1. Pemodelan Kuantitatif Mat & Stat Pertemuan 3: Mata kuliah:K0194-Pemodelan Matematika Tahun:2008

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

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

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

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

6. DYNAMIC MODEL (2) DIAGRAMS RELATIONAL SYMBOLS RATE EQUATIONS LEVELS PARAMETER INFORMATION FLOW SINK AUXILIARY VARIABLES MATERIAL FLOW

7. DYNAMIC MODEL: (3) ORIGINS Computers Equations Other functions Steps Discriminant Function Undestanding Simulation Abstraction Hypothesis Logistic Exponentials

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

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

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

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

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

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

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

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

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

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

18. MULTIVARIATE MODEL (4) CANONICAL CORRELATION Example Correlation Urban area Watershed Partitioned Irrigation regions Eigenvalues Eigenvectors

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

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