# MATA114 Ordinary Differential Equations (4 cr)

**Study level:**

Intermediate studies

**Grading scale:**

0-5

**Language:**

English, Finnish

**Responsible organisation:**

Department of Mathematics and Statistics

**Curriculum periods:**

2020-2021, 2021-2022, 2022-2023

## Description

Basic solution techniques for first and second order ordinary differential equations. Examples of series solutions and numerical methods.

The contents correpond to

Robert A. Adams: Calculus (8th ed.) chapter 18,

or

Boyce and DiPrima: Elementary differential equations and boundary value problems, chapters 1-5.

## Learning outcomes

The aim of the course is to learn how to solve ordinary differential equations of the first and second order. After completing the course, the student

- masters basic terminology related to differential equations
- recognizes and can solve separable equations and separable recoverable equations
- is able to solve the first order linear differential equation
- can solve second order equations that return to the first order
- knows how to apply the ordinal drop to find another solution to a homogeneous equation when one solution is known
- can solve a second order constant coefficient using a homogeneous linear differential equation with a characteristic polynomial
- knows how to find a solution to a second-order linear differential equation by constant variation and constant multiplication by experiment
- is familiar with the series solutions of differential equations
- is familiar with the numerical methods of solving differential equations

## Description of prerequisites

Calculus 3

## Literature

- Boyce W. E., DiPrima R. C., Elementary Differential Equations and Boundary Value Problems, WILEY, ISBN: 978-1-119-38164-8
- Adams, Robert A., Calculus: A Complete Course, 8. laitos, Pearson 2013.; ISBN: 978-0-321-78107-9

## Completion methods

### Method 1

**Evaluation criteria:**

Grade is based on weekly exercises, quizzes and points from the exam.

**Time of teaching:**

Period 4

Select all marked parts

### Method 2

**Evaluation criteria:**

Grade is based on the points from the final exam.

Select all marked parts

**Parts of the completion methods**

x

### Teaching (4 cr)

**Type:**

Participation in teaching

**Grading scale:**

0-5

**Language:**

Finnish

**Study methods:**

Lectures 28h (in Finnish), 7 sets of homework

#### Teaching

##### 8/28–8/28/2020 Exam

##### 3/18–5/23/2021 Lectures

##### 5/19–5/19/2021 Exam

##### 6/2–6/2/2021 Exam

x

### Exam (4 cr)

**Type:**

Exam

**Grading scale:**

0-5

**Evaluation criteria:**

The grade is based on the numbers of points in the final exam.

**Language:**

English, Finnish

**Study methods:**

Independent studying and final exam.