# Math 400 Topics: Numerical Methods

### Course Information

Meeting Times: Monday, Wednesday, and Friday, 1:00 - 1:50 pm

Location: Hirt 209

Office Hours: Monday 3-4, Tuesday 12-1:30, Thursday 8-9:30, Friday 9-11

Prerequisite: Math 265

Location: Hirt 209

Office Hours: Monday 3-4, Tuesday 12-1:30, Thursday 8-9:30, Friday 9-11

Prerequisite: Math 265

### Course Description

This course will introduce students to useful numerical algorithms that can be used to solve or approximate a wide variety of problems in the sciences, engineering, economics, and more. In addition, students will learn how to use mathematical software to implement and expand on these algorithms. Topics to be covered include number systems, error, systems of linear equations, interpolation, root approximation techniques, numerical differentiation and integration, eigenvalue problems and matrix forms.

### Objectives

On successful completion of the course, students should be able to:

- demonstrate an understanding of common numerical methods and their use;
- select appropriate algorithm or technique for a given problem;
- recognize the difference between approximations and an exact solution;
- implement numerical methods in mathematical software;
- explain why a particular numerical method may fail for a given problem;
- analyze the results of a particular method for accuracy;
- communicate your results and analysis using formal mathematical language and notation.

### Required Materials

You will not be required to purchase a textbook or any additional materials. Some materials will be distributed as printouts or pdfs throughout the semester.

The notation and topics used in class will most closely follow along with the textbook

Some assignments will require Scilab, a free and open source program for numerical computation. Scilab is available for Windows, Linux, and Mac OS and can be downloaded at scilab.org. Scilab runs on any computer with at least 2 GB RAM and 600 MB of available hard disk space. You will need an internet connection for the download only. If you do not have a computer on which you can install Scilab, please let me know as soon as possible so we can make alternate arrangements.

The notation and topics used in class will most closely follow along with the textbook

*Numerical Analysis*by Richard Burden and J. Douglas Faires. You are not required to purchase this text, but if you would like an additional resource to follow along with, this would be my recommendation. Any edition would be fine - older editions are inexpensive and will still be useful for many years.Some assignments will require Scilab, a free and open source program for numerical computation. Scilab is available for Windows, Linux, and Mac OS and can be downloaded at scilab.org. Scilab runs on any computer with at least 2 GB RAM and 600 MB of available hard disk space. You will need an internet connection for the download only. If you do not have a computer on which you can install Scilab, please let me know as soon as possible so we can make alternate arrangements.

### Textbook Homework

There will be 8 homework assignments throughout the semester, typically due one week after they are assigned. You may work together, but keep in mind that these problems may appear on exams, so you are strongly recommended to work through them on your own.

For collected problems, you are expected to submit your final work. Problems involving calculations should include work and an explanation of the steps used to arrive at your answer. Proofs should use formal language and notation. Work should be clear and neatly written.

For some assignments, you may be required to submit the code that you are using to arrive at your solution. You may turn in any Scilab assignments as printouts or email them to me directly.

If you are unable to submit your work in class, you can email a clear scan or photo of your work.

For collected problems, you are expected to submit your final work. Problems involving calculations should include work and an explanation of the steps used to arrive at your answer. Proofs should use formal language and notation. Work should be clear and neatly written.

For some assignments, you may be required to submit the code that you are using to arrive at your solution. You may turn in any Scilab assignments as printouts or email them to me directly.

If you are unable to submit your work in class, you can email a clear scan or photo of your work.

### Quizzes

You will be given quizzes on the material regularly. Keeping up with the suggested textbook homework will ensure that you are prepared for the quizzes, which will feature problems very similar to those in the homework. Quiz dates are provided in the course schedule; note that exact topics covered on a quiz is subject to change. Any changes will be announced in class.

Quiz grades will not be based strictly on whether or not you found the correct answer. Your work must also be written clearly, and with proper notation, to receive full credit.

Make up quizzes will only be given for excused absences.

Quiz grades will not be based strictly on whether or not you found the correct answer. Your work must also be written clearly, and with proper notation, to receive full credit.

Make up quizzes will only be given for excused absences.

**All make ups must be completed before the graded quizzes are returned to the class; this will typically be the next class meeting.**### Exams

We will have two midterm exams and a final exam. The final exam will be cumulative, while the midterm exams will focus on more recent material. Exams will be based on homework problems and lecture material. There will not be a coding component of any exams.

You will be able to make up exams for excused absences. If you know in advance that you will not be able to take an exam at its schedule time, please let me know as soon as possible. All make ups must be completed within one week of the exam date. You are required to take the final exam for this course regardless of your average on earlier exams or homework.

The final exam is scheduled for

You will be able to make up exams for excused absences. If you know in advance that you will not be able to take an exam at its schedule time, please let me know as soon as possible. All make ups must be completed within one week of the exam date. You are required to take the final exam for this course regardless of your average on earlier exams or homework.

The final exam is scheduled for

**Friday, May 10, 1:00 pm - 3:00 pm**### Final Grades

##### Basis of Final Grade

Up to 500 points are available to earn throughout the semester, as follows:180 points | Midterm Exams |

Two exams, 90 points each | |

200 points | Homework |

Eight assignments, 25 points each | |

120 points | Final Exam |

##### Grading Scale

Grade | F | D | D+ | C | C+ | B | B+ | A |

Percentage | 0-59 | 60-66 | 67-69 | 70-76 | 77-79 | 80-86 | 87-89 | 90-100 |

Points | 0 | 298 | 333 | 348 | 383 | 398 | 433 | 448 |

### Learning Differences

In keeping with college policy, any student with a disability who needs academic accommodations must call Learning Differences Program secretary at 824-3017, to arrange a confidential appointment with the director of the Learning Differences Program during the first week of classes.

### Mercy Mission

This course supports the mission of Mercyhurst University by creating students who are intellectually creative. Students will foster this creativity by: applying critical thinking and qualitative reasoning techniques to new disciplines; developing, analyzing, and synthesizing scientific ideas; and engaging in innovative problem solving strategies.

## Schedule

The exact topic covered on a particular date is subject to change. Exams and quizzes will be given on the day they are scheduled, though the sections appearing on a quiz may differ. Announcements will be made in class regarding any schedule changes.

Date | Topic | Notes |