The least upper bound property in R, equivalents and consequences. Metric spaces. Completeness, compactness, connectedness. Functions,continuity. Sequences and series of functions. Contraction mapping theorem and applications to calculus: Inverse and implicit function theorems.

### Introduction to Mathematical Analysis (MATH 301)

2021 Fall

Faculty of Engineering and Natural Sciences

Mathematics(MATH)

3

6.00 / 6.00 ECTS (for students admitted in the 2013-14 Academic Year or following years)

Turgay Bayraktar -tbayraktar@sabanciuniv.edu,

English

Undergraduate

--

Formal lecture

Interactive,Communicative,Discussion based learning

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### CONTENT

### OBJECTIVE

Learning the basics of mathematical analysis; i.e. basic theorems and basic techniques in analysis.

### LEARNING OUTCOME

Comprehend the language of analysis

Read and understand definitions, theorems, proofs.

Produce their "own" proofs in some cases.

Comprehend the structure of real numbers and the Euclidean space. Comprehend the basic theorems of Calculus.

Comprehend the topology of the Euclidean space.

Comprehend the notion and use the facts of continuity.

Comprehend the notion and use the facts of differentiability.

Comprehend the notion and use the inverse and implicit function theorems.

Comprehend the notion and use the facts of Riemann integrals.

### Update Date:

### ASSESSMENT METHODS and CRITERIA

Percentage (%) | |

Final | 30 |

Midterm | 30 |

Exam | 30 |

Other | 10 |

### RECOMENDED or REQUIRED READINGS

Textbook |
Elementary Classical Analysis; Marsden & Hoffman, Freeman 1974. |