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

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

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

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

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

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

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

STOCHASTIC MODEL STOCHASTIC Probabilities History Other Models Statistical method Dynamics Stability

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

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

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

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

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

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

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

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

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

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

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Learning Outcomes