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

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

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

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

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

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

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

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

STOCHASTIC MODEL STOCHASTIC Probabilities History Stability Other Models Statistical method Dynamics

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

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

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

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

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

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

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

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

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

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