Differential Equations : Linear, Nonlinear, Ordinary, Partial

Finding And Interpreting The Solutions Of Differential Equations Is A Central And Essential Part Of Applied Mathematics. This Book Aims To Enable The Reader To Develop The Required Skills Needed For A Thorough Understanding Of The Subject. The Authors Focus On The Business Of Constructing Solutions Analytically, And Interpreting Their Meaning, Using Rigorous Analysis Where Needed. Matlab Is Used Extensively To Illustrate The Material. There Are Many Worked Examples Based On Interesting And Unusual Real World Problems. A Large Selection Of Exercises Is Provided, Including Several Lengthier Projects, Some Of Which Involve The Use Of Matlab. The Coverage Is Broad, Ranging From Basic Second-order Odes And Pdes, Through To Techniques For Nonlinear Differential Equations, Chaos, Asymptotics And Control Theory. This Broad Coverage, The Authors' Clear Presentation And The Fact That The Book Has Been Thoroughly Class-tested Will Increase Its Attraction To Undergraduates At Each Stage Of Their Studies. A.c. King, J. Billingham And S.r. Otto. Includes Bibliographical References And Index. Part one: Linear equations 1. Variable coefficient, second order, linear, ordinary differential equations 2. Legendre functions 3. Bessel functions 4. Boundary value problems, Green's functions and Sturm-Liouville theory 5. Fourier series and the fourier transform 6. Laplace transforms 7. Classification, properties and complex variable methods for second order partial differential equations Part two: Nonlinear equations and advanced techniques 8. Existence, uniqueness, continuity and comparison of solutions of ordinary differential equations 9. Nonlinear ordinary differential equations: Phase plane methods 10. Group theoretical methods 11. Asymptotic methods: Basic ideas 12. Asymptotic methods: Differential equations 13. Stability, instability and bifurcations 14. Time-optimal control in the phase plane 15. Introduction to chaotic systems. Differential equations are vital to science, engineering and mathematics, and this book enables the reader to develop the required skills needed to understand them thoroughly. The authors focus on constructing solutions analytically and interpreting their meaning and use MATLAB extensively to illustrate the material along with many examples based on interesting and unusual real world problems. A large selection of exercises is also provided The authors focus on constructing solutions analytically, and interpreting their meaning; MATLAB is used extensively to illustrate the material. The many worked examples, based on interesting real world problems, the large selection of exercises, including several lengthier projects, the broad coverage, and clear and concise presentation will appeal to undergraduates.

For students taking second courses; subject is central and required at second year and above.

Many physical, chemical and biological systems can be described using mathematical models.