Chapter 3: Trigonometric Series
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Source Metadata
Section titled “Source Metadata”| Field | Value |
|---|---|
| Source | Engineering Mathematics: A Series of Lectures Delivered at Union College |
| Year | 1911 |
| Section ID | engineering-mathematics-chapter-03 |
| Location | lines 6064-15155 |
| Status | candidate |
| Word Count | 18269 |
| Equation Candidates In Section | 0 |
| Figure Candidates In Section | 5 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER HI. TRIGONOMETRIC SERIES. A. TRIGONOMETRIC FUNCTIONS. 66. For the engineer, and especially the electrical engineer, a perfect familiarity with the trigonometric functions and trigonometric formulas is almost as essential as familiarity with the multiplication table. To use trigonometric methods efficiently, it is not sufficient to understand trigonometric formulas enough to be able to look them up when required, but they must be learned by heart, and in both directions; that is, an expression similar to the left side of a trigonometric for- mula must immediately recall the right side, and an expression similar to the right side must immediately recall the left side of the formula. Trigonometric functions are defined on the circle, and on the right triangle. Let in the circle, Fig. 28, the direction to the right and upward be considered asSource-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Waves / transmission lines
Section titled “Waves / transmission lines”... important periodic functions in electrical engineering are the alternating currents and e.m.fs. Usually they are, in first approximation, represented by a single trigo- nometric function, as : i = io cos {O—ix))] or, e = eo sin (d—d); that is, they are assumed as sine waves. 108 ENGINEERING MATHEMATICS. f ■ . Theoretically, obviously this condition can never be perfectly attained, and frequently the deviation from sine shape is suffi- cient to require practical consideration/ especially in those cases, where the electric circuit contain ...Impedance / reactance
Section titled “Impedance / reactance”... em, the equa- tion : e = eo{sin ^-0.12 sin (3<9- 2. 3°) -0.23 sin (5^-1.5°) +0.13 sin (7^-6. 2°)1. . (1) In first approximation, the line capacity may be considered as a condenser shunted across the middle of the line; that is, half the line resistance and half the line reactance is in series with the line capacity. As the receiving apparatus do not utilize the higher har- monics of the generator wave, when using the old generators, their voltage has to be transformed up so as to give the first harmonic or fundamental of 44,000 volts. 44,000 volt ...Magnetism
Section titled “Magnetism”... condition of an electric circuit, as a change of load; or, disturbances entering the circuit from the outside or originating in it, etc. Periodic phenomena are the alternating currents and voltages, pulsating currents as those produced by rectifiers, the distribution of the magnetic flux in the air-gap of a machine, or the distribution of voltage around the commutator of the direct-current machine, the motion of the piston in the steam-engine cylinder, the variation of the. mean daily temperature with the seasons of the year, etc. The characteristic o ...Ether references
Section titled “Ether references”... hence, its effective value is 5.07 V2 3.58, while the effective value of the total generator wave, that is, the. square root of the mean squares of the instanta- neous values y, is e = 30.5, thus the 11th harmonic is 11.8 per cent of the total voltage, and whether such a harmonic is safe or not, can now be deter- mined from the circuit constants, more particularly its resist- ance. 82. In general, the successive harmonics decrease; that is, with increasing n, the values of an and bn become smaller, and when calculating a^ and hn by ...Chapter-Local Concept Hits
Section titled “Chapter-Local Concept Hits”| Concept Candidate | Hits In Section | Status |
|---|---|---|
| Ether | 18 | seeded |
| Magnetic permeability | 7 | seeded |
| Frequency | 5 | seeded |
| Light | 4 | seeded |
| Radiation | 1 | seeded |
Chapter-Local Glossary Hits
Section titled “Chapter-Local Glossary Hits”| Term Candidate | Hits In Section | Status |
|---|---|---|
| ether | 18 | seeded |
| electrostatic capacity | 1 | source-located candidate |
Equation Candidates
Section titled “Equation Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
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| No chapter-local candidates yet | - | - |
Figure Candidates
Section titled “Figure Candidates”| Candidate ID | OCR / PDF-Text Candidate | Source Location |
|---|---|---|
engineering-mathematics-fig-046 | of the exactness of the results resulting from the limited num- FiG. 46. ber of numerical values of i, on which the calculation is based. | line 11540 |
engineering-mathematics-fig-047 | able to supply the charging current of the line, due to the Fig. 47. wave shape distortion, more than two generators are required. | line 12032 |
engineering-mathematics-fig-048 | purposes, as short-distance distribution. Fig. 48. In Figs. 47 and 48 are plotted the voltage wave and the current wave, from equations (9) and (14) repsectively, and | line 12041 |
engineering-mathematics-fig-049 | As seen from Fig. 49, the fundamental wave has practically Fig. 49. vanished, and the voltage wave is the seventh harmonic, modi- | line 12109 |
engineering-mathematics-fig-057 | ?ro (62) Fig. 57. Substituting (61) into (62) gives, | line 13829 |
Hidden-Gem Quote Candidates
Section titled “Hidden-Gem Quote Candidates”| Candidate ID | Candidate Passage | Source Location |
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| No chapter-local candidates yet | - | - |
Modern Engineering Reading Prompts
Section titled “Modern Engineering Reading Prompts”- Waves / transmission lines: Map Steinmetz’s wave and line language onto modern distributed constants, propagation velocity, standing waves, and reflections.
- Impedance / reactance: Translate historical opposition terms into modern impedance, admittance, conductance, susceptance, and complex-plane notation.
- Magnetism: Track flux, reluctance, permeability, magnetizing force, and loss language against modern magnetic-circuit terminology.
- Ether references: Verify exact wording before drawing conclusions. Ether language must be separated from later interpretive systems.
- Dielectricity / capacity: Check whether the passage treats capacity, condensers, displacement, or dielectric stress as field storage rather than only circuit algebra.
Ether-Field Interpretive Boundary
Section titled “Ether-Field Interpretive Boundary”- Waves / transmission lines: Standing/traveling wave passages may support richer field interpretations; the page keeps those readings separate from verified Steinmetz wording.
- Magnetism: Centrifugal/divergent magnetic-field readings are interpretive overlays, not automatic historical claims.
- Ether references: If Steinmetz mentions ether, quote only the verified source words first; any broader ether-field synthesis belongs in a labeled interpretive layer.
- Dielectricity / capacity: A Wheeler-style reading may emphasize dielectric compression, field stress, and stored potential, but this page treats that as interpretation unless Steinmetz explicitly says it.
Promotion Checklist
Section titled “Promotion Checklist”- Open the full source text and the scan or raw PDF.
- Verify the chapter boundary and surrounding context.
- Promote exact quotations only after checking the source image.
- Move mathematical candidates into canonical equation pages only after formula typography is corrected.
- Move diagram candidates into the diagram archive only after image extraction, crop verification, and manifest creation.
- Keep Steinmetz wording, modern translation, and ether-field interpretation in separate labeled layers.