Skip to main content
NounStudy
Back to Course Catalog
MTH423Sciences3 Unitsintermediate

Integral Equation

This course, Integral Equations, explores the fundamental concepts and techniques for solving integral equations. It covers linear integral equations, Volterra and Fredholm equations, and various methods for finding approximate solutions. Students will learn to convert ordinary differential equations into integral equations, work with Eigenfunctions and Eigenvectors, and apply Laplace and Fourier transforms to solve integral equations. The course aims to equip students with the skills to solve a wide range of integral equations.

Generate AI Study Notes

Transform this course into personalized study materials with AI

156h
Study Time
13
Weeks
12h
Per Week
intermediate
Math Level
Course Keywords
Integral EquationsVolterra EquationsFredholm EquationsEigenfunctionsLaplace Transforms

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
Theoretical Focus

Course Topics

Key areas covered in this course

1

Linear Integral Equations

2

Volterra Integral Equations

3

Fredholm Integral Equations

4

Degenerate Kernels

5

Eigenfunctions and Eigenvectors

6

Laplace Transforms

7

Fourier Transforms

8

Symmetric Kernels

9

Orthogonal Functions

Total Topics9 topics

Requirements

Knowledge and skills recommended for success

MTH311: Real Analysis

MTH315: Complex Analysis

MTH321: Differential Equations

💡 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 assessments

Comprehensive evaluation of course material understanding

Written Assessment

final examination

Comprehensive evaluation of course material understanding

Written Assessment

Career Opportunities

Explore the career paths this course opens up for you

Applied Mathematician

Apply your skills in this growing field

Numerical Analyst

Apply your skills in this growing field

Mathematical Modeler

Apply your skills in this growing field

Data Scientist

Apply your skills in this growing field

Research Scientist

Apply your skills in this growing field

Industry Applications

Real-world sectors where you can apply your knowledge

EngineeringPhysicsFinanceComputer ScienceData Analysis

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Preliminary Concepts

6h

Unit 1: Linear Integral Equation: Preliminary Concepts

6 study hours
  • •Understand the basic concepts of linear integral equations.
  • •Investigate the equations describing the displacement of a loaded elastic string.
  • •Solve shop stocking problems.
Week
2

Module 1: Preliminary Concepts

6h

Unit 2: Conversion of Ordinary Differential Equations into Integral Equations

6 study hours
  • •Convert ordinary differential equations into integral equations.
  • •Transform Sturm-Lowville problems to integral equations.
  • •Practice transformations and conversions.
Week
3

Module 1: Preliminary Concepts

6h

Unit 3: Classification of Linear Integral Equation

6 study hours
  • •Classify linear integral equations.
  • •Find approximate solutions for integral equations.
  • •Solve related exercises.
Week
4

Module 2: Volterra Integral Equation

6h

Unit 1: S2 Volterra Integral Equation

6 study hours
  • •Recognize Volterra integral equations.
  • •Identify the three types of Volterra integral equations.
  • •Determine the Resolvent kernel of a Volterra equation.
Week
5

Module 2: Volterra Integral Equation

6h

Unit 2: Convolution Type Kernels

6 study hours
  • •Solve convolution type kernels of the Volterra integral using Laplace transform.
  • •Practice inverse transforms and convolution.
Week
6

Module 3: Fredholm Equations

6h

Unit 1: Fredholm Equations with Degenerate Kernels

6 study hours
  • •Solve Fredholm equations with degenerate kernels.
  • •Apply the general method of solution of Fredholm equations.
  • •Work through examples.
Week
7

Module 3: Fredholm Equations

6h

Unit 2: Eigenfunctions and Eigenvectors

6 study hours
  • •Work with Eigenfunctions and Eigenvectors.
  • •Prove that symmetric and continuous kernels possess at least one Eigenvalue.
  • •Solve related problems.
Week
8

Module 3: Fredholm Equations

6h

Unit 3: Representation of a Function by a Series of Orthogonal

6 study hours
  • •Prove that functions can be represented by series of orthogonal functions.
  • •Expand K in a series of Eigenfunctions.
  • •Define positive kernels.
Week
9

Module 4: Integral Transforms

6h

Unit 1: Calculation of 1st Eigenvalue

6 study hours
  • •Apply the convolution theorem.
  • •Calculate the first Eigenvalue of an integral equation.
  • •Use the variational formula.
Week
10

Module 4: Integral Transforms

6h

Unit 2: The Application of the Transform

6 study hours
  • •Recognize integral Laplace transforms as transforms.
  • •Derive the solution of integral equations using inverse Laplace transform.
  • •Apply Laplace transform through worked examples.
Week
11

Module 1: Preliminary Concepts

4h

Unit 1: Linear Integral Equation: Preliminary Concepts

4 study hours
  • •Review Module 1: Linear Integral Equations and Preliminary Concepts
  • •Solve additional problems related to preliminary concepts and classifications
Week
12

Module 2: Volterra Integral Equation

4h

Unit 1: S2 Volterra Integral Equation

4 study hours
  • •Review Module 2: Volterra Integral Equations
  • •Practice solving Volterra equations using Resolvent Kernel and Laplace Transforms
Week
13

Module 3: Fredholm Equations

4h

Unit 1: Fredholm Equations with Degenerate Kernels

4 study hours
  • •Review Module 3: Fredholm Equations
  • •Practice solving Fredholm equations with degenerate kernels and Eigenfunction expansions

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.

Access PDF Material

Study Tips & Exam Preparation

Expert tips to help you succeed in this course

1

Review all unit summaries and key definitions thoroughly

2

Practice solving a variety of integral equations from each module

3

Focus on mastering Laplace and Fourier transform techniques

4

Create concept maps linking different types of integral equations and solution methods

5

Work through past exam papers to familiarize yourself with the exam format

6

Prioritize understanding the underlying principles rather than memorizing formulas

7

Allocate sufficient time for practice problems and review of challenging units

8

Form a study group to discuss concepts and solve problems collaboratively

9

Ensure a strong understanding of calculus and linear algebra concepts

10

Pay close attention to the assumptions and limitations of each solution method

Related Courses

Other courses in Sciences that complement your learning

CIT474

Introduction to Expert Systems

2 Units
CHM414

Photochemistry And Pericyclic Reactions

2 Units
CHM423

Coordination Chemistry

3 Units
View All Sciences Courses