Paperback
ISBN:9781107650244
Publication date:July 2012
356pages
Dimensions: 216 x 140 mm
Weight: 0.45kg
Not yet published - available from July 2012
Andrew Russell Forsyth (1858-1942) was an influential Scottish mathematician notable for incorporating the advances of Continental mathematics within the British tradition. Originally published in 1890, this book constitutes the first of six volumes in Forsyth's Theory of Differential Equations series, concentrating specifically on exact equations and Pfaff's problem. The text contains detailed information on the development of these areas and substantial contributions made to them. All sources are quoted in their proper connection and a few fresh investigations are added. Examples are given, where necessary, in order to provide illustrations of various methods. This book will be of value to anyone with an interest in differential equations and the history of mathematics.
1. Single exact equation
2. System of exact equations
3. Historical summary of methods of treating Pfaff's problem
4. Pfaff's reduction, completed as by Gauss and Jacobi
5. Grassmann's method
6. Natani's method
7. Application to partial differential equations of the first order
8. Clebsch's method
9. Tangenital transformations
10. Lie's method
11. Frobenius' method
12. Abstract of Darboux's method
13. Systems of Pfaffians
Index.
Paperback
ISBN:9781107640252
Publication date:July 2012
356pages
Dimensions: 216 x 140 mm
Not yet published - available from July 2012
Andrew Russell Forsyth (1858-1942) was an influential Scottish mathematician notable for incorporating the advances of Continental mathematics within the British tradition. Originally published in 1900, this book constitutes the second of six volumes in Forsyth's Theory of Differential Equations series, concentrating specifically on ordinary equations which are not linear. The text contains detailed information on the development of this area and substantial contributions made to it. All sources are quoted in their proper connection and a few fresh investigations are added. Examples are given, where necessary, in order to provide illustrations of various methods. This book will be of value to anyone with an interest in differential equations and the history of mathematics.
1. Introductory
2. Cauchy's theorem on the existence of regular integrals of a system of equations
3. Classes of non-ordinary points connected with the form of the equation of the first order and first degree in the derivative
4. Influence, upon the integral, of an accidental singularity of the first kind possessed by the equation
5. Reduction of the differential equation to final typical forms, valid in the vicinity of an accidental singularity of the second kind
6. The character of the integrals possessed by the respective reduced forms of the original equation in the vicinity of the accidental singularity of the second kind
7. Effect, upon the integral, of essential singularities of the equation
8. Branch-points of an equation of the first order and any degree, as determined by the equation: singular and particular solutions
9. Differential equations of the first order having their integrals free from parametric branch-points
10. Equations of first order with uniform integrals, and with algebraical integrals.
Paperback
ISBN:9781107630123
Publication date:July 2012
402pages
Dimensions: 216 x 140 mm
Weight: 0.51kg
Not yet published - available from July 2012
Andrew Russell Forsyth (1858?1942) was an influential Scottish mathematician notable for incorporating the advances of Continental mathematics within the British tradition. Originally published in 1900, this book constitutes the third of six volumes in Forsyth's Theory of Differential Equations series, concentrating specifically on ordinary equations which are not linear. The text contains detailed information on the development of this area and substantial contributions made to it. All sources are quoted in their proper connection and a few fresh investigations are added. Examples are given, where necessary, in order to provide illustrations of various methods. This book will be of value to anyone with an interest in differential equations and the history of mathematics.
Summary Email a friend
11. Reduced forms of systems of equations of the first order in the vicinity of singularities of the derivatives
12. The integrals of the reduced forms of a system of equations, chiefly of two dependent variables
13. Systems of equations with multiform values of the derivatives
singular solutions
14. Equations of the second order and the first degree
15. Equations of the second order and any degree
16. Equations of the second order with sub-uniform integrals: with some general considerations
17. General theorems on algebraic integrals: Bruns's theorem
Index.
Paperback
Series: Cambridge Studies in Advanced Mathematics(No. 97)
ISBN:9781107405820
Publication date:July 2012
570pages
Dimensions: 229 x 152 mm
Not yet published - available from July 2012
Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. This 2006 text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises.
Preface
Notation
1. Dirichlet series-I
2. The elementary theory of arithmetic functions
3. Principles and first examples of sieve methods
4. Primes in arithmetic progressions-I
5. Dirichlet series-II
6. The prime number theorem
7. Applications of the prime number theorem
8. Further discussion of the prime number theorem
9. Primitive characters and Gauss sums
10. Analytic properties of the zeta function and L-functions
11. Primes in arithmetic progressions-II
12. Explicit formulae
13. Conditional estimates
14. Zeros
15. Oscillations of error terms
Appendix A. The Riemann-Stieltjes integral
Appendix B. Bernoulli numbers and the Euler-MacLaurin summation formula
Appendix C. The gamma function
Appendix D. Topics in harmonic analysis.