Pemodelan Matematika

1. Pemodelan Matematika Setiap teknokrat profesional, seyogianya dapat menyelesaikan masalahnya dengan menggunakan metoda dan prosedur standart matematis yang dapat dipertanggung-jawabkan Matematika Terapan

2. Matematika Terapan

3. Rumus struktur ethena dan polymerisasinya Matematika Terapan

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5. 7anpemodelan matematika adalah : Menyelesaikan masalah secara rinci dan terorganisir baik (bermanfaat – menguntungkan) dan disiplin terpelihara (tanggung-jawab) Matematika Terapan

6. Materi berasal dari sumber informasi mutakhir terkini Matematika Terapan

7. Mathematical Model A mathematical model is an abstract model that uses mathematical language to describe the behaviour of a system. Mathematical models are used particularly in the natural sciences and engineering disciplines (such as physics, biology, and electrical engineering) but also in the social sciences (such as economics, sociology and political science); physicists, engineers, computer scientists, and economists use mathematical models most extensively. Matematika Terapan

8. Examples of mathematical models a. Population Growth. A simple (though approximate) model of population growth is the Malthusian growth model. The preferred population growth model is the logistic function. , laju pertumbuhan bakteri, atau populasi kehidupan (integer) N, jumlah populasi dan t, waktu Matematika Terapan

9. Penyelesaian Matematika Terapan

10. Model of a particle in a potential-field. • In this model we consider a particle as being a point of mass m which describes a trajectory which is modeled by a function x: R → R3 given its coordinates in space as a function of time. The potential field is given by a function V:R3 → R and the trajectory is a solution of the differential equation Note this model assumes the particle is a point mass, which is certainly known to be false in many cases we use this model, for example, as a model of planetary motion. Matematika Terapan

11. Model of rational behavior for a consumer. • Model of rational behavior for a consumer. In this model we assume a consumer faces a choice of n commodities labelled 1,2,...,n each with a market price p1, p2,..., pn. The consumer is assumed to have a cardinal utility function U (cardinal in the sense that it assigns numerical values to utilities), depending on the amounts of commodities x1, x2,..., xn consumed. The model further assumes that the consumer has a budget M which she uses to purchase a vector x1, x2,..., xn in such a way as to maximize U(x1, x2,..., xn). The problem of rational behavior in this model then becomes an optimization problem, that is: Max U(x1,x2,...,xn) subject to: Matematika Terapan

12. This model has been used in general equilibrium theory, particularly to show existence and Pareto optimality of economic equilibria. However, the fact that this particular formulation assigns numerical values to levels of satisfaction is the source of criticism (and even ridicule). However, it is not an essential ingredient of the theory and again this is an idealization. • Neighbour-sensing model explains the mushroom formation from the initially chaotic fungal network. Matematika Terapan

13. Teknik Analisa System Matematika Terapan

14. Systems engineering Systems engineering has triple bases: a physical (natural) science basis, an organizational and social science basis, and an information science and knowledge basis. The natural science basis involves primarily matter and energy processing. The organizational and social science basis involves human, behavioral, economic, and enterprise concerns. The information science and knowledge basis is derived from the structure and organization inherent in the natural sciences and in the organizational and social sciences. Matematika Terapan

15. Systems engineering Matematika Terapan

16. The scope of Systems Engineering activities Matematika Terapan

17. Matematika Terapan Tools for graphic representations

18. Common graphical representations include: • Functional Flow Block Diagram (FFBD) • Data Flow Diagram (DFD) • N2 (N-Squared) Chart • Use Case and • Sequence Diagram. Matematika Terapan

19. b. Flow of water from an orifice Pada kondisi konstan h = h p pada t =0 Matematika Terapan

20. c. Heat Flow Matematika Terapan

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22. Penampilan dalam karya tulis (komunikatif) Matematika Terapan

23. d. Salt dissolving ing water Bila x gram garam dimasukkan ke dalam M gram air pada waktu t = 0, maka terdapat berapa gram yang tidak dilarutkan dalam waktu yang ke t? Laju pelarutan yang terjadi, adalah dx/dt, adalah proporsional, (a) banyaknya garam, x, tidak terlarut dalam waktu ke, t, (b) beda antara konsentrasi jenuh, X/M, dan konsentrasi aktual, (xo – x)/M. (X adalah banyaknya gram garam yankan menjenuhkan). Sehingga : Matematika Terapan

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25. e. Atmospheric pressure at any height Pertambahan tekanan antara dua titik di atmosfir yang berbeda ketinggiannya dh yaitu dP = -  g dh, bilaadalah densitas pada ketinggian h. Tetapi  adalah dihubungkan dengan P oleh ekspresi P – = Poo – ) ini valid pada expansi adiabatik udara bilabernilai 1.42. Quantitas Podanopada level permukaan laut nilai P dan  Matematika Terapan

26. dP = - (P/Po)1/o g dh hasil integralnya adalah : (P/Po) (-1)/  = 1 -  - 1 o g h  Po Nilainya konstan ketika P = Po pada h = 0 Matematika Terapan

27. Model selanjutnya f, g, h dan i Difoto copy sendiri bahan ini …… nanti Matematika Terapan

28. Aremania & Aremanita Matematika Terapan

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31. Stop Matematika Terapan