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MTH213Sciences3 Unitsintermediate

Numerical Analysis I

This course introduces students to numerical methods for solving mathematical problems. It covers interpolation techniques, including Lagrange's and Newton's forms, and their applications in approximating function values. The course also explores direct and iterative methods for solving linear algebraic equations, along with eigenvalue problems. Additionally, it reviews essential calculus concepts and introduces numerical techniques for finding roots of non-linear equations, such as the bisection and Newton-Raphson methods.

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150h
Study Time
13
Weeks
12h
Per Week
intermediate
Math Level
Course Keywords
Numerical AnalysisInterpolationLinear EquationsRoot FindingEigenvalues

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

Interpolation Techniques

2

Lagrange's Interpolation

3

Newton's Interpolation

4

Linear Algebraic Equations

5

Direct and Iterative Methods

6

Eigenvalue Problems

7

Non-Linear Equations

8

Root Finding Algorithms

9

Error Analysis

10

Taylor's Theorem

Total Topics10 topics

Requirements

Knowledge and skills recommended for success

MTH112

MTH121

MTH122

💡 Don't have all requirements? Don't worry! Many students successfully complete this course with basic preparation and dedication.

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

Final Examination

Comprehensive evaluation of course material understanding

Computer Based Test

Career Opportunities

Explore the career paths this course opens up for you

Data Analyst

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Financial Analyst

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Engineering Analyst

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Research Scientist

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Statistician

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Industry Applications

Real-world sectors where you can apply your knowledge

EngineeringFinanceData ScienceScientific ResearchComputer Science

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Interpolation

3h

Unit 1: Interpolation (Lagrange's Form)

3 study hours
  • •Read the unit introduction to understand the concept of interpolation.
  • •Study Lagrange's form of interpolation and work through examples.
  • •Practice computing approximate values at non-tabular points.
  • •Solve inverse interpolation problems.
Week
2

Module 1: Interpolation

3h

Unit 2: Newton's Form of the Interpolating Polynomial

3 study hours
  • •Study Newton's form of the interpolating polynomial.
  • •Learn about divided differences and their tabular representation.
  • •Practice computing interpolating polynomial errors.
  • •Relate divided differences to derivatives of functions.
Week
3

Module 1: Interpolation

3h

Unit 3: Interpolation at Equally Spaced Points

3 study hours
  • •Study forward, backward, and central differences.
  • •Learn about Newton's Forward-Difference and Backward-Difference formulas.
  • •Practice applying difference formulas to solve interpolation problems.
  • •Establish relationships between different types of differences.
Week
4

Module 2: Solution of Linear Algebraic Equations

3h

Unit 1: Direct Method

3 study hours
  • •Review preliminaries of linear algebraic equations.
  • •Study Cramer's rule and its applications.
  • •Learn about direct methods for solving linear algebraic equations.
  • •Practice solving problems using Cramer's rule.
Week
5

Module 2: Solution of Linear Algebraic Equations

3h

Unit 2: Inverse of A Square Matrix

3 study hours
  • •Study the method of adjoints for finding the inverse of a square matrix.
  • •Learn about the Gauss-Jordan reduction method.
  • •Practice solving problems using the Gauss-Jordan method.
  • •Study LU decomposition method.
Week
6

Module 2: Solution of Linear Algebraic Equations

3h

Unit 3: Iterative Methods

3 study hours
  • •Study the general iterative methods for solving linear equations.
  • •Learn about the Jacobi's iteration method.
  • •Practice solving problems using Jacobi's iteration method.
  • •Study the Gauss-Seidel iteration method.
Week
7

Module 2: Solution of Linear Algebraic Equations

3h

Unit 4: Eigen-Values and Eigen-Vectors

3 study hours
  • •Study the Eigen value problem.
  • •Learn about the power method for finding Eigen values.
  • •Practice solving problems using power method.
  • •Study the inverse power method.
Week
8

Module 3: Solution of Non-Linear Equations in one Varibale

3h

Unit 1: Review of Calculus

3 study hours
  • •Review the three fundamental theorems of calculus.
  • •Study Taylor's theorem and its applications.
  • •Learn about round-off and truncation errors.
  • •Practice solving problems related to errors.
Week
9

Module 3: Solution of Non-Linear Equations in one Varibale

3h

Unit 2: Iteration Methods for Locating Root

3 study hours
  • •Study iteration methods for locating roots.
  • •Learn about tabulation and graphical methods.
  • •Practice solving problems using tabulation and graphical methods.
  • •Study Bisection method and fixed point iteration method.
Week
10

Module 3: Solution of Non-Linear Equations in one Varibale

3h

Unit 3: Chord Methods for Finding Root

3 study hours
  • •Study chord methods for finding roots.
  • •Learn about Repuler-Falsi method.
  • •Practice solving problems using Repuler-Falsi method.
  • •Study Newton – Raphson method and convergence criterion.
Week
11

Module 3: Solution of Non-Linear Equations in one Varibale

3h

Unit 4: Approximate Root of Polynomial Equation

3 study hours
  • •Study approximate root of polynomial equation.
  • •Learn about some results on roots of polynomial equation.
  • •Practice solving problems related to roots of polynomial equation.
  • •Study Birge-Vieta method and Graeffe's Root squaring method.
Week
12

Module 1: Interpolation

3h

Unit 3: Interpolation at Equally Spaced Points

3 study hours
  • •Review Module 1: Interpolation
  • •Solve additional exercises on Interpolation (Lagrange's Form).
  • •Solve additional exercises on Newton's Form of the Interpolating Polynomial.
  • •Solve additional exercises on Interpolation at Equally Spaced Points.
Week
13

Module 2: Solution of Linear Algebraic Equations

3h

Unit 4: Eigen-Values and Eigen-Vectors

3 study hours
  • •Review Module 2: Solution of Linear Algebraic Equations
  • •Solve additional exercises on Direct Methods.
  • •Solve additional exercises on Inverse of A Square Matrix.
  • •Solve additional exercises on Iterative Methods.
  • •Solve additional exercises on Eigen-Values and Eigen-Vectors.

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 concept maps linking Module 1 interpolation techniques

2

Practice solving linear systems using direct/iterative methods from Module 2 weekly

3

Focus on understanding the conditions for convergence of iterative methods

4

Review calculus theorems from Unit 1 and their applications in error analysis

5

Practice applying Newton-Raphson and chord methods from Module 3 to various functions

6

Work through all Tutor-Marked Assignments (TMAs) and review feedback carefully

7

Create a summary sheet of key formulas and theorems for quick reference during the exam

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