ENGINEERING MATHEMATICS

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Contents

Instance of use of exponential form in solution of differential
50
CHAPTER n THE POTENTIAL SERIES AND EXPONENTIAL
52
Use of series for approximation of small terms Instance
58
Solution of the general differential equation by means of
62
B Differential Equations
64
Involution of solution Exponential function
70
Instance of condenser discharge through resistance
76
Solution by trigonometric functions
82
exponential function by the method of indeterminate coefficients
86
Instance of condenser discharge through resistance and induc tance Exponential solution and evaluation of constants
88
Imaginary exponents of exponential functions Reduction to trigonometric functions The oscillating functions
91
Explanation of tables of exponential functions
92
TRIGONOMETRIC SERIES A Trigonometric Functions 66 Definition of trigonometric functions on circle and right triangle
94
Sign of functions in different quadrants
95
Relations between sin cos tan and cot
97
Negative supplementary and complementary angles
98
Relations between two angles and between angle and double angle
102
Differentiation and integration of trigonometric functions Definite integrals
103
The binomial relations
104
Trigonometric formulas of the triangle
105
Constant transient and periodic phenomena Univalent peri odic function represented by trigonometric series
106
Alternating sine waves and distorted waves
107
Evaluation of the Constants from Instantaneous Values Cal culation of constant term of series
108
Calculation of coscoefficients
110
Calculation of sincoefficients
113
Instance of calculating 11th harmonic of generator wave
114
Discussion Instance of complete calculation of pulsating cur rent wave
116
Alternating waves as symmetrical waves Calculation of sym metrical wave
117

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Page 103 - sin 2a = 2 sin a cos a, cos 2a = cos 2 a —sin 2 or,
Page 238 - the radiation is proportional to the fourth power of the absolute temperature. This is the law
Page 275 - Indeed, the most important part of engineering work—and also of other scientific work—is the determination of the method of attacking the problem, whatever it may be,
Page 21 - product is the sum of the logarithms of the factors, thus log,,
Page 192 - The second term in the denominator is small compared with the first term, and
Page 143 - is given as the square root of the sum of squares of the
Page 293 - With the most brilliant engineering design, however, if in the numerical calculation of a single structural member an error has been made, and its strength thereby calculated wrong, the rotor of the machine flies to pieces by centrifugal forces, or the bridge collapses, and with it the reputation of the engineer.
Page 15 - positive is chosen to the right and upward, negative to the left and downward, as indicated in Fig.
Page 275 - be reduced to a small fraction of what it would otherwise be,
Page 72 - with a proportionality factor L, which is called the inductance of the circuit.

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