Binmore K.G. Mathematical Analysis: A Straightforward Approach

2nd edition. — Cambridge University Press, 1982. — 376 p. — ISBN10: 0521288827.For the second edition of this very successful text, Professor Binmore has written two chapters on analysis in vector spaces. The discussion extends to the notion of the derivative of a vector function as a matrix and the use of second derivatives in classifying stationary points. Some necessary concepts from linear algebra are included where appropriate. The first edition contained numerous worked examples and an ample collection of exercises for all of which solutions were provided at the end of the book. The second edition retains this feature but in addition offers a set of problems for which no solutions are given. Teachers may find this a helpful innovation.Preface to the first edition
Preface to the second edition
Real numbers
Continuum property
Natural numbers
Convergent sequences
Subsequences
Series
Functions
Limits of functions
Continuity
Differentiation
Mean value theorems
Monotone functions
Integration
Exponential and logarithm
Power series
Trigonometric functions
The gamma function
Vectors
Vector derivatives
Appendix
Solutions to exercises
Further problems
Suggested further reading
Notation