Download for FREE in 4 easy steps...
You can also read this in Bookboon.com Premium
Mathematical modeling is the most effective bridge connecting mathematics and many disciplines such as physics, biology, computer science, engineering, and social sciences.
300+ Business books exclusively in our Premium eReader
- No adverts
- Advanced features
- Personal library
Users who viewed this item also viewed
An Introduction to Matlab
Applied Mathematics by Example: Theory
Blast Into Math!
Applied Mathematics by Example: Exercises
Matrix Methods and Differential Equations - A Practical Introduction
An introduction to partial differential equations
Mathematical Models in Portfolio Analysis
Elementary Algebra Exercise Book I
About the book
Mathematical modeling is the most effective bridge connecting mathematics and many disciplines such as physics, biology, computer science, engineering, and social sciences. A mathematical model, which is a mathematical description of a real system, can potentially help to explain a system, to uncover the underlying mechanisms via hypotheses and data fitting, to examine the effects of different components, and to make predictions.
Mathematical Modeling I – preliminary is designed for undergraduate students. Two other followup books, Mathematical Modeling II – advanced and Mathematical Modeling III – case studies in biology, will be published. II and III will be designed for both graduate students and undergraduate students. All the three books are independent and useful for study and application of mathematical modeling in any discipline.
- 2 Discrete-time models
- An example – bacterial reproduction
- Solution and equilibrium of a discrete model
- General theory and analytical methods
- Optimization of discrete models
- Continuous-time models
- Motivation and derivation of continuous models
- Differential equation models
- Separation of variables
- Linear equations
- Optimization of continuous models
- Sensitivity analysis
- Systems of difference equations (discrete)
- Analytical methods
- Some examples
- Systems of differential equations (continuous)
- Some motivation examples
- Analytical methods
- Higher dimensional systems
- Bifurcation analysis
- Saddle-node bifurcation
- Transcritical bifurcation
- Pitchfork bifurcation
- Generic saddle-node bifurcation
- Saddle-node, transcritical, and pitchfork bifurcations in two-dimensional systems
- Introduction of Hopf bifurcations
- Normal form of Hopf bifurcation
- Generic Hopf bifurcation
- Matlab programming
- Data fitting
About the Author
Professor Hao Wang is a faculty member in the Department of Mathematical & Statistical Sciences at the University of Alberta, an advisory board member of Centre for Mathematical Biology, an associate editor for International Journal of Numerical Analysis & Modeling – Series B, an editor for Nonlinear Dynamics and Systems Theory (an international journal of research and surveys), an editor for a special issue of The Canadian Applied Mathematics Quarterly, and an associate faculty member for Faculty of 1000 Biology.
Dr. Wang has strong interests in interdisciplinary research of mathematical biology. His research group is working on areas as diverse as modeling stoichiometry-based ecological interactions, microbiology, infectious diseases, predator-prey interactions, habitat destruction and biodiversity, risk assessment of oil sands pollution. Mathematical models include ordinary differential equations, delay differential equations, partial differential equations, stochastic differential equations, integral differential/difference equations.
The embed frame is free to use for private persons, universities and schools. It is not allowed to be used by any company for commercial purposes unless it is for media coverage. You may not modify, build upon, or block any portion or functionality of the embed frame, including but not limited to links back to the bookboon.com website.
The Embed frame may not be used as part of a commercial business offering. The embed frame is intended for private people who want to share eBooks on their website or blog, professors or teaching professionals who want to make an eBook available directly on their page, and media, journalists or bloggers who wants to discuss a given eBook
If you are in doubt about whether you can implement the embed frame, you are welcome to contact Thomas Buus Madsen on firstname.lastname@example.org and seek permission.