**Level:**Intermediate**Status:**Ready**Offered by:**Kadir Has University

Academic Institution offering the course | Kadir Has University |
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Mode of Delivery (in class / online / blended) |
Blended |

Prerequisites by topic | Calculus of one and several variables. |

Language of Instruction | English |

Course Objectives | To give a basic understanding of elementrary methods of mathematical analysis beyond first year 's calculus courses. |

Course Contents | Number systems, Basics of mathematical reasoning, Topology of metric spaces, Sequences and series, Continuity, Derivatives, Riemann integral, Function spaces. |

Learning Outcomes of the Course Unit |
1. To solve the engineering problems using mathematical tools. 2. To construct models for real world problems under certain measures of accuracy. 3. To be able to approach to the applied mathematics problems in a logical systematic way. |

Week | Subjects |
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1 | Rational, Real and Complex numbers |

2 | A quick introduction to logic and reasoning |

3 | Introduction to point-set topology and metric spaces |

4 | Compactness, Connectedness, Completeness |

5 | Sequences of real and complex numbers |

6 | Numerical series and power series |

7 | Topologicsl properties under continuity |

8 | Derivative as linear transformation |

9 | The Riemann-Stieltjes integral |

10 | Sequence of functions and uniform convergence |

11 | Taylor and Weierstrass approximation theorems |

12 | Fourier Series |

13 | Special functions: Exponentials and Logarithms |