What Are the Best Textbooks for an Introduction to Mathematical Modeling?

[dandy_stepper]

Hello all, I have recently started a course at my University called Introduction to Mathematical Modeling. However, the course does not require/recommend a textbook, and I am someone who really depends on having a textbook in order to learn. I have asked the professor to recommend me some textbooks, but I also wanted to get a second opinion from the people on this forum. This is a description of the course:
This is a project-oriented course offering the opportunity to discover how various real world problems can be described and analyzed with the aid of simple mathematical models and computer simulations.Possible project topics include operation of a fuse, spread of pollutants in a river, propagation of an infectious disease, traffic flow on a highway, oscillating chemical reactions, population growth in biology,etc.
Also, the prereqs for this course are Multivariable Calculus and Differential Equations. Any recommendations would be greatly appreciated. Thank you.

 

[S.G. Janssens]

Two books that I recommend a lot are:

Strogatz, Nonlinear Dynamics and Chaos (nice and easy read, inspiring but not rigorous at all, maybe a bit below your current level)
Hirsch, Smale & Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos (higher level, has project ideas at the end of each chapter, good balance between rigour and accessibility)

Both books should give you plenty of ideas for feasible projects for your course, as long as you stick to ODEs. PDEs do not receive any attention. (However, some ODE systems appear in these books as approximations of PDE.)

EDIT: If you care to look into performing bifurcation analyses, I could help you with more specialized references as well.

 

[dandy_stepper]

Thank you very much. Coincidentally, the second book was one that my professor also recommended, so I think that is one that I will certainly be purchasing. As for the bifurcation analyses, I am not sure if I need something that specific at this point in the semester (1 class in). However, I will keep in mind your offer in mind and if needs be I will ask later on if that is ok? Thanks again for the help

 

[S.G. Janssens]

Thank you very much. Coincidentally, the second book was one that my professor also recommended, so I think that is one that I will certainly be purchasing.

Ah that is a nice coincidence. Yes, it is quite a good book from which you can also benefit in later years.

As for the bifurcation analyses, I am not sure if I need something that specific at this point in the semester (1 class in). However, I will keep in mind your offer in mind and if needs be I will ask later on if that is ok? Thanks again for the help

Sure, that would be my pleasure. There is good literature as well as free and user friendly software available for this. I think the book by Hirsch, Smale and Devaney will certainly get you started, but if you are interested in more feel free to ask.

Good luck and enjoy!

 

[Xiuh]

There is a book on mathematical modelling written by Eck, Garcke & Knabner that I like a lot, but there is one little problem: It is written in german and I don't know if it has been translated. If this poses no problem for you then check it out!

http://www.amazon.com/dp/3540749675/?tag=pfamazon01-20

 

[dandy_stepper]

Thank you for the recommendation. Unfortunately, I cannot speak German whatsoever, so this book would be wasted on me.

 

[dandy_stepper]

Also I just noticed that I did not create this thread in the proper place, so I apologize to whomever had to move it.

 

[Ray Vickson]

Hello all, I have recently started a course at my University called Introduction to Mathematical Modeling. However, the course does not require/recommend a textbook, and I am someone who really depends on having a textbook in order to learn. I have asked the professor to recommend me some textbooks, but I also wanted to get a second opinion from the people on this forum. This is a description of the course:
This is a project-oriented course offering the opportunity to discover how various real world problems can be described and analyzed with the aid of simple mathematical models and computer simulations.Possible project topics include operation of a fuse, spread of pollutants in a river, propagation of an infectious disease, traffic flow on a highway, oscillating chemical reactions, population growth in biology,etc.
Also, the prereqs for this course are Multivariable Calculus and Differential Equations. Any recommendations would be greatly appreciated. Thank you.

SIAM (Society for Industrial and Applied Mathematics) puts out a series of relevant books and mongraphs. For example, the book "Mathematical Modelling: Classroom Notes in Applied Mathematics" by N.S. Klamkin, SIAM 1987, has a number of articles on all kinds of interesting real-world and not-so-real-world applications, ranging from long articles to one page notes.

The excellent book "Industrial Mathematics: a course in real-world problem solving", by Friedman and Littman, SIAM (1994) covers a number of applications in considerable depth. A list of chapters is: Introduction; Preface to the Student; Chapter 1: Crystal Precipitation; Chapter 2: Air Quality Modeling; Chapter 3: Electron Beam Lithography; Chapter 4: Development of Color Film Negative; Chapter 5: How Does a Catalytic Converter Function?; Chapter 6: The Photocopy Machine; Chapter 7: The Photocopy Machine (Continued); Index.

For more details, see http://bookstore.siam.org/ot42/ .

 

[dandy_stepper]

SIAM (Society for Industrial and Applied Mathematics) puts out a series of relevant books and mongraphs. For example, the book "Mathematical Modelling: Classroom Notes in Applied Mathematics" by N.S. Klamkin, SIAM 1987, has a number of articles on all kinds of interesting real-world and not-so-real-world applications, ranging from long articles to one page notes.

The excellent book "Industrial Mathematics: a course in real-world problem solving", by Friedman and Littman, SIAM (1994) covers a number of applications in considerable depth. A list of chapters is: Introduction; Preface to the Student; Chapter 1: Crystal Precipitation; Chapter 2: Air Quality Modeling; Chapter 3: Electron Beam Lithography; Chapter 4: Development of Color Film Negative; Chapter 5: How Does a Catalytic Converter Function?; Chapter 6: The Photocopy Machine; Chapter 7: The Photocopy Machine (Continued); Index.

For more details, see http://bookstore.siam.org/ot42/ .

Thank you, that book sounds particularly helpful. One thing I did notice is that a working knowledge of Fortran, C, or Pascal is required. Unfortunately, I only have knowledge of MatLab/Python, do you think these would be sufficient? From my limited understanding, MatLab is sort of a simpler version of Fortran, so perhaps that could work. Either way I think I will give it a shot, much appreciated.

 

[S.G. Janssens]

There is a book on mathematical modelling written by Eck, Garcke & Knabner that I like a lot, but there is one little problem: It is written in german and I don't know if it has been translated. If this poses no problem for you then check it out!

http://www.amazon.com/dp/3540749675/?tag=pfamazon01-20

How rigorous is this from a functional analytic point of view? I'm always curious to find books that take a rigorous, functional analytic approach towards modeling.

 

[S.G. Janssens]

Also I just noticed that I did not create this thread in the proper place, so I apologize to whomever had to move it.

I wish every (new) member would be as decent.