Innovative Mathematical Education for Maritime Students
Discover the cutting-edge approach to mathematical education tailored for maritime students, featuring topics like RLC circuit analysis, differential equations, and more. Explore insights from MareMathics Teachers Training and Meetings in Tallinn with expert Miro Petkovi. Dive into practical applications and theoretical foundations of mathematics in the maritime field.
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Presentation Transcript
Innovative Approach in Mathematical Education for Maritime Students 2019-1-HR01-KA203-061000 MareMathics Teachers Training - Tallinn Miro Petkovi , mag. ing. University of Split Faculty of Maritime Studies MareMathics Teachers Meeting Tallin 2022, 26 27 April
Innovative Approach in Mathematical Education for Maritime Students 2019-1-HR01-KA203-061000 Series RLC Circuit Analysis Differential equations Maremathics section 8. Derivative Maremathics section 6.1 and 6.2 Properties of Continuous Real Function Maremathics section 6.8 MareMathics Teachers Meeting Tallin 2022, 26 27 April MareMathics Teachers Meeting Tallin 2022, 26 27 April
Innovative Approach in Mathematical Education for Maritime Students 2019-1-HR01-KA203-061000 Series RLC Circuit Analysis What will happen immediately after the closing of the switch at t=0 s ? Current is still 0 A since inductor L does not allow sudden change of the current, (First condition) Resistor voltage is 0 V, Voltage on capacitor is 0 V because he is fully discharged According to Kirchoff voltage law we conclude that at t=0 s, the inductor voltage is equal to the source voltage. (Second condition) ??0 = ???(? = 0) ??(? = 0) ?? =? = ? ?? ? MareMathics Teachers Meeting Tallin 2022, 26 27 April MareMathics Teachers Meeting Tallin 2022, 26 27 April
Innovative Approach in Mathematical Education for Maritime Students 2019-1-HR01-KA203-061000 Series RLC Circuit Analysis At t=0 s : ??? + ??? + ??? = ? We apply voltage drop for each element: ? ? ? + ??? ? +1 ? ? ? ?? = ? ?? Now this equation will be derived by time and divided by L and we will obtain homogenous linear differential equation of second order: ??2? ??2 ? ?? +? ?? ? 1 + ???(?) = 0 MareMathics Teachers Meeting Tallin 2022, 26 27 April MareMathics Teachers Meeting Tallin 2022, 26 27 April
Innovative Approach in Mathematical Education for Maritime Students 2019-1-HR01-KA203-061000 Series RLC Circuit Analysis ??2? ??2 +? ?? ? ?? 1 + ???(?) = 0 ? Figure 1. Maremathics section 9.3.2 Differential equations MareMathics Teachers Meeting Tallin 2022, 26 27 April MareMathics Teachers Meeting Tallin 2022, 26 27 April
Innovative Approach in Mathematical Education for Maritime Students 2019-1-HR01-KA203-061000 Series RLC Circuit Analysis Figure 2. Maremathics section 9.3.2 Differential equations ?2+? 1 Our characteristic equation is : ?? + ??= 0 2 ? ? ? 2 4 ? ?? ?1,2= MareMathics Teachers Meeting Tallin 2022, 26 27 April MareMathics Teachers Meeting Tallin 2022, 26 27 April
Innovative Approach in Mathematical Education for Maritime Students 2019-1-HR01-KA203-061000 Series RLC Circuit Analysis We solve this equation for following set of parameters: R = 15 ; L = 0.5 mH ; C = 10 F ; U = 3 V 2 ??= 10 000 ? ? 4 ?1= 10 000 ?2= 20 000 ? = Discriminant: Figure 3. The general solution when the discriminant is greater than 0 MareMathics Teachers Meeting Tallin 2022, 26 27 April MareMathics Teachers Meeting Tallin 2022, 26 27 April
Innovative Approach in Mathematical Education for Maritime Students 2019-1-HR01-KA203-061000 Series RLC Circuit Analysis So the general solution of the differential equation: ? ? = ?1? 10000?+ ?2? 20000? First condition say that at t=0 s , ? 0 = 0 ? ?1= ?2 Second condition say that at t=0 s , ??(?=0) =? ?? ? ?? ??= 10000?1? 10000?+ 20000?1? 20000? ? ?= 10000?1 ?1= 0.6 Figure 4. Maremathics section 6.2. MareMathics Teachers Meeting Tallin 2022, 26 27 April MareMathics Teachers Meeting Tallin 2022, 26 27 April
Innovative Approach in Mathematical Education for Maritime Students 2019-1-HR01-KA203-061000 Series RLC Circuit Analysis Finally, particular solution of differential equation is: ? ? = 0.6? 10000? 0.6? 20000? Figure 6. Marematics section 6.8 Figure 5. Response of series RLC circuit from 0 ms to 1 ms MareMathics Teachers Meeting Tallin 2022, 26 27 April MareMathics Teachers Meeting Tallin 2022, 26 27 April
Innovative Approach in Mathematical Education for Maritime Students 2019-1-HR01-KA203-061000 Thank you for your attention! "This project has been funded with support from the European Commission. This publication [communication] reflects the views only of the author, and the Commission cannot be held responsible for any use which may be made of the information contained therein". MareMathics Teachers Meeting Tallin 2022, 26 27 April
