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Learning Outcomes

Learning Outcomes. Mahasiswa dapat memahami pemodelan kuantitaif yang ada di bidang Matematika danStatistika. Outline Materi:. Pengertian Model Matematika & Statistika Sistem Modelling Dynamic model Matrix model Stochastic model Multivariate model Optimization model.

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Learning Outcomes

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  1. Learning Outcomes • Mahasiswa dapat memahami pemodelan kuantitaif yang ada di bidang Matematika danStatistika..

  2. Outline Materi: • Pengertian Model Matematika & Statistika • Sistem Modelling • Dynamic model • Matrix model • Stochastic model • Multivariate model • Optimization model

  3. PEMODELAN KUANTITATIF : MATEMATIKA DAN STATISTIKA MODEL STATISTIKA: FENOMENA STOKASTIK MODEL MATEMATIKA: FENOMENA DETERMINISTIK

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

  5. DYNAMICMODEL (2) DIAGRAMS SYMBOLS RELATIONAL AUXILIARYVARIABLES LEVELS MATERIALFLOW RATE EQUATIONS PARAMETER INFORMATION FLOW SINK

  6. DYNAMIC MODEL: (3) ORIGINS Abstraction Equations Steps Computers Hypothesis Discriminant Function Simulation Otherfunctions Undestanding Exponentials Logistic

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

  8. MATRIX MODEL(2) DEVELOPMENT Interactions Groups Stochastic Materials cycles Size Markov Models Development stages

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

  10. STOCHASTIC MODEL (2) Spatial patern Distribution Example Pisson Poisson Negative Binomial Binomial Negative Binomial Fitting Test Others

  11. STOCHASTIC MODEL (3) ADDITIVE MODELS Example Basic Model Error Estimates Analysis Parameter Variance Orthogonal Block Effects Experimental Significance Treatments

  12. STOCHASTIC MODEL (4) REGRESSION Model Example Error Decomposition Equation Linear/ Non-linear functions Theoritical base Oxygen uptake Reactions Experimental Empirical base Assumptions

  13. STOCHASTIC MODEL (5) MARKOV Analysis Example Assumptions Analysis Disadvantage Advantages Transition probabilities Raised mire

  14. MULTIVARIATE MODELS(1) METHODS VARIATE Variable Classification Dependent Descriptive Predictive Principal Component Analysis Discriminant Analysis Independent Cluster Analysis Reciprocal averaging Canonical Analysis

  15. MULTIVARIATE MODEL(2) PRINCIPLE COMPONENT ANALYSIS Requirement Example Correlation Objectives Environment Eigenvalues Eigenvectors Organism Regions

  16. MULTIVARIATE MODEL(3) CLUSTER ANALYSIS Example Spanning tree Multivariate space Demography Rainfall regimes Minimum Similarity Single linkage Distance Settlement patern

  17. MULTIVARIATEMODEL (4) CANONICAL CORRELATION Example Correlation Partitioned Watershed Urban area Eigenvalues Eigenvectors Irrigation regions

  18. MULTIVARIATE MODEL(5) Discriminant Function Example Discriminant Calculation Villages Vehicles Test Structures

  19. 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

  20. Terima kasih, Semoga berhasil

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