• Derive the one-sided Laplace transform for a function of time
• Apply standard Laplace transform properties to compute the transform of a time-varying function

Objectives for Lecture #2

• Understand how the frequency domain is useful to solving ordinary differential equations
• Convert nth-order ordinary differential equations into the frequency domain
• Define the impulse function and establish its Laplace transform
• Apply the initial and final value theorems to determine initial and final values of a time-varying function
• Apply time periodicity theorem to derive the Laplace transform of a periodic time function
• Recognize standard Laplace transform pairs
• Explain the concept of partial fraction expansion and how it relates to the Inverse Laplace transform
• Define a strictly proper rational polynomial and show how one may be derived by long division

Objectives for Lecture #3

• Define frequency-domain poles and zeros
• Explain the concept of partial fraction expansion and how it relates to the Inverse Laplace transform
• Define a strictly proper rational polynomial and show how one may be derived by long division
• Identify the proper partial fraction expansion for rational polynomials with simple poles and repeated simple poles
• Calculate the partial fraction expansion coefficients for terms with simple and repeated simple poles
• Inverse Laplace transform a rational polynomial that has been partial fraction expanded

Objectives for Lecture #4

• Identify the proper partial fraction expansion for rational polynomials with non-repeated complex poles
• Calculate the partial fraction expansion coefficients for terms with complex poles
• Inverse Laplace transform a partial-fraction-expanded rational polynomial containing complex poles

Objectives for Lecture #5

• Derive the s-domain representation of resistors, inductors, and capacitors, including initial conditions
• Analyze circuits with zero initial conditions and an arbitrary input to derive the complete response (natural + steady-state response) using Laplace transform techniques
• Analyze circuits with initial conditions and an arbitrary input to derive the complete response (forced + initial-condition response)
• Use circuit analysis techniques to solve for time-domain inductor and capacitor initial conditions

Objectives for Lecture #6

• Apply standard circuit analysis techniques (nodal, mesh, superposition, source transform) to derive the complete circuit response using Laplace transform techniques
• Identify the natural, forced, steady-state, and initial condition responses

Objectives for Lecture #7

• Define the transfer function for a Linear-Time-Invariant (LTI) circuit
• Derive transfer functions for circuits using circuit analysis techniques
• Show how a transfer function may be used to find the forced response

Objectives for Lecture #8

• Explain what constitutes a 2nd-order circuit
• Derive the solutions for unforced series and parallel RLC 2nd-order circuits using the Laplace transform
• Define the damping factor, damping frequency and undamped natural frequency for 2nd-order circuits
• Define the conditions for over-damped, under-damped, and critically-damped responses
• Solve for the step response of a 2nd-order series RLC circuit
• Solve for parameters in a series RLC circuit that will result in an over-damped, under-damped, or critically-damped step response

Objectives for Lecture #9

• Solve for the step response of a 2nd-order parallel RLC circuit and for general 2nd-order RLC circuits
• Solve for parameters in a parallel RLC circuit that will result in an over-damped, under-damped, or critically-damped step response

Objectives for Lecture #10

• Explain the physical meaning of the unit impulse response and how it connects with the transfer function
• Derive the impulse response expression from an s-domain transfer function
• Derive the convolution integral from the transfer function definition and Laplace transform properties
• Explain when numerical convolution might be required or preferred
• Evaluate the convolution integral using mathematical integration, determining the correct integration limits and assigning the proper time interval for the solution

Objectives for Lecture #11

• Evaluate the convolution integral using graphical techniques

Objectives for Lecture #12

• Derive the sinusoidal steady-state response from a transfer function and an assumed sinusoidal input
• Define frequency response and explain what information a frequency response plot conveys
• Explain the purpose of logarithmic frequency scales in frequency response plots
• Define absolute gain and gain in decibels and explain the advantage of decibels
• Derive the magnitude and phase expressions from a transfer function

Objectives for Lecture #13

• Define a Bode plot
• Manipulate a transfer function to identify poles, zeros, and gain factor
• Show how to factor a transfer function into terms to generate the Bode plot (gain factor + real poles and zeros)
• Derive how the Bode plot can be assembled from individual terms of the factored transfer function
• Derive the Bode plot characteristics for real poles and zeros

