The University of Newcastle, Australia
Available in 2019

Course handbook

Description

Numerical methods are now at the heart of applied mathematics. Many significant practical problems cannot be solved by analytical methods - their solutions can only be approximated through numerical methods. Since numerical methods do not give exact solutions to problems it is important to analyse their accuracy. It is also important to understand the stability, efficiency and robustness of a numerical scheme.

This course introduces concepts in numerical analysis emphasising the development of numerical algorithms to provide solutions to common problems formulated in science and engineering. This will develop the basic understanding of numerical algorithms, their computer implementation, applicability and limitations.


Availability2019 Course Timetables

Callaghan

  • Semester 1 - 2019

Learning outcomes

On successful completion of the course students will be able to:

1. Understand floating point numbers, computer arithmetic and the role of errors in numerical analysis.

2. Understand the applicability and limitations of a range of important numerical schemes and their role in science and mathematics.

3. Develop their own numerical algorithms for real-world problems, implement them in a computer, visualise and interpret their solutions.

4. Understand accuracy, consistency, stability and convergence of a numerical method, and the concepts of well- and ill-conditioned problems.


Content

  • Computer arithmetic
  • Solving nonlinear equations
  • Interpolation
  • Numerical differentiation and integration
  • Solving systems of linear equations
  • Least squares approximation

Assumed knowledge

MATH3820Numerical MethodsNumerical methods are now at the heart of applied mathematics. Many significant practical problems cannot be solved by analytical methods - their solutions can only be approximated through numerical methods. Since numerical methods do not give exact solutions to problems it is important to analyse their accuracy. It is also important to understand the stability, efficiency and robustness of a numerical scheme.

This course introduces concepts in numerical analysis emphasising the development of numerical algorithms to provide solutions to common problems formulated in science and engineering. This will develop the basic understanding of numerical algorithms, their computer implementation, applicability and limitations.FSCITFaculty of Science724School of Mathematical and Physical Sciences1030005940Semester 1 - 2019CALLAGHANCallaghan2019MATH2310 Computer arithmetic Solving nonlinear equations Interpolation Numerical differentiation and integration Solving systems of linear equations Least squares approximation YOn successful completion of this course, students will be able to:1Understand floating point numbers, computer arithmetic and the role of errors in numerical analysis.2Understand the applicability and limitations of a range of important numerical schemes and their role in science and mathematics.3Develop their own numerical algorithms for real-world problems, implement them in a computer, visualise and interpret their solutions.4Understand accuracy, consistency, stability and convergence of a numerical method, and the concepts of well- and ill-conditioned problems. Written Assignment: Written Assignment 1Written Assignment: Written Assignment 2Quiz: In-class quizFormal Examination: Final examination CallaghanLectureFace to Face On Campus3hour(s)per Week for0Full Term0Tutorial and computer lab work will be integrated with lectures as required.


Assessment items

Written Assignment: Written Assignment 1

Written Assignment: Written Assignment 2

Quiz: In-class quiz

Formal Examination: Final examination


Contact hours

Callaghan

Lecture

Face to Face On Campus 3 hour(s) per Week for Full Term

Tutorial and computer lab work will be integrated with lectures as required.