Single-Course English 5 ECTS

Advanced Engineering Mathematics 2

Overall Course Objectives

To provide participants with tools, including infinite series, to solve differential equations and systems of differential equations.

Learning Objectives

  • Determine the solutions to nth order homogeneous differential equations
  • Determine the solutions to linear homogeneous systems of differential equations
  • Master the transfer function and apply it to solution of inhomogeneous differential equations
  • Determine and argue for the stability of linear systems of differential equations
  • Know the differences between various types of convergence (absolute, conditional, point-wise, uniform) of infinite series and identify them
  • Estimate the number of terms which is needed in order to obtain a desired approximation of an infinite series
  • Find the Fourier series for simple periodic functions, clarify their convergence properties, and approximation-theoretic properties
  • Apply Fourier series, power series and various other types of infinite series to solution of differential equations
  • Determine the Fourier transform of simple functions
  • Apply Maple to calculations and control of the results

Course Content

Solution of homogeneous/inhomogeneous differential equations and systems of differential equations. Transfer functions. Infinite series, power series, Fourier series. Applications of infinite series and power series for solving differential equations. Stability. Introduction to the Fourier transform. Solutions via MAPLE.

Recommended prerequisites

01002/01004/01005/01006/01015/01920, Knowledge of complex numbers, matrix calculations, eigenvalues and eigenvectors for matrices, systems of linear first order differential equations and linear differential equations of first and second order.

Teaching Method

Lectures and exercises. Projects in selected weeks.

Faculty

See course in the course database.

Registration

Language

English

Duration

13 weeks

Institute

Compute

Place

DTU Lyngby Campus

Course code 01034
Course type Bachelor
Semester start Week 35
Semester end Week 48
Days Mon 8-12
Price

7.500,00 DKK

Registration