as of 8/24/2019 |

**REAL ANALYSIS** |

Country - Partner Institution - Programs: | Australia - University of Melbourne - 'Australian Universities' |

UC Course Subject | Mathematics |

Number & Suffix: | 127 |

Full UC Title: | REAL ANALYSIS |

Transcript Title: | REAL ANALYSIS |

UC QTR Units - Division: | 6.0 - Upper Division |

Course Description: | This course explores mathematical analysis through selected applications and a careful theoretical framework. Students employ methods of proof such as mathematical induction and proof by contradiction. The important distinction between the real numbers and the rational numbers is emphasized and used to motivate rigorous notions of convergence and divergence of sequences, including the Cauchy criterion. These ideas are extended to cover the theory of infinite series, including common tests for convergence and divergence. A similar treatment of continuity and differentiability of functions of a single variable leads to applications such as the Mean Value Theorem and Taylor's theorem. The definitions and properties of the Riemann integral allow rigorous proof of the Fundamental Theorem of Calculus. The course examines convergence properties of sequences and series with applications to power series representations of elementary functions and their generation by Taylor series. It also introduces Fourier series as a way to represent periodic functions. |

Language of Instruction: | English |

Partner Title: | REAL ANALYSIS |

Partner University Department: | Mathematics and Statistics |

Partner University Course Number: | MAST20026 |