# 2019/2020

## 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 programme is based on a combination of academic, problem oriented and interdisciplinary approaches and organised based on the following types of instruction that combine skills and re-flection: - lectures - class teaching - project work - workshops - exercises (individually and in groups) - teacher feedback - professional reflection - portfolio work - laboratory work

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

## Exam

### Exams

 Name of exam Advanced calculus Type of exam Written exam 4-hour examination. ECTS 5 Assessment 7-point grading scale Type of grading Internal examination Criteria of assessment The criteria of assessment are stated in the Examination Policies and Procedures

 Danish title Avanceret calculus Module code N-ED-B3-3 Module type Course Duration 1 semester Semester Autumn ECTS 5 Language of instruction English Empty-place Scheme Yes Location of the lecture Campus Esbjerg Responsible for the module Henrik Garde

## Organisation

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