  • Tutorial Mathematics of Engineering I
  • Examination Mathematics of Engineering I
Components to be offered in the Current Semester: