Suharmadi Sanjaya - Matematika ITS

BACKGROUND A Good course has a clear purpose: Applied Mathematics is alive and very vigorous Teaching of Apllied Mathematics need a fresh approach It must provide a frame work into which the applications will fit The central topics are : Differential Equations & Matrix Equations The Continous and Discrete

They reinforce each other because they go in paralel, one side is Calculus ; on the other is Algebra To see the cooperation between Calculus & Linear Algebra is to see one of the best parts of modern Applied Mathematics Background

The right approach is not to model a few isolated examples, but, the more important goal is to find ideas that are shared by a wide range of applications The contribution is to recognize and explain the underlying pattern It aims to explain what is essential as far as posible

Background Emphasis must go to Equilibrium equations ( Boundary Value problems (BVP ) ) & Dynamics Equations ( Initial Value Problems (IVP) ) Supported Subjects : Applied Analysis Mathematical Modelling & Optimization Scientific Computation ( Computer can do, without being dominated by it )

Dynamics & Equilibrium Discrete & Continous Calculus & Aljabar Matrix & Differential Equation System Ax = b 2 nd- Order Differential Equation One Variable Partial Differential Equations Two Point BVP Initial Value Problems BVP – Eliptic Laplace Poisson Mixed BVP & IVP Parabolics & Hyperbolics Establish Gaussian Elimination Matrix Factorization Technique Underlying Geometri Recognize The associated Minimum Principle Matrix PD Presentasi

Kompetensi  Kompetensi Utama: Mampu mengkonstruksi model matematika pada masalah diskrit & kontinyu (masalah Equilibrium & Dynamics ) serta melakukan simulasi model tersebut.  Kompetensi pendukung: Memahami konsep pemodelan matematika & simulasi  Kompetensi Lainnya Menguasai tehnik pemrogaman (m file & GUI Matlab ) Memahami konsep penelitian Memahami tatatulis ilmiah standar nasional

PERSAMAAN LINIER Model yang paling sederhana dan penting pada matematika terapan adalah sistem persamaan linier misalnya Sistem persamaan tersebut terdiri atas 2 anu dengan 2 persamaan, tentu saja sangat mudah untuk diselesaikan