Mathematical methods 2 for Electrical engineering and Renewable energy

Numerical methods in all themes if relevant. Complex number, eigenvalues, eigenvectors, systems of differential equations, powerseries, taylorseries, function of two and more variables, partial differentiation, extrema value problems, laplace transform, transfer functions and fourier series

The candidate should demonstrate knowledge of the following:

• Complex numbers; polar form and Euler's formula
• Computation of characteristic polynomials, eigenvalues and eigenvectors of a square matrix
• Convergence of series, particularly geometric series
• Power series, including Taylor's theorem with remainder and Taylor series of well-known functions.
• Integration and derivation of power series.
• Functions of several variables.
• Partial and total derivatives
• Linearization around a stationary point and its applications
• Coupled differential equations, state-space models,
• Laplace transformation and Fourier series.

The candidate should acquire and display the following skills:

• Use of computational devices for numerical calculations and graphical representations in topics relevant to the course.
• Basic computations with complex numbers and phasor analysis,
• Calculation and manipulations of series.
• Partial derivation and application in classification of local extrema of a function of two variables.
• State space models of dynamic systems, eigenvalues and stability, numerical solutions of differential equations, Laplace transforms of common functions and properties of the Laplace transform, inverse Laplace transform, solving differential equations using the Laplace transform, transfers functions and Bode plots, poles and zeros, Fourier series of common waveforms, odd and even functions and frequency response of linear systems.

General competence:

• Use of mathematics to model and solve theoretical and practical problems in situations relevant to their own field, in academic and professional contexts.
• Use of computational tools to visualize and solve mathematical problems.

Lectures and exercises. Exercises will be based on assignments and digital learning elements using Blackboard. Use of computerized simulation and analysis tools will also be included. Compulsory work: At least 4 of 6 exercises must be approved for admission to the exam.