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Differential equations are not usually found directly. However, the weather forecasts broadcast in the morning news are also used to design the cars and airplanes that we normally use. It is also used in ship designs and large structures such as bridges.
It may also be used for structural calculations at your home. It is also used for calculations of water and gas flows. In addition, why is the smartphone's signal coming in? Differential equations are also used in the calculation of electromagnetic waves. Differential equations are used in the design of many products that are essential to daily life.
Electrical and electronic engineering is expressed using mathematics to handle invisible electricity and electromagnetic waves. The transient phenomenon of the electric circuit is not studied so much, and the curriculum advances. I don't think there are many studies of transient phenomena until Laplace transformation, which is learned in control engineering.
Therefore, almost no books have been found that solve the differential equation solution, the Laplace transform solution, and Heaviside's operational calculus.
In this book, the transient response to AC power is calculated. Compared to direct current, it becomes much more difficult with alternating current.
1. Introduction ・・・8
2. Basic theory of transient phenomena ・・・9
(1)First order differential equation
(2)Laplace transform
(3)Heaviside's operational calculus
(4)Other mathematics
(5)Electric circuit
3．Transient phenomenon
3.1 ＜Example 1＞ ・・・60
RL series circuit
3-1-1 Calculation of transient phenomena by differential
equations
3-1-2 Calculation of transient phenomena by Laplace
transform
3-1-3 Calculation of transient phenomena by Laplace
transform（Another solution）
3-1-4 Calculation of transient phenomena by Heaviside's
operational calculus
3.2 ＜Example 2＞ ・・・79
RL series circuit
3-2-1 Calculation of transient phenomena by differential
equations
3-2-2 Calculation of transient phenomena by Laplace
transform
3-2-3 Calculation of transient phenomena by Laplace
transform（Another solution）
3-2-4 Calculation of transient phenomena by Heaviside's
operational calculus
3.3 ＜Example 3＞ ・・・104
RL series circuit
3-3-1 Calculation of transient phenomena by differential
equations
3-3-2 Calculation of transient phenomena by Laplace
transform
3-3-3 Calculation of transient phenomena by Laplace
transform（Another solution）
3-3-4 Calculation of transient phenomena by Heaviside's
operational calculus
3.4 ＜Example 4＞ ・・・137
RC series circuit
3-4-1 Calculation of transient phenomena by differential
equations
3-4-2 Calculation of transient phenomena by Laplace
transform
3-4-3 Calculation of transient phenomena by Laplace
transform（Another solution）
3-4-4 Calculation of transient phenomena by Heaviside's
operational calculus
3.5 ＜Example 5＞ ・・・181
RLC series circuit
3-5-1 Calculation of transient phenomena by differential
equations
3-5-2 Calculation of transient phenomena by Laplace
transform
3-5-3 Calculation of transient phenomena by Heaviside's
operational calculus
3.6 ＜Example 6＞ ・・・238
RL series-parallel circuit
3-6-1 Calculation of transient phenomena by differential
equations
3-6-2 Calculation of transient phenomena by Laplace
transform
3-6-3 Calculation of transient phenomena by Heaviside's
operational calculus
3.7 ＜Example 7＞ ・・・257
RL series-parallel circuit
3-7-1 Calculation of transient phenomena by differential
equations
3-7-2 Calculation of transient phenomena by Laplace
transform
3-7-3 Calculation of transient phenomena by Heaviside's
operational calculus
3.8 ＜Example 8＞ ・・・280
RC series-parallel circuit
3-8-1 Calculation of transient phenomena by differential
equations
3-8-2 Calculation of transient phenomena by Laplace
transform
3-8-3 Calculation of transient phenomena by Heaviside's
operational calculus
3.9 ＜Example 9＞ ・・・310
RC series-parallel circuit
3-9-1 Calculation of transient phenomena by differential
equations
3-9-2 Calculation of transient phenomena by Laplace
transform
3-9-3 Calculation of transient phenomena by Heaviside's
operational calculus
3.10 ＜Example 10＞ ・・・334
RL、RC series-parallel circuit
3-10-1 Calculation of transient phenomena by differential
equations
3-10-2 Calculation of transient phenomena by Laplace
transform
3-10-3 Calculation of transient phenomena by Heaviside's
operational calculus
References ・・・358
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