Objectives for Lecture #14

• Derive a Bode plot by combining the effects of multiple terms
• Derive the Bode plot characteristics for non-repeated complex poles and zeros
• Show the impact of the damping factor on straight-line approximations for complex poles and zeros
• Derive transfer functions from straight-line Bode plot approximations

Objectives for Lecture #15

• Define resonance and determine the conditions necessary for resonance in a 2nd-order series or parallel circuit
• Explain the use of circuits that exhibit resonance
• Define the characteristics of a circuit in resonance in terms of power factor, impedance/admittance, and current/voltage
• Manipulate the transfer function to compute the resonant frequency, bandwidth, cutoff frequencies, and Q

Objectives for Lecture #16

• Explain the frequency response characteristics of ideal low-pass, high-pass, band-pass, and band-stop filters and compute the output of an ideal filter given its frequency response and an assumed input
• Distinguish between passive and active filters
• Explain the characteristics of non-ideal filters and define the terminology passband, transition band, and stopband
• Derive the transfer functions for simple 1st-order passive filters
• Recognize standard passive filter transfer functions
• Analyze a circuit or transfer function to determine its filter type

Objectives for Lecture #17

• Derive the transfer functions for simple 2nd-order passive filters
• Recognize standard passive filter transfer functions
• Analyze a circuit or transfer function to determine its filter type
• Choose circuit parameters to implement a desired passive filter transfer function

Objectives for Lecture #18

• Explain the advantages and disadvantages of active filters
• Derive active filter transfer functions using ideal op-amp analysis
• Derive wide-band band-pass/band-stop active filter design equations through analysis of cascaded low-pass and high-pass circuits
• Choose circuit parameters to implement a desired passive filter transfer function

Objectives for Lecture #19

• Explain the purpose of impedance and frequency scaling
• Derive the effect of impedance and frequency scaling on the cut-off frequency, bandwidth, and Q
• Design filters using prototype circuits and combined impedance and frequency scaling

Objectives for Lecture #20

• Determine the period and fundamental frequency for a periodic signal
• Explain the purpose of the trigonometric Fourier series and derive the equivalent magnitude/angle form
• Distinguish between the fundamental and harmonics
• Derive expressions for the Fourier series coefficients
• Derive the Fourier series for a simple periodic waveform

Objectives for Lecture #21

• Derive the Fourier series for more complex periodic waveforms
• Use the Fourier series to make circuit calculations

Objectives for Lecture #22

• Identify even, odd, and half-wave symmetry in periodic waveforms
• Utilize symmetry to simplify the determination of Fourier series
• Use the Fourier series to make circuit calculations

Objectives for Lecture #24

• Solve for the real, reactive, apparent, and complex power of a circuit and determine the power factor (leading or lagging)
• Use the power triangle to relate the power components of a given circuit
• Explain the purpose of performing power factor correction
• Determine the reactive power and capacitance required to obtain a specified power factor

Objectives for Lecture #25

• Define three-phase wye and delta connections
• Define a balanced three-phase voltage source and a balanced three-phase load impedance
• Define line-to-neutral,  line-to-line, and phase voltages and delta, line, and phase currents
• Determine the phasor diagram representation for a given balanced set
• Define phase sequence and given a phase quantity, calculate the remaining terms of a desired balanced phase sequence
• Determine the transformation between a balanced Y impedance connection and a balanced delta impedance connection
• Define a neutral wire and explain its purpose
• Analyze a balanced Y-Y circuit with a zero-impedance neutral
• Analyze a balanced Y-Y circuit with a non-zero-impedance neutral 

Objectives for Lecture #26

• Define a neutral wire and explain its purpose
• Analyze a balanced Y-Y circuit with a zero-impedance neutral
• Analyze a balanced Y-Y circuit with a non-zero-impedance neutral 

Objectives for Lecture #27

• Analyze a 3-phase circuit with a balanced Y-source and delta-load, delta-source and delta load, and delta-source and Y-load
• Derive relationships between line and phase quantities for a Y-source and a delta-load

