Along with presenting the many topics of analysis, this book guides readers to make the necessary connections between calculus and the secondary curriculum. In addition, this book provides readers with a solid foundation so that their future instruction and classroom teaching is based on fundamental understanding. The book begins with an outline of typical AP calculus topics. To help students review the discussed topics, sets of exercises are included and are similar to those in the upper range of a standard calculus text. The book moves on to analysis with more rigorous investigations. The topology of the line is discussed as well as limits and continuity, making sure to include unusual examples in order to direct a reader's thinking beyond intuitive reasoning and on to more rigorous understanding. The dichotomy of pointwise and uniform convergence is then addressed and is followed by differentiation and integration. In an effort to broaden the reader's perspective, Riemann-Stieltjes integrals areintroduced. Also introduced is the Lebesgue measure as the generalization of the Euclidean length of an interval. The book concludes with a collection of different topics that an instructor can use to further extend and enhance the class. The author has chosen diverse subjects to allow for varied approaches tothe subject.
- ISBN: 978-0-470-37136-7
- Editorial: John Wiley & Sons
- Encuadernacion: Cartoné
- Páginas: 280
- Fecha Publicación: 07/08/2009
- Nº Volúmenes: 1
- Idioma: Inglés