logging in or signing up MATHEMATICAL MODELING AND ITS APPLICATION manish.nandi Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 1807 Category: Entertainment License: All Rights Reserved Like it (3) Dislike it (0) Added: October 09, 2010 This Presentation is Public Favorites: 2 Presentation Description No description available. Comments Posting comment... By: Rajiv64 (11 month(s) ago) Sir, Excellent Presentation. My Request is to please add some references . Saving..... Post Reply Close Saving..... Edit Comment Close By: goodaobo (13 month(s) ago) i want this ppt Saving..... Post Reply Close Saving..... Edit Comment Close By: zinowinsky (15 month(s) ago) Thanks for your post. I would love to make a request to have a copy of the ppt to help on my studies. I would be very glad if you could mail it to me. zinowinsky@yahoo.com Thanks once again.God Bless Saving..... Post Reply Close Saving..... Edit Comment Close Premium member Presentation Transcript MATHEMATICAL MODELING AND ITS APPLICATION : MATHEMATICAL MODELING AND ITS APPLICATION By Manish Nandi Assistant Professor Introduction: : Introduction: A natural question which must have arisen in our mind is “What is Mathematical Modeling?” Mathematical Modeling consists of simplifying Real World problems and representing them as Mathematical problems(Mathematical Model), solving the mathematical problems and interpreting these solutions in language of the Real World. In simple form- Conversion of Real World phenomena under certain conditions into Mathematical formulation is known as Mathematical Modeling. Introduction cond…… : Introduction cond…… Performing experiments to understand & solve Real World problems may be risks & expensive. Mathematical Modeling is the only recourse in such situation. The use of mathematics in solving Real World problems has become widespread especially due to the increasing computation power of digital computer and computing methods both of which have facilitated the handling of length and complicated problems. Introduction cond……. : Introduction cond……. Mathematical Models are basically of two kinds……… (i) Empirical Models & (ii) Theoretical Models. Experiments (i) Empirical Models Observation Mathematical (ii) Theoretical Models Statistical Computer based Introduction cond…….. : Introduction cond…….. The importance of Mathematical Modeling as a discipline to be studied and cultivated, has been realised only during the last three or four decades. Three Main Steps:We can divide the Modeling process into three main steps. : Three Main Steps:We can divide the Modeling process into three main steps. Modeling Formulation Solution Evaluation Stating the Identifying Mathematical Question Relevant Factor Description Mathematical Model follows the process: : Mathematical Model follows the process: Start Formulation Solution Evaluation No Yes Satisfied Stop Why mathematical modeling? : Why mathematical modeling? Mathematical modeling is the art of translating problems from an application area into tractable mathematical formulations whose theoretical and numerical analysis provides insight, answers, and guidance useful for the originating application. Mathematical Modeling is indispensable in many applications. is successful in many further applications. gives precision and direction for problem solution. enables a thorough understanding of the system modeled. prepares the way for better design or control of a system. allows the efficient use of modern computing capabilities. A list of applications : A list of applications All areas mentioned have numerous mathematical challenges Anthropology Modeling, classifying and reconstructing skulls Archaeology Reconstruction of objects from preserved fragments Classifying ancient artifices Architecture Virtual reality Artificial intelligence Computer vision Image interpretation Robotics Speech recognition Optical character recognition Reasoning under uncertainty Application Cond……… : Application Cond……… Arts Computer animation (Jurassic Park) Astronomy Detection of planetary systems Correcting the Hubble telescope Origin of the universe Evolution of stars Biology Protein folding Humane genome project Population dynamics Morphogenesis Evolutionary pedigrees Spreading of infectious diseases (AIDS) Animal and plant breeding (genetic variability) Application Cond…. : Application Cond…. Chemical engineering Chemical equilibrium Planning of production units Chemistry Chemical reaction dynamics Molecular modeling Electronic structure calculations Computer science Image processing Realistic computer graphics (ray tracing) Criminalistic science Finger print recognition Face recognition Application Cond……. : Application Cond……. Economics Labour data analysis Electrical engineering Stability