Mathematical Analysis

<body> <table border="0" cellpadding="5" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table1"> <tr> <td width="50%" valign="top"> <table border="0" cellpadding="0" cellspacing="0" style="border-collapse: collapse" bordercolor="#111111" width="100%" id="table2"> <tr> <td width="100%" bgcolor="#333366"> <p class="header_yellow" align="center">Contents</td> </tr> <tr> <td width="100%" class="explanatory_text"> <table border="1" cellpadding="0" cellspacing="5" style="border-collapse: collapse" bordercolor="#CCCCFF" bgcolor="#CCCCFF" width="100%" id="table3"> <tr> <td class="contents_expanded"> <p class="contents_compressed">Preface</p> <p class="contents_compressed">1 The Real and Complex Number Systems</p> <p class="contents_compressed">2  Some Basic Notions of Set Theory</p> <p class="contents_compressed">3  Elements of Point Set Topology</p> <p class="contents_compressed">4  Limits and Continuity</p> <p class="contents_compressed">5  Derivatives</p> <p class="contents_compressed">6  Functions of Bounded Variation and Rectifiable Curves</p> <p class="contents_compressed">7  The Riemann-Stieltjes Integral</p> <p class="contents_compressed">8  Infinite Series and Infinite Products</p> <p class="contents_compressed">9  Sequences of Functions</p> <p class="contents_compressed">10  The Lebesgue Integral</p> <p class="contents_compressed">11  Fourier Series and Fourier Integrals</p> <p class="contents_compressed">12  Multivariable Differential Calculus</p> <p class="contents_compressed">13  Implicit Functions and Extremum Problems</p> <p class="contents_compressed">14  Multiple Riemann Integrals</p> <p class="contents_compressed">15  Multiple Lebesgue Integrals</p> <p class="contents_compressed">16  Cauchy's Theorem and the Residue Calculus</td> </tr> </table> </td> </tr> </table> </td> <td width="50%" valign="top" class="body"> <p class="body_expanded">This is one of the classic books in analysis. It provides a critical transition from elementary calculus to measure theory. More importantly, it introduces the reader to some of the abstract thinking that pervades modern analysis and advanced finance. The exposition is so clear and well planned that this book is perfect for self study. </p> <p class="body_expanded">Topics include: point set topology, limits and continuity, derivatives, Riemann-Stieltjes and Lebesgue integrals, basic measure theory, infinite series and products, sequences of functions, Fourier analysis and much more. If you want to improve your mathematical skills to a level where you can study advanced topics in derivatives pricing and market theory, this book is a critical first step. I cannot recommend it highly enough. </p> <p align="center" class="body"> </p> </td> </tr> </table> </body>