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PHY314Sciences2 Unitsintermediate

Nurimal Computations

This course introduces students to the fundamental concepts and techniques of numerical analysis. It covers various types of errors in numerical computations and methods to minimize them. Key topics include curve-fitting, solving linear systems of equations, finding roots of algebraic and transcendental equations, numerical integration, and working with finite difference schemes. Students will also learn to solve initial value problems of ordinary differential equations and write C++ programs for solving numerical problems.

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91h
Study Time
13
Weeks
7h
Per Week
intermediate
Math Level
Course Keywords
Numerical AnalysisC++ ProgrammingCurve FittingLinear EquationsFinite Differences

Course Overview

Everything you need to know about this course

Course Difficulty

Intermediate Level
Builds on foundational knowledge
65%
intermediate
📊
Math Level
Moderate Math
🔬
Learning Type
Hands-on Practice

Course Topics

Key areas covered in this course

1

Error Analysis

2

Curve Fitting

3

Linear Systems

4

Root Finding

5

Numerical Integration

6

Ordinary Differential Equations

Total Topics6 topics

Ready to Start

No specific requirements needed

This course is designed to be accessible to all students. You can start immediately without any prior knowledge or specific preparation.

Assessment Methods

How your progress will be evaluated (3 methods)

Assignments

Comprehensive evaluation of course material understanding

Written Assessment

Tutor-Marked Assignments

Comprehensive evaluation of course material understanding

Written Assessment

End of Course Examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Data Analyst

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Computational Physicist

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Numerical Analyst

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Software Engineer

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Research Scientist

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

EngineeringPhysicsFinanceData ScienceScientific Research

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1:

3h

Unit 1: Approximations and Errors in Numerical Computations

3 study hours
  • •Understand the importance of errors in numerical analysis.
  • •Learn to round numbers to a specific number of significant figures.
  • •Explore different types of errors and methods to reduce them.
Week
2

Module 1:

3h

Unit 2: Approximations and Errors in Numerical Computations

3 study hours
  • •Linearise a given equation to plot a linear graph.
  • •Derive equations for least squares linear fit.
  • •Fit a linear graph to a set of data.
Week
3

Module 1:

3h

Unit 3: Linear Systems of Equations

3 study hours
  • •Write a system of linear equations in an augmented matrix form.
  • •Solve a system of linear equations using Gaussian elimination.
  • •Apply Gauss-Jordan elimination and LU decomposition methods.
Week
4

Module 1:

3h

Unit 4: Roots of Algebraic and Transcendental Equations

3 study hours
  • •Find the root of an equation using the bisection method.
  • •Apply the Newton-Raphson method to find roots.
  • •Compare different methods for obtaining the zero of a function.
Week
5

Module 1:

3h

Unit 5: Finite Differences and Interpolation

3 study hours
  • •Deduce a polynomial from its difference table.
  • •Derive Newton's forward and backward interpolation formulas.
  • •Fit a polynomial to a given set of data.
Week
6

Module 1:

3h

Unit 6: Numerical Integration

3 study hours
  • •Numerically integrate a function using the Trapezoidal rule.
  • •Apply Simpson's one-third and three-eighth rules.
  • •Deduce the error involved in approximating an analytical integral with a numerical one.
Week
7

Module 1:

3h

Unit 7: Initial Value Problems of Ordinary Differential Equations

3 study hours
  • •Reduce a higher-order ODE to a system of first-order ODEs.
  • •Solve a first-order ODE using Picard's method.
  • •Apply the Euler method and Modified Euler method.
Week
8

Module 1:

3h

Review of Units 1 & 2

3 study hours
  • •Practice problems on approximations and errors in numerical computations.
  • •Review significant digits and arithmetic precision.
  • •Complete Tutor-Marked Assignment (TMA) 1.
Week
9

Module 1:

3h

Review of Units 3 & 4

3 study hours
  • •Practice problems on linear systems of equations.
  • •Review Gaussian elimination and Gauss-Jordan elimination.
  • •Complete Tutor-Marked Assignment (TMA) 2.
Week
10

Module 1:

3h

Review of Units 5 & 6

3 study hours
  • •Practice problems on finite differences and interpolation.
  • •Review Newton's forward and backward interpolation formulas.
  • •Complete Tutor-Marked Assignment (TMA) 3.
Week
11

Module 1:

3h

Review of Unit 7

3 study hours
  • •Practice problems on initial value problems of ordinary differential equations.
  • •Review Picard's method and Runge-Kutta methods.
  • •Complete Tutor-Marked Assignment (TMA) 4.
Week
12

Module 1:

4h

Final Revision: Numerical Methods

4 study hours
  • •Consolidate understanding of numerical methods.
  • •Focus on key concepts and techniques.
  • •Prepare for the final examination.
Week
13

Module 1:

4h

Final Revision: C++ Programming

4 study hours
  • •Consolidate understanding of C++ programming.
  • •Focus on writing programs for solving numerical problems.
  • •Final preparation for the examination.

This study schedule is in beta and may not be accurate. Please use it as a guide and consult the course outline for the most accurate information.

Course PDF Material

Read the complete course material as provided by NOUN.

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Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Create a detailed study schedule allocating time for each unit

2

Practice solving numerical problems from each unit using C++

3

Focus on understanding the underlying principles of each method

4

Review and practice past TMA questions

5

Create concept maps linking different numerical methods and their applications

6

Practice writing C++ code for implementing numerical algorithms from Units 7-9 weekly

7

Focus on understanding error analysis and its impact on numerical solutions

8

Review all examples and exercises in the study material

9

Practice time management during mock exams

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