Objectives for Lecture #28

• Define the purpose of a per-phase equivalent circuit and establish the steps necessary to convert a general three-phase circuit into its per-phase equivalent
• Analyze a balanced three-phase circuit using its per-phase equivalent circuit and general circuit analysis techniques
• Derive line and delta quantities from per-phase analysis results

Objectives for Lecture #29

• Show that the instantaneous power of a balanced three-phase source is constant and explain why this is desirable
• Establish expressions for 3-phase real, reactive, apparent, and complex power in terms of phase and line quantities
• Compute the various types of three-phase circuit power
• Given a transmission system and information about load power and voltage, calculate the required sending voltage and transmission efficiency

Objectives for Lecture #30

• Given a balanced source, line impedance, and load impedance, calculate the load power and transmission efficiency using per-phase equivalent circuit analysis

Objectives for Lecture #31

• Define magnetic field, flux density, flux, field intensity, Ampere's law, permeability, reluctance and mmf
• Derive a magnetic equivalent circuit given the parameters of a core and winding
• Explain the advantages of a magnetic equivalent circuit containing mmf sources and reluctances
• Make calculations for a simple magnetic equivalent circuit

Objectives for Lecture #32

• Explain the construction of a single-phase transformer and define the terminology primary and secondary
• Define the assumptions for an ideal single-phase transformer
• Derive the voltage and current relationships for an ideal single-phase transformer
• Derive how voltages, currents, and impedances are reflected across an ideal transformer
• Solve for current, voltage and power on the source and load sides of a transformer using reflected quantities
• Calculate the efficiency of a circuit using step-up and step-down ideal transformers
• Explain why transformers are used in power distribution, circuit isolation, and impedance matching

Objectives for Lecture #33

• Define flux linkage, self inductance, leakage inductance, magnetizing inductance, and mutual inductance
• Define Faraday's law and relate it to flux linkages
• Derive a magnetic equivalent circuit of two coupled coils, each with leakage flux
• Derive the T-equivalent circuit for a real transformer including winding resistance, leakage reactance, magnetizing reactance, and core loss
• Use the open-circuit and short-circuit tests to calculate transformer parameters
• Discuss aiding and opposing coupling

Objectives for Lecture #35

• Define the concepts of torque, speed, and induced voltages in rotating machines
• Define the Lorentz force Law and correctly apply the right-hand rule
• Explain the elements of a rotating machine, including stator, stator windings, rotor, and rotor windings

Objectives for Lecture #36

• Define the attributes of a symmetrically-wound AC machine stator
• Explain how a balanced-set of stator current results in a rotating magnetic field -- illustrate the strength of the resultant field and the speed and direction of rotation

Objectives for Lecture #37

• Illustrate how a 4,6,8,...-pole machine stator is constructed and derive the speed of the resulting rotating field
• Explain the construction of a 3-phase synchronous machine
• Explain the operation of slip rings and brushes
• Explain the operation of synchronous motors and generators in terms of interacting magnetic fields on the stator and rotor
• Explain power flow and efficiency in motors and generators
• Derive the expression for the induced torque produced by the interaction of two rotating magnetic fields

Objectives for Lecture #38

• Derive the per-phase equivalent circuit for a synchronous machine
• Derive the expression for the induced voltage in the stator of a 3-phase synchronous machine
• Define the rotor angle, synchronous reactance, and excitation voltage

Objectives for Lecture #39

• Explain the flow of real power through a synchronous machine for motor and generator operation
• Derive an expression for the mechanical power given a loss-less machine
• Work steady-state problems using the synchronous machine equivalent circuit and steady-state power/torque relationships
• Define the phasor diagram for generator and motor operation

Objectives for Lecture #40

• Define naval shipboard power distribution terminology: ring bus, switchboard, circuit breaker, ungrounded distribution, delta distribution, split plant, vital and non-vital loads, load shedding
• Introduce the concept of Integrated Power Systems and the use of electric drive for propulsion and the integration of new high energy weapons