of electric curcuits Microchip analysis Power supply network optimization Finance Risk analysis Value estimation of options Fluid mechanics Wind channel Turbulence Application Cond……. : Application Cond……. Geosciences Prediction of oil or ore deposits Map production Earth quake prediction Internet Web search Optimal routing Linguistics Automatic translation Application Cond…… : Application Cond…… Materials Science Microchip production Microstructures Semiconductor modeling Mechanical engineering Stability of structures (high rise buildings, bridges, air planes) Structural optimization Crash simulation Medicine Radiation therapy planning Computer-aided tomography Blood circulation models Application Cond….. : Application Cond….. Meteorology Weather prediction Climate prediction (global warming, what caused the ozone hole?) Music Analysis and synthesis of sounds Neuroscience Neural networks Signal transmission in nerves Pharmacology Docking of molecules to proteins Screening of new compounds Application Cond……. : Application Cond……. Political Sciences Analysis of elections Psychology Formalizing diaries of therapy sessions Space Sciences Trajectory planning Flight simulation Shuttle re entry Transport Science Air traffic scheduling Taxi for handicapped people Automatic pilot for cars and airplanes Also… : Also… Mathematical Model of Urban & regional planning Population Environmental Water Resources Optimal utilization of exhaustible & renewable resources Land distribution Forestry and so on. Types of Modeling : Types of Modeling Linear or Non-linear. Static or Dynamic. Discrete or Continuous. Deterministic or Probabilistic. Some Example of Mathematical Models : Some Example of Mathematical Models Find the mass of the Earth (without using a balance). Find the temperature at the centre of the Sun (without taking a thermometer there). Find the volume of blood inside the body of a person (without bleeding the person to death). Estimate the population of India in the year 2050 AD (without waiting till than). Estimate the total expenditure for an owner to run his Rubber garden in the next five year (without waiting). THANK YOU : THANK YOU You do not have the permission to view this presentation. In order to view it, please contact the author of the presentation.
MATHEMATICAL MODELING AND ITS APPLICATION manish.nandi Download Post to : URL : Related Presentations : Share Add to Flag Embed Email Send to Blogs and Networks Add to Channel Uploaded from authorPOINT lite Insert YouTube videos in PowerPont slides with aS Desktop Copy embed code: (To copy code, click on the text box) Embed: URL: Thumbnail: WordPress Embed Customize Embed The presentation is successfully added In Your Favorites. Views: 1807 Category: Entertainment License: All Rights Reserved Like it (3) Dislike it (0) Added: October 09, 2010 This Presentation is Public Favorites: 2 Presentation Description No description available. Comments Posting comment... By: Rajiv64 (11 month(s) ago) Sir, Excellent Presentation. My Request is to please add some references . Saving..... Post Reply Close Saving..... Edit Comment Close By: goodaobo (13 month(s) ago) i want this ppt Saving..... Post Reply Close Saving..... Edit Comment Close By: zinowinsky (15 month(s) ago) Thanks for your post. I would love to make a request to have a copy of the ppt to help on my studies. I would be very glad if you could mail it to me. zinowinsky@yahoo.com Thanks once again.God Bless Saving..... Post Reply Close Saving..... Edit Comment Close Premium member Presentation Transcript MATHEMATICAL MODELING AND ITS APPLICATION : MATHEMATICAL MODELING AND ITS APPLICATION By Manish Nandi Assistant Professor Introduction: : Introduction: A natural question which must have arisen in our mind is “What is Mathematical Modeling?” Mathematical Modeling consists of simplifying Real World problems and representing them as Mathematical problems(Mathematical Model), solving the mathematical problems and interpreting these solutions in language of the Real World. In simple form- Conversion of Real World phenomena under certain conditions into Mathematical formulation is known as Mathematical Modeling. Introduction cond…… : Introduction cond…… Performing experiments to understand & solve Real World problems may be risks & expensive. Mathematical Modeling is the only recourse in such situation. The use of mathematics in solving Real World problems has become widespread especially due to the increasing computation power of digital computer and computing methods both of which have facilitated the handling of length and complicated problems. Introduction cond……. : Introduction cond……. Mathematical Models are basically of two kinds……… (i) Empirical Models & (ii) Theoretical Models. Experiments (i) Empirical Models Observation Mathematical (ii) Theoretical Models Statistical Computer based Introduction cond…….. : Introduction cond…….. The importance of Mathematical Modeling as a discipline to be studied and cultivated, has been realised only during the last three or four decades. Three Main Steps:We can divide the Modeling process into three main steps. : Three Main Steps:We can divide the Modeling process into three main steps. Modeling Formulation Solution Evaluation Stating the Identifying Mathematical Question Relevant Factor Description Mathematical Model follows the process: : Mathematical Model follows the process: Start Formulation Solution Evaluation No Yes Satisfied Stop Why mathematical modeling? : Why mathematical modeling? Mathematical modeling is the art of translating problems from an application area into tractable mathematical formulations whose theoretical and numerical analysis provides insight, answers, and guidance useful for the originating application. Mathematical Modeling is indispensable in many applications. is successful in many further applications. gives precision and direction for problem solution. enables a thorough understanding of the system modeled. prepares the way for better design or control of a system. allows the efficient use of modern computing capabilities. A list of applications : A list of applications All areas mentioned have numerous mathematical challenges Anthropology Modeling, classifying and reconstructing skulls Archaeology Reconstruction of objects from preserved fragments Classifying ancient artifices Architecture Virtual reality Artificial intelligence Computer vision Image interpretation Robotics Speech recognition Optical character recognition Reasoning under uncertainty Application Cond……… : Application Cond……… Arts Computer animation (Jurassic Park) Astronomy Detection of planetary systems Correcting the Hubble telescope Origin of the universe Evolution of stars Biology Protein folding Humane genome project Population dynamics Morphogenesis Evolutionary pedigrees Spreading of infectious diseases (AIDS) Animal and plant breeding (genetic variability) Application Cond…. : Application Cond…. Chemical engineering Chemical equilibrium Planning of production units Chemistry Chemical reaction dynamics Molecular modeling Electronic structure calculations Computer science Image processing Realistic computer graphics (ray tracing) Criminalistic science Finger print recognition Face recognition Application Cond……. : Application Cond……. Economics Labour data analysis Electrical engineering Stability of electric curcuits Microchip analysis Power supply network optimization Finance Risk analysis Value estimation of options Fluid mechanics Wind channel Turbulence Application Cond……. : Application Cond……. Geosciences Prediction of oil or ore deposits Map production Earth quake prediction Internet Web search Optimal routing Linguistics Automatic translation Application Cond…… : Application Cond…… Materials Science Microchip production Microstructures Semiconductor modeling Mechanical engineering Stability of structures (high rise buildings, bridges, air planes) Structural optimization Crash simulation Medicine Radiation therapy planning Computer-aided tomography Blood circulation models Application Cond….. : Application Cond….. Meteorology Weather prediction Climate prediction (global warming, what caused the ozone hole?) Music Analysis and synthesis of sounds Neuroscience Neural networks Signal transmission in nerves Pharmacology Docking of molecules to proteins Screening of new compounds Application Cond……. : Application Cond……. Political Sciences Analysis of elections Psychology Formalizing diaries of therapy sessions Space Sciences Trajectory planning Flight simulation Shuttle re entry Transport Science Air traffic scheduling Taxi for handicapped people Automatic pilot for cars and airplanes Also… : Also… Mathematical Model of Urban & regional planning Population Environmental Water Resources Optimal utilization of exhaustible & renewable resources Land distribution Forestry and so on. Types of Modeling : Types of Modeling Linear or Non-linear. Static or Dynamic. Discrete or Continuous. Deterministic or Probabilistic. Some Example of Mathematical Models : Some Example of Mathematical Models Find the mass of the Earth (without using a balance). Find the temperature at the centre of the Sun (without taking a thermometer there). Find the volume of blood inside the body of a person (without bleeding the person to death). Estimate the population of India in the year 2050 AD (without waiting till than). Estimate the total expenditure for an owner to run his Rubber garden in the next five year (without waiting). THANK YOU : THANK YOU