Advanced Mathematics 2 for Mathematics and Technology

• 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
• 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

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.

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