## Mathematical Analysis II

OBJECTIVES

LEARNING OUTCOMES:
One learns power series, differential calculus of several variables, line integral, multiple integral and surface and volume integral. One obtains the ability to calculate partial derivatives of elementary and composed functions, calculate various integrals and apply theorems of Green, Gauss and Stokes to facilitate the computations.

KNOWLEDGE AND UNDERSTANDING:
To know the definitions of basic conepts (convergence of series, partial derivatives, extremal points, multiple integral, line integal, surface integral and volume integral) and apply various theorems to execute concrete computations.

APPLYING KNOWLEDGE AND UNDERSTANDING:
To identify the theorems and techniques to apply to the given problems and execute computations correctly.

MAKING JUDGEMENTS:
To understand mathematical concepts for the given problems and to divide them into smaller problems that can be solved with the knowledge obtained during the course.

COMMUNICATION SKILLS:
To frame the problems in the obtained concepts, express the logic and general facts that are used during the computations.LEARNING SKILLS:

To know precisely basic mathematical concepts and apply them to some simple examples in physics.

COURSE SYLLABUS

• Sequences and series of functions, Taylor series
• Differential calculus of scalar and vector fields
• Applications of differential calculus, extremal points
• Basic differential equations
• Line integrals
• Multiple integrals
• Surface integrals, Gauss and Stokes theorems

## Electrical Network Analysis

Electrical quantities and SI units. Electrical energy and electrical power. Passive and active sign convention. Passive and active elements. Ideal voltage and current sources. Basic ideal electric components: resistance, inductance, capacitance. Models of real components. Ohm-s law. Series and Parallel connection of components. Topological circuital laws: Kirchhoff’s Voltage Law (KVL) and Kirchhoff’s Current Law (KCL). Mesh Current Method, Node Voltage Method. Sinusoidal functions: average and RMS (Root Mean Square) values.

Sinusoidal steady state circuit analysis. Phasors. Impedance and admittance. Analysis of circuits in AC steady state. Electrical power in the time domain and in sinusoidal steady state: active power, reactive power, complex power. Power factor correction. Maximum power transfer in AC. Application of superposition theorem in circuit analysis. Thevenin’s and Norton’s theorems.

Frequency response: first order electrical filters. Resonance: series and parallel resonant circuits.

Mutual inductance and ideal transformer. Three-Phase systems. Introduction to the power distribution and transportation grid. Time response and transient analysis. The unit step function, unit impulse function, exponential function, first-order circuits. Laplace transform method, Laplace transform of some typical functions, initial-value and final-value theorems, partial-fractions expansions, analysis of circuits in the s-domain. Network functions and circuit stability.

Electrical measurement bridges. Introductions to the electrical safety and electricity distribution system: description and prospects. Basics of designing a power plant. Effects of electricity on the human body and relative protection systems. Introduction to electrical machines: Tranformer and DC motor.