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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 a DC power supply is calculated.
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 Heaviside's
operational calculus
3.2 ＜Example 2＞ ・・・70
RC 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 Heaviside's
operational calculus
3.3 ＜Example 3＞ ・・・86
RC series circuit(q = Q0)
3-3-1 Calculation of transient phenomena by differential
equations
3-3-2 Calculation of transient phenomena by Laplace
transform
3.4 ＜Example 4＞ ・・・98
RLC 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 Heaviside's
operational calculus
3.5 ＜Example 5＞ ・・・134
RL series circuit with switch
3-5-1 Calculation of transient phenomena by differential
equations
3-5-2 Calculation of transient phenomena by Laplace
transform
3.6 ＜Example 6＞ ・・・141
RL series circuit with switch and two resistors
3-6-1 Calculation of transient phenomena by differential
equations
3-6-2 Calculation of transient phenomena by Laplace
transform
3.7 ＜Example 7＞ ・・・152
RL series circuit with switch and two resistors
3-7-1 Calculation of transient phenomena by differential
equations
3-7-2 Calculation of transient phenomena by Laplace
transform
3.8 ＜Example 8＞ ・・・158
RL series-parallel circuit with switch
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＞ ・・・170
RL series circuit with switch and two resistors and
two inductances
3-9-1 Calculation of transient phenomena by differential
equations
3-9-2 Calculation of transient phenomena by Laplace
transform
3.10 ＜Example 10＞ ・・・181
RL series circuit with two switches
3-10-1 Calculation of transient phenomena by differential
equations
3-10-2 Calculation of transient phenomena by Laplace
transform
3.11 ＜Example 11＞ ・・・200
RL series-parallel circuits with switch
3-11-1 Calculation of transient phenomena by differential
equations
3-11-2 Calculation of transient phenomena by Laplace
transform
3.12 ＜Example 12＞ ・・・206
RC circuit with two capacitors
3-12-1 Calculation of transient phenomena by differential
equations
3-12-2 Calculation of transient phenomena by Laplace
transform
3.13 ＜Example 13＞ ・・・214
RC circuit with switch
3-13-1 Calculation of transient phenomena by differential
equations
3-13-2 Calculation of transient phenomena by Laplace
transform
3.14 ＜Example 14＞ ・・・231
RC series-parallel circuit with switch
3-14-1 Calculation of transient phenomena by differential
equations
3-14-2 Calculation of transient phenomena by Laplace
transform
3-14-3 Calculation of transient phenomena by Heaviside's
operational calculus
3.15 ＜Example 15＞ ・・・248
RC series circuit with two switches
3-15-1 Calculation of transient phenomena by differential
equations
3-15-2 Calculation of transient phenomena by Laplace
transform
3.16 ＜Example 16＞ ・・・265
LC series circuit
3-16-1 Calculation of transient phenomena by differential
equations
3-16-2 Calculation of transient phenomena by Laplace
transform
3-16-3 Calculation of transient phenomena by Heaviside's
operational calculus
3.17 ＜Example 17＞ ・・・278
LC series circuit(q = Q0)
3-17-1 Calculation of transient phenomena by differential
equations
3-17-2 Calculation of transient phenomena by Laplace
transform
3.18 ＜Example 18＞ ・・・286
RC series circuit(q = Q0)
3-18-1 Calculation of transient phenomena by differential
equations
3-18-2 Calculation of transient phenomena by Laplace
transform
References ・・・295
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