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MODEL & MATHEMATICS Disarikan oleh : Prof Dr Ir Soemarno MS

MODEL & MATHEMATICS Disarikan oleh : Prof Dr Ir Soemarno MS. WHAT IS SYSTEM MODELLING ?. Worthwhile. Recognition. Problems . Amenable. Compromise. Complexity. Definitions. Simplification. Bounding. Objectives. Hierarchy. Identification . Priorities. Goals. Generality.

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MODEL & MATHEMATICS Disarikan oleh : Prof Dr Ir Soemarno MS

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  1. MODEL & MATHEMATICS Disarikanoleh: Prof Dr IrSoemarno MS

  2. WHAT IS SYSTEM MODELLING ? Worthwhile Recognition Problems Amenable Compromise Complexity Definitions Simplification Bounding Objectives Hierarchy Identification Priorities Goals Generality Solution Family Generation Selection Modelling Inter-relationship Feed-back Stopping rules Evaluation Sensitivity & Assumptions Implementation

  3. PHASES OF SYSTEM MODELLING Recognition Definition and bounding of the problems Identification of goals and objectives Generation of solution MODELLING Evaluation of potential courses of action Implementation of results

  4. MODEL & MATEMATIK: Term Tipe Konstante Variabel Parameter Likelihood Dependent Populasi Probability Analitik Independent Maximum Sampel Simulasi Regressor

  5. MODEL & MATEMATIK: Definition Preliminary Mathematical Goodall Mapping Rules Formal Expression Representational Maynard-Smith Predicted values Words Homomorph Model Comparison Physical Symbolic Data values Simulation Mathematical Simplified

  6. MODEL & MATEMATIK: Relatives Disadvantages Advantages Distortion Precise Opaqueness Abstract Complexity Transfer Replacement Communication

  7. MODEL & MATEMATIK: Families Basis Choices Types Dynamics Compartment Stochastic Multivariate Network

  8. BEBERAPA PENGERTIAN MODEL DETERMINISTIK: Nilai-nilai yang diramal (diestimasi, diduga) dapat dihitung secara eksak. MODEL STOKASTIK: Model-model yang diramal (diestimasi, diduga) tergantung pada distribusi peluang POPULASI: Keseluruhan individu-individu (atau area, unit, lokasi dll.) yang diteliti untuk mendapatkan kesimpulan. SAMPEL: sejumlah tertentu individu yang diambil dari POPULASI dan dianggap nilai-nilai yang dihitung dari sampel dapat mewakili populasi secara keseluruhan PARAMETER: Nilai-nilai karakteristik dari populasi KONSTANTE, KOEFISIEAN: nilai-nilai karakteristik yang dihitung dari SAMPEL VARIABEL DEPENDENT: Variabel yang diharapkan berubah nilainya disebabkan oleh adanya perubahan nilai dari variabel lain VARIABEL INDEPENDENT: variabel yang dapat menyebabkan terjadinya perubahan VARIABEL DEPENDENT.

  9. BEBERAPA PENGERTIAN MODEL FITTING: Proses pemilihan parameter (konstante dan/atau koefisien yang dapat menghasilkan nilai-nilai ramalan paling mendekati nilai-nilai sesungguhnya ANALYTICAL MODEL: Model yang formula-formulanya secara eksplisit diturunkan untuk mendapatkan nilai-nilai ramalan, contohnya: MODEL REGRESI MODEL MULTIVARIATE EXPERIMENTAL DESIGN STANDARD DISTRIBUTION, etc SIMULATION MODEL: Model yang formula-formulanya diturunkan dengan serangkaian operasi arithmatik, misal: Solusi persamaan diferensial Aplikasi matrix Penggunaan bilangan acak, dll.

