Advanced Mathematics 2 for Mathematics and Technology

• Master the general solution method for linear, nth order, differential equations with constant coefficients
• Master the general solution method for linear homogeneous systems of differential equations with constant coefficients
• Apply different solution techniques, including transfer functions, for obtaining particular solutions to inhomogeneous differential equations
• Determine and argue for the stability of linear systems of differential equations
• Understand the differences between various types of convergence (absolute, conditional, point-wise, uniform) of infinite series and determine the convergence type in concrete cases
• Estimate the number of terms needed in order to obtain a desired accuracy in the approximation of an infinite series
• Find the Fourier series for simple periodic functions, determine their convergence properties, and approximation-theoretic properties
• Apply Fourier series and power series methods to the solution of differential equations
• Master convergence tests (including Leibniz’s test, ratio test, comparison test, equivalence test, integral test, n term test) for series of complex numbers
• Be able to recognize both homogeneous and inhomogeneous linear differential equations and distinguish the cases corresponding to constant and nonconstant coefficients
• 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

Solution of homogeneous/​inhomogeneous differential equations and systems of differential equations. Transfer functions. Stability. Infinite series, power series, Fourier series. Applications of infinite series on differential equations. Solutions via computer software. Central definitions, concepts, and proofs within these topics. Introduction to non-linear differential equations.

• 36 – 49 (Wed 8-12)

01002/01004/01005/02525, Linear algebra, Vector spaces, Eigenvalue problems, Systems of linear differential equations, Complex numbers and the complex exponential function, Taylor expansions, Limits, Continuity, Differentiability. Course 02525 supplements 01002 treatment of what a mathematical proof is and of limits and continuity. Without course 02525 there is an additional note you have to study.

Lectures and problem sessions

Information regarding re-exam: The homework can only be re-used to the first coming re-exam.