# MAT-01366 Mathematics 3, 5 cr

#### Person responsible

Sampsa Pursiainen

#### Lessons

Implementation | Period | Person responsible | Requirements |

MAT-01366 2019-01 | 3 |
Sampsa Pursiainen |
Exam and weekly course exercises. |

#### Learning Outcomes

On this course the students learn basic techniques such as integration by parts and changing of integration variables in integration of simple functions. The students learn to compute antiderivatives of rational functions and to analyze and compute improper integrals. The students also learn to solve simple separable differential equations, compute general solutions of homogeneous second order differential equations with constant coefficients, and to compute the particular solution of a nonhomogeneous differential equation using the method of "shrewd quessing". After the course the students are capable of analyzing the limit of a sequence, computing the sum of a geometric series, and testing the convergence of a series with positive terms. The students also learn how to determine the interval of convergence of a power series, form Taylor polynomials of functions, and simple Taylor series. 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. |
Antiderivative and basic integration techniques. Proper and improper integrals. | Applications of integration in, e.g., determining areas and volumes of geometrical shapes, and computing the length of a curve. | Numerical integration, trapezoid rule and Simpson's formula. Computing the Riemann sums. |

2. |
Ordinary linear differential equations of first and second order. Separable first order differential equations. | Higher order differential equations. Modeling specific real world problems, such as growth of populations, with differential equations. | Existence and uniqueness results, matrix notation for linear systems. |

3. |
Limit of a sequence, increasing and decreasing sequences. | ||

4. |
Series (geometric, with positive terms, alternating, Taylor series) and their convergence. | Approximating a function with a polynomial. | Testing convergence. Computing limits and integrals using series. Estimating the error in polynomial approximations of functions. |

5. |
Using Matlab as a tool in solving the exercise problems. |

#### Instructions for students on how to achieve the learning outcomes

For grade 5, the student masters the core course content as well as completementary knowledge. For 3-4, the student is understands the core content and has a working knowledge of the complementary knowledge issues. For 1-2, the student has a working knowledge of the core content.

#### Assessment scale:

Numerical evaluation scale (0-5)

#### Study material

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

Book | Calculus 6e, Early Transcendentials, Matrix Version | Edwards & Penney | Chapters 5, 7, 8 and 10. | No |

#### Prerequisites

Course | Mandatory/Advisable | Description |

MAT-01266 Mathematics 2 | Mandatory |

#### Correspondence of content

There is no equivalence with any other courses