Mathematical Modeling

[faizan2722]

I shall be grateful if someone can recommend me some book(s) that gives comprehensive knowledge on Mathematical Modeling of Mechanical Systems.

 

Mostly books on Mathematical Modeling give the knowledge with respect to Controls. In other words, they only discuss differential equations; however, differential equations might not be the only branch of mathematics that is used to define any mechanical system.

[mathematic]

Suggestion: Look for books on the mechanical systems themselves. They should contain discussions of the relevant math modeling.

[studiot]

Not sure what you want here, tell us more about your interest and the level you expect to find.

 

You may find looking up the subjects of

 

Engineering Mechanics

Mechanics of Machines

Contact Mechanics

Engineering Tribology

Acceleration Diagrams

Engineering Fluid Mechanics

Transport Phenonema

Heat engines

 

 

 

But you will find differential equations pretty common.

 

Two books come to mind

 

Mathematical Modelling

 

by Berry and Houston

 

An introduction to the subject taking you from upper high school into university.

 

The Mathematical Mechanics

 

by Mark Levi.

 

A delightful book where the author sets out to use mechanics to provee mathematical theorems and achieves a useful blend of mechanics and maths.

Edited November 26, 2013 by studiot

[ajb]

In other words, they only discuss differential equations; however, differential equations might not be the only branch of mathematics that is used to define any mechanical system.

It depends on your tastes and interests. Classical mechanics is tightly related to symplectic geometry. You could consult the book by Abraham and Marsden "Foundations Of Mechanics". It is an old book and as such missed many new developments, but it is a great place to start.

[imatfaal]

I love these online courses from edx.org

 

take a look at this one (I haven't done this one yet)

https://www.edx.org/course/mitx/mitx-2-03x-dynamics-1102

 

I cannot find a link to it - but if you can find 8Mrev from MIT - its a great booster course for Mechanics. There is also 801x which is Walter Lewin's famous introductory physics/mechanics course. There is a mathematics and modelling course - but doesn't seem to be running.

[EdEarl]

Really complex models, for example modeling the climate and weather of the Earth requires a program that use many different simpler physical models of events that occur over many decades of time. For example, modeling a storm requires modeling lightening, with electrical events that occur in picoseconds, fluid dynamics to model airflow and raindrops that occur in microseconds to days, electrostatics to model how charges in clouds affect airflow, raindrops, snowflakes, etc., the physics of crystal formation as water freezes into snow, sleet, or hail, and other things too.

[faizan2722]

Not sure what you want here, tell us more about your interest and the level you expect to find.

 

You may find looking up the subjects of

 

Engineering Mechanics

Mechanics of Machines

Contact Mechanics

Engineering Tribology

Acceleration Diagrams

Engineering Fluid Mechanics

Transport Phenonema

Heat engines

 

 

 

But you will find differential equations pretty common.

 

Two books come to mind

 

Mathematical Modelling

 

by Berry and Houston

 

An introduction to the subject taking you from upper high school into university.

 

The Mathematical Mechanics

 

by Mark Levi.

 

A delightful book where the author sets out to use mechanics to provee mathematical theorems and achieves a useful blend of mechanics and maths.

I am interested in seeking information with respect to "Mathematical Modeling Fundamentals" in Thermodynamics, Heat Transfer and also Mechanics of Materials.

[Bignose]

I am interested in seeking information with respect to "Mathematical Modeling Fundamentals" in Thermodynamics, Heat Transfer and also Mechanics of Materials.

If you hope to avoid differential equations in any of these topics, as per your 1st post above, you're going to be out of luck. Differential equations are very prevalent in all 3 of these topics. If you are truly looking for 'comprehensive knowledge' in these areas, you can't avoid the differential equation.

 

If you are truly looking for comprehensive knowledge of thermodynamics see Tester and Model's Thermodynamics and Its Applications. Tough, tough book, but if you get through it you will be an expert.

 

For Heat Transfer, I liked Engineering Heat Transfer by Rathore and Kapuno, though I personally prefer to study the abstractions wherein momentum, heat, and mass transfer are seen as very similar/analogous phenomena. Bird, Stewart, and Lightfoot's Transport Phenomena is the classic in that field.

 

I am not as familiar with the mechanics of materials texts, so someone else will have to give you recommendations there.

Edited November 27, 2013 by Bignose