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Advanced Mathematics

Analytic Geometry

Course #: 6561A-B
Duration: 20 hours
Course Prerequisites: Plane Trigonometry (2309A-B); Introduction to Algebra, Geometry, and Trigonometry (Block X02);
What Students Learn: PART 1 (6561A). Number Line; Rectangular Coordinates; Length and Midpoint of Line Segment; Graph of Linear Equation; Slope, Intercept, and Angle of Inclination of Straight Line; Finding Equation for Line from Slope and One Point and from Two Points; Intersection of Two Lines; Angle Between Two Lines; Perpendicular Lines; Parallel Lines.
PART 2 (6561B). Conic Sections and Methods of Analytic Geometry; Circle as a Locus; Equation of Circle; Translation of Axes; Equation of Ellipse; Problems Concerning Ellipse; Equation of Parabola in Various Positions; Equation of Hyperbola; Asymptotes of Hyperbola; Tangents of Conic Sections and Their Equations; Meaning of Functions; Exponential, Logarithmic, and Trigonometric Functions; Polar Coordinate System; Relations Between Polar and Rectangular Coordinates; Three-Dimensional Coordinate System.

Special Notes: Covers subject at an advanced, in-depth level.

Calculus: Function and Use

Course #: 6618A-D
Duration: 40 hours
Course Prerequisites: Plane Trigonometry (2309A-B); Analytic Geometry (6561A-B);
What Students Learn: PART 1 (6618A). Basic Discussion of Continuity, Limits, and Average Rate of Change; Exact Rate of Change; Derivatives; Application of Derivatives.
PART 2 (6618B). The Antiderivative; The Integral; Application of the Integral to Variable Quantities such as Velocity, Distance, Area, Volume Charge, Voltage, and Power.
PART 3 (6618C). Derivatives of Trigonometric, Exponential, and Logarithmic Functions; Applications.
PART 4 (6618D). More Forms of Integrals; Additional Applications such as: Areas and Volumes of Conics, First Moments, Centroids and Centers of Gravity, Second Moments and Moments of Inertia, Work on Variable Loads, and Transients in Electric Circuits.

Special Notes: Covers subject at an advanced, in-depth level.

Nature of Electricity

Course #: 086001
Duration: 5 hours
Course Prerequisites: Basic Industrial Math (Block X21);
What Students Learn:

  • Explain the operation of a simple circuit.
  • Define the terms: conductor, insulator, and resistor.
  • Demonstrate that unlike charges attract and like charges repel.
  • List the dangers and benefits of static electricity.
  • Define the terms: volt, ampere, and ohm.
  • Describe common notations and prefixes used to identify electrical and electronic values.
  • Identify carbon resistors, potentiometers, and rheostats, and explain how they work.
  • Identify the common electrical symbols used in schematic diagrams.
  • Explain the difference between a series and parallel circuit.

    • Circuit Analysis and Ohm's Law

    Course #: 086002
    Duration: 5 hours
    Course Prerequisites: Basic Industrial Math (Block X21);
    What Students Learn:

  • Find the total resistance in series, parallel, and series-parallel circuits.
  • Use Ohm's law to calculate the current, voltage, or resistance in circuits.
  • Calculate the amount of power supplied and dissipated in a DC circuit.
  • List the steps for finding current, voltage, and resistance with a digital or analog meter.

    • Conductors, Insulators, and Batteries

    Course #: 086005
    Duration: 5 hours
    Course Prerequisites: Basic Industrial Math (Block X21);
    What Students Learn:

  • Describe the various types of conductors and discuss their conductivity.
  • Explain the American Wire Gage System of sizing copper conductors.
  • Determine the size of conductor needed for an application.
  • Identify the various types of insulating materials and their temperature ratings.
  • Explain the difference between a dry cell and a storage battery.
  • How to connect cells together to obtain more voltage, more current, or more of both voltage and current.
  • Describe the proper safety precautions used when working with storage batteries.
  • Describe how to properly clean and care for storage batteries.
  • Discuss the instruments used for testing storage batteries.
  • Explain how NiCad, lithium, and other types of special batteries operate, and describe their ratings.

