Single-Course Danish 5 ECTS

# Advanced Mathematics 2 for Mathematics and Technology

## Overall Course Objectives

To provide the participants with tools, e.g., infinite series, to solve ordinary linear differential equations. By the mathematical approach the student will gain sufficient matureness to be able to deal with more advanced topics within mathematical analysis and its aplications.

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
• Distinguish between linear/nonlinear systems and test the behaviour of nonlinear systems
• Determine and argue for the stability of linear systems of differential equations
• Master central convergence issues
• 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 and various other types of infinite series to solution of differential equations
• Master selected proofs within the theory for infinite series and differential equations
• Construct proofs for simple claims within the theory for infinite series and differential equations

Course Content

Transfer functions. Infinite series, power series, Fourier series. Applications of infinite series on differential equations, the exponential matrix. Introduction to non-linear differential equations. Stability. Central definitions, concepts, and proofs within these topics.

Recommended prerequisites

01002/01004/01005, Linear algebra, Vector spaces, Eigenvalue problems, Systems of linear differential equations, Complex numbers and the complex exponential function, Taylor expansions, Limits, Continuity, Differentiability

Teaching Method

Lectures and problem sessions

Faculty

See course in the course database.

## Registration

Language Danish 13 weeks Compute DTU Lyngby Campus 01025 Bachelor Week 35 Week 48 Mon 8-12
Price 7.500,00 DKK