  10. DYNAMIC MODEL MODELLING SIMULATION Equations Dynamics Computer FORMAL Language ANALYSIS Special General DYNAMO CSMP CSSL BASIC

  11. DYNAMIC MODEL DIAGRAMS SYMBOLS RELATIONAL AUXILIARY VARIABLES LEVELS MATERIAL FLOW RATE EQUATIONS PARAMETER INFORMATION FLOW SINK

  12. DYNAMIC MODEL: ORIGINS Abstraction Equations Steps Computers Hypothesis Discriminant Function Simulation Other functions Undestanding Logistic Exponentials

  13. MATRIX MODEL MATHEMATICS Matrices Eigen value Operations Elements Dominant Additions Substraction Multiplication Inversion Types Eigen vector Square Rectangular Diagonal Identity Vectors Scalars Row Column

  14. MATRIX MODEL DEVELOPMENT Interactions Groups Stochastic Materials cycles Size Markov Models Development stages

  15. STOCHASTIC MODEL STOCHASTIC Probabilities History Other Models Statistical method Dynamics Stability

  16. STOCHASTIC MODEL Spatial patern Distribution Example Pisson Poisson Negative Binomial Binomial Negative Binomial Fitting Test Others

  17. STOCHASTIC MODEL ADDITIVE MODELS Basic Model Example Error Estimates Analysis Parameter Variance Orthogonal Block Effects Experimental Significance Treatments

  18. STOCHASTIC MODEL REGRESSION Model Example Error Decomposition Equation Linear/ Non-linear functions Theoritical base Oxygen uptake Reactions Experimental Empirical base Assumptions

  19. STOCHASTIC MODEL MARKOV Analysis Example Assumptions Analysis Disadvantage Advantages Transition probabilities Raised mire

  20. MULTIVARIATE MODELS METHODS VARIATE Variable Classification Dependent Descriptive Predictive Principal Component Analysis Discriminant Analysis Independent Cluster Analysis Reciprocal averaging Canonical Analysis

  21. MULTIVARIATE MODEL PRINCIPLE COMPONENT ANALYSIS Requirement Example Correlation Objectives Environment Eigenvalues Eigenvectors Organism Regions

  22. MULTIVARIATE MODEL CLUSTER ANALYSIS Example Spanning tree Multivariate space Demography Rainfall regimes Minimum Similarity Single linkage Distance Settlement patern

  23. MULTIVARIATE MODEL CANONICAL CORRELATION Example Correlation Partitioned Watershed Urban area Eigenvalues Eigenvectors Irrigation regions

  24. MULTIVARIATE MODEL Discriminant function Example Discriminant Calculation Villages Vehicles Test Structures

  25. OPTIMIZATION MODEL OPTIMIZATION Dynamic Meanings Indirect Non-Linear Linear Simulation Objective function Minimization Constraints Experimentation Solution Examples Maximization Optimum Transportation Routes Optimum irrigation scheme Optimum Regional Spacing

  26. MODELLING PROCESS System analysis Introduction Processes Model Space Time Niche Elements Bounding Systems Definition Word Models Impacts Factorial Confounding Alternatives Separate Combinations Hypotheses Data Plotting Outliers Modelling Analysis Test Choices Estimates Validation Conclusion Integration Communication

  27. MODELLING PROCESSES HYPOTHESES Decision Table Relevance Processes Relationships Variable Linkages Linear Impacts Non-Linear Species Interactive Sub-systems

  28. HYPOTHESES Hypotheses of Relevance: Mengidentifikasi dan mendefinisikan variabel dan subsistem yang relevan dengan permasalahan yang diteliti Hypotheses of Processes: Menghubungkan subsistem (atau variabel) di dalam permasalahan yang diteliti dan mendefinisikan dampak (pengaruh) terhadap sistem yang diteliti Hypotheses of relationships: Merumuskan hubungan-hubungan antar variabel dengan menggunakan formula-formula matematik (fungsi linear, non-linear, interaksi, dll)

  29. MODELLING PROCESSES VALIDATION Verification Critical Test Sensitivity Analysis Subjectives Uncertainty Analysis Resources Objectivities Experiments Interactions Reasonableness

  30. ROLE OF THE COMPUTER Roles Speed Data Algoritm Introduction Reasons Manual Calculator Computer Comparison Speed Techniques Errors Plotting Implication Repetition Checking Waste 9/10 Modelling Data FORTRAN BASIC ALGOL Program High level Algoritms Language Machine code DYNAMO. Etc. Special Information Development Conclusions Programming

  31. ROLE OF THE COMPUTER DATA Machine readable Cautions Availability Format Sampling Punched card Exchange Paper tape Format Reanalysis Magnetic Tape Data banks Disc

  32. MODEL & MATHEMATICS

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