    • Alternating Current

    Course #: 086007
    Duration: 5 hours
    Course Prerequisites: DC Principles (Block A21); Basic Industrial Math (Block X21);
    What Students Learn:

  • Draw a graph of an AC voltage and describe how AC voltage is created.
  • Explain AC cycle terms: "alternation," "peak," "positive," and "negative."
  • Define the time period of an AC voltage as expressed in degrees.
  • List the characteristic values of an AC cycle and describe the relationship between the values.
  • Define phase angle and describe how it relates to reactive circuits.
  • Calculate power for single-phase and three-phase circuits.
  • Describe how a 220 VAC single-phase circuit operates.
  • Illustrate the phase relationship of three-phase wave forms.
  • Determine real power by reading a power factor meter.
  • Describe delta and wye three-phase circuit connections.

    • Alternating Current Circuits

    Course #: 086008
    Duration: 5 hours
    Course Prerequisites: DC Principles (Block A21); Basic Industrial Math (Block X21);
    What Students Learn:

  • Identify electric circuits in terms of their circuit characteristics.
  • List several circuit characteristics that are used to describe a circuit for a particular load application.
  • Connect electrical components in series and parallel circuits.
  • Control loads from one or two switch points.
  • Describe how delta- and wye-connected three phase circuits are different.
  • Explain how grounding a circuit increases its safety.
  • Recognize the difference between control circuits and power circuits.

    • Heat, Part 1

    Course #: 686001
    Duration: 10 hours
    Course Prerequisites: Logarithms (5254); Introduction to Algebra, Geometry, and Trigonometry (Block X02);
    What Students Learn: The Nature of Heat; Temperature and its Measurement; The Measurement of Quantity of Heat; Expansion and Contraction; Change of State; Transfer of Heat; Heat and Work Relationships.

    Special Notes:

  • This course requires Logarithm Tables (0975).
  • This updated course replaces course 2582A.
  • The entire course consists of study units 686001-686002.

    • Heat, Part 2

    Course #: 686002
    Duration: 10 hours
    Course Prerequisites: Logarithms (5254); Introduction to Algebra, Geometry, and Trigonometry (Block X02);
    What Students Learn: Relationship between Pressure, Volume, Temperature, Weight of Gases, and the Gas Constant; Expansion of Gases; Compression of Gases; Closed Cycles; Carnot's Engine.

    Special Notes:

  • This course requires Logarithm Tables (0975).
  • This updated course replaces course 2582B.
  • The entire course consists of study units 686001-686002.

    • Light

    Course #: 6255A-B
    Duration: 20 hours
    Course Prerequisites: Plane Trigonometry (2309A-B); Logarithms (5254);
    What Students Learn: PART 1 (6255A). Nature of Light; Measuring of Light or Photometry, including Candle Power, Luminous Flux, Illumination, and Brightness; Reflection of Light and its Application on Mirrors; Kinds of Optical Mirrors, such as Plane, Concave and Convex Spherical, Parabolic, and Elliptic; Refraction of Light and Prisms.
    PART 2 (6255B). Images Obtained by Convex and Concave Lenses; Optical Instruments, such as Magnifier, Microscope, Telescope. Projector, Field Glasses, and Others; Interference of Light; Color of Light and Spectra; Polarized Light; Lasers; Examples for Practice in each Section.

    Sound

    Course #: 6078
    Duration: 10 hours
    Course Prerequisites: Plane Trigonometry (2309A-B); Logarithms (5254);
    What Students Learn: Relation of Sound to Wave Motion; Motion of Particles in a Medium; Harmonic Motion; Velocity, Frequency, and Wave-Length; Nature, Properties and Sources of Sound; Transmission Media; Wave Fronts; Sensitivity of Human Ear; Infrasonics and Ultrasonics; Velocity of Sound in Air, Water, and Solids; Doppler Effect; Reflection; Diffusion; Reverberation; Focusing of Sound; Absorption of Sound; Refraction; Diffraction; Reinforcement and Interference; Resonance; Forced Vibration; Musical Sounds; Vibration of Stretched Strings; Overtones in Harmonics; Vibrations of Air Columns; Closed Pipes and Open Pipes; Vibrations of Reeds, Membranes, and Plates; Sirens; Harmony and Discord; Diatonic Scale; Characteristics of Sound; Loudness; Decibels; Determining Sound Direction; Quality and Waveform; Reproduction of Sound; Transducers; Microphones.

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