# MAT-01166 Mathematics 1, 5 cr

#### Person responsible

Janne Kauhanen

#### Lessons

Implementation | Period | Person responsible | Requirements |

MAT-01166 2019-01 | 1 |
Janne Kauhanen |
Final exam, weekly exercises, and peer-reviewed exercises in Moodle. |

#### Learning Outcomes

On this course the students learn how to compute and use the limit, the derivative, and complex numbers. The students learn how to justify their claims using mathematical methods and to present their solutions orally as well as in written form.

#### Content

Content |
Core content |
Complementary knowledge |
Specialist knowledge |

1. |
Sets and set operations. Methods of proof, mathematical induction. Real numbers: algebraic properties, the absolute value, intervals. | Quantifiers. The field structure of the real number system. | |

2. |
The definition of a function. Real valued functions of a real variable: monotonicity and the inverse function, the composition of functions. The basic properties of elementary functions. | Injectivity, surjectivity and bijectivity, the pre-image. The definition of elementary functions. Hyperbolic functions. | |

3. |
The limit of a function and the basic properties of the limit. One-sided limits, infinite limits, and limits at infinity. l'Hospital's rule. Continuity. | The epsilon-delta definition and proofs. The Squeeze Theorem. Properties of continuous functions: the Intermediate Value Theorem and the Extreme Value Theorem. | |

4. |
The derivative: the definition, the linear approximation, algebraic operations, the Chain Rule, the derivative of an inverse function, extrema and critical points, monotonicity. Derivatives of the elementary functions. | The Mean Value Theorem, the Taylor polynomial and Taylor's Formula. | |

5. |
Complex numbers: definition and algebraic operations, the conjugate, the modulus, the exponential (trigonometric) form, finding the roots. | Zeros and factorization of a polynomial with real coefficients. | |

6. |
Using Matlab as a tool in solving the exercise problems. |

#### Study material

Type |
Name |
Author |
ISBN |
URL |
Additional information |
Examination material |

Book | Mathematical Analysis I | Claudio Canuto, Anita Tabacco | 978-88-470-0875-5 | Springer E-kirja/E-book | No |

#### Correspondence of content

There is no equivalence with any other courses