Advanced Calculus

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

Extent and expected workload

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

Exam

Exams

Name of examAdvanced calculus
Type of exam
Written exam
4-hour examination.
ECTS5
Assessment7-point grading scale
Type of gradingInternal examination
Criteria of assessmentAs stated in the Joint Programme Regulations.

Facts about the module

Danish titleAvanceret calculus
Module codeN-ED-B3-3
Module typeCourse
Duration1 semester
SemesterAutumn
ECTS5
Language of instructionEnglish
Empty-place SchemeYes
Location of the lectureCampus Esbjerg
Responsible for the module

Organisation

Study BoardStudy Board of Energy
DepartmentDepartment of Energy Technology
FacultyFaculty of Engineering and Science