Program Overview

Applied Engineering Mathematics

Introduction

The Applied Engineering Mathematics module is designed to provide students with a comprehensive understanding of fundamental methods in vector analysis, Laplace transforms, and complex analytic functions. This module is based on knowledge achieved in the modules Calculus and Linear Algebra or similar.

Prerequisite/Recommended Prerequisite for Participation in the Module

The module is based on knowledge achieved in the modules Calculus and Linear Algebra or similar.

Content, Progress, and Pedagogy of the Module

Learning Objectives

Knowledge

• Have knowledge about fundamental methods in vector analysis in the 2 and 3-dimensional space, and have knowledge about applications of the theory to engineering.
• Have knowledge about the Laplace transform and how to apply it to solve differential equations exemplified by problems from e.g., mechanics, electronics, or heat transfer.
• Have knowledge about complex analytic functions.
• Have an understanding of power series and Taylor series.
• Have an understanding of how complex analytic functions and power series can be applied to study physical systems.

Skills

• Be able to use vector calculus, within the topics:
  • Inner product (dot product)
  • Vector product (cross-product)
  • Vector and scalar functions and vector fields
  • Space curves, tangents, and arc length
  • Vector differential calculation: Gradient, divergence, curl
  • Vector integral calculation: Line integrals, path independence of line integrals, double integrals, Green's theorem in the plane, and surface integrals.
• Be able to apply the theory of Fourier series, within the topics:
  • Fourier series and trigonometric series
  • Periodic functions
  • Even and odd functions
  • Complex Fourier Series.
• Be able to apply the theory of Laplace transformations, within the topics:
  • Definition of the Laplace transformation. Inverse transformation. Linearity and s-translation.
  • Transformation of elementary functions, including periodic, impulse, and step functions.
  • Transformation of derivatives and integrals.
  • Solution of differential equations.
  • Convolution and integral equations.
  • Differentiation and integration of transformed systems of ordinary differential equations.
• Be able to apply complex analytical functions to conformal mapping and complex integrals within the topics:
  • Complex numbers and the complex plane.
  • Polar form of complex numbers.
  • Exponential functions.
  • Trigonometric and hyperbolic functions.
  • Logarithmic functions and general power functions.
  • Complex integration: Line integrals in the complex plane.
  • Cauchy's integral theorem.

Competences

• Be able to use vector calculus, series, Laplace transforms, and complex analytic functions to solve fundamental engineering problems.

Type of Instruction

The program is based on a combination of academic, problem-oriented, and interdisciplinary approaches and organized based on the following types of instruction that combine skills and reflection:

• Lectures
• Class teaching
• Project work
• Workshops
• Exercises (individually and in groups)
• Teacher feedback
• Professional reflection
• Portfolio work
• Laboratory work.

Extent and Expected Workload

Since it is a 5 ECTS course, the workload is expected to be 150 hours for the student.

Exam

Exams

• Name of exam: Applied Engineering Mathematics
• Type of exam: Written exam, 4-hour examination.
• ECTS: 5
• Assessment: 7-point grading scale
• Type of grading: Internal examination
• Criteria of assessment: As stated in the Joint Programme Regulations.

Facts about the Module

• Danish title: Anvendt ingeniřrmatematik
• Module code: N-EN-B3-3
• Module type: Course
• Duration: 1 semester
• Semester: Autumn
• ECTS: 5
• Language of instruction: Danish and English
• Empty-place Scheme: Yes
• Location of the lecture: Campus Aalborg, Campus Esbjerg
• Responsible for the module: Morten Nielsen, Henrik Garde
• Used in:
  • Curriculum for the Bachelor of Science (BSc) Programme in Energy Engineering 2015, Aalborg
  • Curriculum for the Bachelor of Science (BSc) Programme in Energy Engineering 2015, Esbjerg
  • Curriculum for the Bachelor of Engineering (BE) Programme in Sustainable Energy Engineering 2015, version 3
  • Bachelor of Engineering in Mechanical Engineering 2017
  • Bachelor of Science (BSc) in Engineering (Mechanical Engineering and Manufacturing) 2017
  • Bachelor of Engineering in Mechanical Engineering 2016
  • Bachelor of Science (BSc) in Engineering (Mechanical Engineering and Manufacturing) 2016
  • Curriculum for the Bachelor of Science (BSc) in Applied Industrial Electronics

Organisation

• Study Board: Study Board of Energy
• Department: Department of Energy Technology
• Faculty: Faculty of Engineering and Science