Sale!

A Second Course in Mathematical 1st Edition by Analysis J C Burkill ISBN 0521523435 9780521523431

Original price was: $50.00.Current price is: $35.00.

A Second Course in Mathematical Analysis J. C. Burkill Digital Instant Download

Author(s): J. C. Burkill, H. Burkill
ISBN(s): 9780521523431, 0521523435
Edition: New
File Details: PDF, 84.75 MB
Year: 2002
Language: english
SKU: EB-44678426 Category: Tags: ,

A Second Course in Mathematical 1st Edition by Analysis J C Burkill – Ebook PDF Instant Download/Delivery: 0521523435, 9780521523431
Full download A Second Course in Mathematical 1st Edition after payment

Product details:

ISBN 10: 0521523435 
ISBN 13: 9780521523431
Author: Analysis J C Burkill

The classic analysis textbook from Burkill and Burkill is now available in the Cambridge Mathematical Library. This straightforward course, based on the idea of a limit, is for students of mathematics and physics who have acquired a working knowledge of calculus and are ready for a more systematic approach. The treatment given here also brings in other limiting processes, such as the summation of infinite series and the expansion of trigonometric functions as power series. Particular attention is given to clarity of exposition and the logical development of the subject matter.

A Second Course in Mathematical 1st Table of contents:

Part I: General Analysis and Real Functions (Chapters 1-9 concentrate on this)

  1. Sets and functions

    • Sets and numbers
    • Bounds
    • Functions
    • Cardinality of sets

  2. Metric spaces

    • Metric spaces, open and closed sets
    • Convergent sequences
    • Completeness
    • Compact sets
    • Connected sets

  3. Continuous functions on metric spaces

    • Continuous functions
    • Continuous functions on compact sets
    • Uniform continuity

  4. Limits in the spaces R and Rn

    • Limits
    • Upper and lower limits
    • Limits of functions
    • Derivatives
    • Power series

  5. Uniform convergence

    • Uniform convergence of sequences of functions
    • Uniform convergence of series of functions
    • Power series

  6. Integration

    • The Riemann integral
    • Properties of the Riemann integral
    • The Riemann–Stieltjes integral
    • Improper integrals
    • Rectifiable curves

  7. Functions from Rm to Rn

    • Open and closed sets in Rn
    • Functions from Rm to Rn
    • The derivative of a function from Rm to Rn
    • Inverse and implicit functions

  8. Integrals in Rn

    • Multiple integrals
    • Change of variables in multiple integrals
    • Line integrals
    • Green’s theorem
    • Surface integrals
    • Stokes’ theorem
    • Divergence theorem

  9. Fourier series

    • Orthogonal functions
    • Fourier series
    • Convergence of Fourier series
    • Parseval’s theorem

Part II: Complex Function Theory (Chapters 10-14 concentrate on this)

  1. Complex function theory

    • Complex numbers
    • Functions of a complex variable
    • Analytic functions
    • Power series

  2. Complex integrals, Cauchy’s theorem

    • Complex integration
    • Cauchy’s theorem
    • Deformation of contours
    • Simply and multiply connected domains

  3. Expansions, singularities, residues

    • Taylor’s series
    • Laurent’s series
    • Singularities
    • Residues
    • The residue theorem

  4. General theorems, analytic functions

    • Conformal mapping
    • Maximum modulus principle
    • Liouville’s theorem
    • The fundamental theorem of algebra

  5. Applications to special functions

    • The Gamma function
    • The Zeta function
    • Elliptic functions

People also search for A Second Course in Mathematical 1st:

    
a second course in mathematical
    
burkill a second course in mathematical analysis pdf
    
a second course in mathematical analysis pdf
    
a second course in mathematical analysis burkill
    
a second course in probability

 

Tags: Analysis J C Burkill, Second, Mathematical