Chapter 2: Potential Series And Exponential Function
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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-02 |
| Location | lines 3492-6063 |
| Status | candidate |
| Word Count | 7738 |
| Equation Candidates In Section | 0 |
| Figure Candidates In Section | 0 |
| Quote Candidates In Section | 0 |
Opening Source Excerpt
Section titled “Opening Source Excerpt”CHAPTER II. POTENTIAL SERIES AND EXPONENTIAL FUNCTION. A. GENERAL. 39. An expression such as y-xk w represents a fraction; that is, the result of division, and hke any fraction it can be calculated; that is, the fractional form eliminated, by dividing the numerator by the denominator, thus : l-x l = l+x + x2 + a:3 + . . . l-x x—x^ - x-—x^ -^x\ Hence, the fraction (1) can also be expressed in the form: ( 2/=TX~^-'^"^^ + ^^'^^'^' • • (2) This is an infinite series of successive powers of x, or a poten- tial series. In the same manner, by dividing through, the expression y^ih' ■ ^^^ can be reduced to the infinite series, y=j^ = l-x-hx^-x^+- |(4) 52 POTENTIAL SERIES AND EXPONENTIAL FUNCTION. 53 The infinite series (2) or (4) isSource-Located Theme Snippets
Section titled “Source-Located Theme Snippets”Field language
Section titled “Field language”... rent functions, until one is found which satisfies the equation. In electrical engineering, currents and voltages are dealt with as functions of time. The current and c.m.f. giving the power lost in resistance are related to each other by Ohm's law. Current also produces a magnetic field, and this magnetic field by its changes generates an e.m.f. — the e.m.f. of self- inductance. In this case, e.m.f. is related to the change of current; that is, the differential coefficient of the current, and thus also to the differential coefficient of e.m.f., since the e. ...Dielectricity / capacity
Section titled “Dielectricity / capacity”... his case, e.m.f. is related to the change of current; that is, the differential coefficient of the current, and thus also to the differential coefficient of e.m.f., since the e.m.f. POTENTIAL SERIES AND EXPONENTIAL FUNCTION. 65 is related to the current by Ohm's law. In a condenser, the current and therefore, b}^ Ohm's law, the e.m.f., depends upon and is proportional to the rate of change of the e.m.f. impressed upon the condenser; that is, it is proportional to the differential coefficient of e.m.f. Therefore, in circuits having resistance and indu ...Complex quantities
Section titled “Complex quantities”... (1) can also be expressed in the form: ( 2/=TX~^-'^"^^ + ^^'^^'^' • • (2) This is an infinite series of successive powers of x, or a poten- tial series. In the same manner, by dividing through, the expression y^ih' ■ ^^^ can be reduced to the infinite series, y=j^ = l-x-hx^-x^+- |(4) 52 POTENTIAL SERIES AND EXPONENTIAL FUNCTION. 53 The infinite series (2) or (4) is another form of representa- tion of the expression (1) or (3), just as the periodic decimal fraction is another representation of the common fraction (for instance 0.6 ...Magnetism
Section titled “Magnetism”... rent functions, until one is found which satisfies the equation. In electrical engineering, currents and voltages are dealt with as functions of time. The current and c.m.f. giving the power lost in resistance are related to each other by Ohm's law. Current also produces a magnetic field, and this magnetic field by its changes generates an e.m.f. — the e.m.f. of self- inductance. In this case, e.m.f. is related to the change of current; that is, the differential coefficient of the current, and thus also to the differential coefficient of e.m.f., since ...Chapter-Local Concept Hits
Section titled “Chapter-Local Concept Hits”| Concept Candidate | Hits In Section | Status |
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| Ether | 5 | seeded |
| Light | 2 | seeded |
| Frequency | 1 | seeded |
Chapter-Local Glossary Hits
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| ether | 5 | seeded |
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Modern Engineering Reading Prompts
Section titled “Modern Engineering Reading Prompts”- Field language: Read for whether field language is mechanical, geometrical, causal, descriptive, or simply a convenient engineering model.
- Dielectricity / capacity: Check whether the passage treats capacity, condensers, displacement, or dielectric stress as field storage rather than only circuit algebra.
- Complex quantities: Track how Steinmetz preserves geometric rotation and quadrature while translating the same operation into symbolic form.
- 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.
Ether-Field Interpretive Boundary
Section titled “Ether-Field Interpretive Boundary”- Field language: Field-pressure or field-gradient interpretations can be explored here only after the explicit source passage and modern engineering translation are kept distinct.
- 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.
- 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.
Promotion Checklist
Section titled “Promotion Checklist”- Open the full source text and the scan or raw PDF.
- Verify the chapter boundary and surrounding context.
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- Move mathematical candidates into canonical equation pages only after formula typography is corrected.
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