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Pemodelan Matematika

Setiap teknokrat profesional, seyogianya dapat menyelesaikan masalahnya dengan menggunakan metoda dan prosedur standart matematis yang dapat dipertanggung-jawabkan

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Rumus struktur ethena dan polymerisasinya

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7an pemodelan matematika adalah :

Menyelesaikan masalah secara rinci dan terorganisir baik

(bermanfaat – menguntungkan) dan disiplin terpelihara (tanggung-jawab)

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Materi berasal dari sumber informasi mutakhir terkini

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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.

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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

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Penyelesaian

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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.

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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:

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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.

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Teknik Analisa System

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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.

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Systems engineering

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The scope of Systems Engineering activities

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Tools for graphic representations

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Common graphical representations include:

• Functional Flow Block Diagram (FFBD) • Data Flow Diagram (DFD) • N2 (N-Squared) Chart • Use Case and

• Sequence Diagram.

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b. Flow of water from an orifice

Pada kondisi konstan h = h p pada t =0

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c. Heat Flow

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Penampilan dalam karya tulis (komunikatif)

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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 :

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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 Po dan o pada level permukaan laut nilai P dan

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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

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Model selanjutnya f, g, h dan i

Difoto copy sendiri bahan ini …… nanti

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Aremania & Aremanita

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Stop