## Topic outline

### General

*Hello everyone, and welcome to your***Numerical Methods***My name is***Dejen ketema**and I already your instructor for the course. I am looking forward to working together and getting the semester started of strong. I want to welcome everyone, and I would encourage you to post a short informal hello message in the "Personal Introductions" discussion forum just to let me know you received my welcome message, and to briefly introduce yourself to your fellow classmates.*Although the official start date for the course is in the next lab session, all students (who have officially registered) now have access to the***Numerical Method**course site, so feel free to start exploring a little bit of your online learning environment—All details of the course can be found within the online course site, syllabus and chapter wise files.*As you get started, I'll answer any questions as they arise, or point you to our tech support forum for more technical questions. Please post your specific questions about chapters in the Getting Started forum, and also feel free to post general questions or comments to the "Main Discussion Forum". I will post all information message depending on our progress, the official course start date May 2020**I look forward to working with you this semester and getting off to a strong start!**Enrollment key:***Numerical***Best!**Dejen Ketema**Department of mathematics**Debre Berhan University*

### Course syllabus

This course introduces students to numerical method. Students will use computers to solve nonlinear equations, solve systems of linear equations, approximate integrals, fit data sets, and find solution of differential equation. This course will primarily use MatLab/Python for performing the numerical computations, so basics of MatLab will be taught. Practical examples will be used to demonstrate the usefulness of this course for a variety of problems.

### Objective 1

#### Understand the implications of digital number representation and digital arithmetic for computational science and engineering.

- Outcome 1.1: Understand the fundamental principles of digital computing, including number representation and arithmetic operations.
- Outcome 1.2: Understand the linkage between accuracy, stability and convergence
- Outcome 1.3: Perform error analysis for arithmetic operations.
- Outcome 1.4: Understand the propagation of errors through complex numerical algorithms.
- Outcome 1.5: Perform numerical stability analysis.

### Objective 2

#### Develop and implement numerically stable and accurate algorithms for all the basic tasks of computational science and engineering:

- Outcome 2.1: Develop stable algorithms for solving linear systems of equations.
- Outcome 2.2: Develop efficient and stable algorithms for finding roots of non-linear equations.
- Outcome 2.3: Implement numerically stable recursion algorithms for evaluating mathematical functions.
- Outcome 2.4: Understand the use of interpolation for numerical differentiation and integration.
- Outcome 2.5: Develop stable solution algorithms for ordinary differential equations.

- Outcome 1.1: Understand the fundamental principles of digital computing, including number representation and arithmetic operations.
- It is expected that students will conduct themselves within the standards outlined in the student code of conduct, disciplinary procedure and student due process. Disciplinary action will be taken by the instructor as necessary. See more information at the http://intranet.amu.edu.et/policy-and-guidelines
- Students are expected to come to class in a timely manner, prepared for the day’s work. Full participation for the entire class period in activities, class exercises and discussions is required.
- Please
**turn off all cell phones**, pagers, etc. You will be released from class with an unexcused absence for making or accepting telephone calls or text messages in the classroom. - It is the student’s responsibility to make up missed material. This includes, but is not limited to, obtaining missed lecture notes from another student (not from the instructor), and finding out about any modifications of schedules or assignments announced during class time.
**Weekly**assignments are posted with a specific due date. It is the student’s responsibility to complete the assignment on time.**Academic dishonesty**will result in a grade of zero for the assignment and will be reported to Academic Affairs. It may result in further disciplinary action. Academic dishonesty includes, but is not limited to, cheating, which includes unauthorized collaboration and plagiarism.- Missed Exams: Students will receive a ZERO for any missed exam, except for written/documented excuses (illness, personal/family crises, etc.).
- Even the
**visual presence of a Cell Phone**during an**Exam**will result in a**ZERO**for that Exam.

### Chapter One: Error

Under this chapter we will discuses the flowing basic concepts :

- Definition of numerical analysis and scientific computing
- Mathematical modeling
- Type of error and its sources
- Error measurements
- Algorithm and it's stability, convergence
- Introduction to MATLAB.

Here we are discus about Modeling, Error and its measurement.

Please you try to answer the following key question of chapter one

- What is finite precision
- List the source of error
- Define error measurements
- Define mathematical modeling
- Define Accuracy and precision
- change 35.625 in to binary system

Please you try to answer the following key question of chapter one

- What is finite precision
- List the source of error
- Define error measurements
- Define mathematical modeling
- Define Accuracy and precision
- change 35.625 in to binary system

Please you try to answer the following key question of chapter one

- What is finite precision
- List the source of error
- Define error measurements
- Define mathematical modeling
- Define Accuracy and precision
- change 35.625 in to binary system

Please you try to answer the following key question of chapter one

- What is finite precision
- List the source of error
- Define error measurements
- Define mathematical modeling
- Define Accuracy and precision
- change 35.625 in to binary system

### Chapter Two

This chapter is study about the

**solutions of nonlinear equation with in single variable.**The algorithm that we are see detail's in this chapter are:- Bisection method
- False position method
- Fixed point iteration
- Newton's method
- Secant method

Discuss the following basic idea of the chapter

- Write the algorithms of all methods
- List the similarity and difference between all methods

Discuss the following basic idea of the chapter

- Write the algorithms of all methods
- List the similarity and difference between all methods

Discuss the following basic idea of the chapter

- Write the algorithms of all methods
- List the similarity and difference between all methods

Discuss the following basic idea of the chapter

- Write the algorithms of all methods
- List the similarity and difference between all methods

### Chapter Three

### In this chapter we are focus on Solutions of System of Linear Equation

Basic concept on this chapter are:

- Revised direct methods Cramer's rule, Gauss elimination and inverse method.
- Discuss matrix decomposition methods

2.2. Cholesky factorization

3. Iteration method,

- Jacobi and
- Gauss-Seidel method

4. Eigenvalue Problem

- Power method
- Inverse power method

- Newton's method for multivariate

### Chapter Four

### Interpolation

In this chapter we are focused about finite difference and Interpolation. the main sub topics are- Finite difference
- Lagrangian Interpolation
- Newton dividing difference interpolation
- Spline interpolation

### Chapter Five

### Least Square Estimation

Here in this chapter we are study about approximation theory and curve fitting.

### Chapter six

### Numerical differentiation and integration

In this chapter the main ideal that learn here are

- Numerical differentiation
- Numerical integration

### Chapter Seven

### Solution of Differential Equation

Under this chapter we are concern on

- Solution of ODE
- Solution PDE