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PHY312Sciences3 Unitsadvanced

Mathematical Methods For Physics Ii

This course provides essential mathematical methods for solving physics problems. It explores the relationship between functions and variables, Jacobian applications, and functional dependence. The course covers multiple, line, and improper integrals, offering a comprehensive understanding of mathematical techniques crucial for advanced physics studies. Students will learn to apply these methods to various scientific problems.

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120h
Study Time
13
Weeks
9h
Per Week
advanced
Math Level
Course Keywords
Partial Differential EquationsFourier SeriesLegendre PolynomialsBessel FunctionsMathematical Methods

Course Overview

Everything you need to know about this course

Course Difficulty

Advanced Level
For experienced practitioners
90%
advanced
∑
Math Level
Advanced Math
📖
Learning Type
Theoretical Focus

Course Topics

Key areas covered in this course

1

Partial Differential Equations

2

Fourier Series and Transforms

3

Legendre Polynomials

4

Bessel Functions

5

Hermite Polynomials

6

Laguerre Polynomials

Total Topics6 topics

Requirements

Knowledge and skills recommended for success

Calculus I

Calculus II

Ordinary 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 assignments

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

Physicist

Apply your skills in this growing field

Applied Mathematician

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

TelecommunicationsAerospaceMedical ImagingFinancial ModelingAcoustics

Study Schedule Beta

A structured 13-week journey through the course content

Week
1

Module 1: Partial Differential Equations with Applications in Physics

4h

Unit 1: Partial Differential Equations

4 study hours
  • •Study the definition of partial differential equations.
  • •Understand linear second-order partial differential equations.
  • •Solve exercises on identifying the order and linearity of PDEs.
Week
2

Module 1: Partial Differential Equations with Applications in Physics

4h

Unit 2: Fourier Series

4 study hours
  • •Learn about Fourier series and their properties.
  • •Evaluate Fourier coefficients for different functions.
  • •Solve problems involving Fourier series expansions.
Week
3

Module 2: Application of Fourier to PDEs (Legendre polynomials and Bessel Functions)

4h

Unit 1: Legendre Polynomials

4 study hours
  • •Study Legendre polynomials and their properties.
  • •Solve Legendre's equation.
  • •Practice using the generating function and Rodrigue's formula.
Week
4

Module 2: Application of Fourier to PDEs (Legendre polynomials and Bessel Functions)

4h

Unit 2: Bessel Functions

4 study hours
  • •Learn about Bessel functions and their properties.
  • •Solve Bessel's differential equation.
  • •Practice using recurrence relations and generating functions.
Week
5

Module 3: Application of Fourier to PDEs (Hermite Polynomials and Laguerre Polynomials)

4h

Unit 1: Hermite Polynomials

4 study hours
  • •Study Hermite polynomials and their properties.
  • •Solve Hermite's differential equation.
  • •Practice using the generating function and Rodrigues' formula.
Week
6

Module 3: Application of Fourier to PDEs (Hermite Polynomials and Laguerre Polynomials)

4h

Unit 2: Laguerre Polynomials

4 study hours
  • •Study Laguerre polynomials and their properties.
  • •Solve Laguerre's differential equation.
  • •Practice using the generating function and Rodrigues' formula.
Week
7

Module 1: Partial Differential Equations with Applications in Physics

4h

Unit 1: Partial Differential Equations

4 study hours
  • •Review partial differential equations and their applications.
  • •Practice solving wave equations and heat conduction equations.
Week
8

Module 1: Partial Differential Equations with Applications in Physics

4h

Unit 2: Fourier Series

4 study hours
  • •Review Fourier series and their applications.
  • •Practice evaluating Fourier coefficients and solving forced vibration problems.
Week
9

Module 2: Application of Fourier to PDEs (Legendre polynomials and Bessel Functions)

4h

Unit 1: Legendre Polynomials

4 study hours
  • •Review Legendre polynomials and their applications.
  • •Practice solving problems related to angular momentum in quantum mechanics.
Week
10

Module 2: Application of Fourier to PDEs (Legendre polynomials and Bessel Functions)

4h

Unit 2: Bessel Functions

4 study hours
  • •Review Bessel functions and their applications.
  • •Practice using recurrence relations and solving problems involving Bessel functions.
Week
11

Module 3: Application of Fourier to PDEs (Hermite Polynomials and Laguerre Polynomials)

4h

Unit 1: Hermite Polynomials

4 study hours
  • •Review Hermite polynomials and their applications.
  • •Practice solving problems related to the harmonic oscillator in quantum mechanics.
Week
12

Module 3: Application of Fourier to PDEs (Hermite Polynomials and Laguerre Polynomials)

4h

Unit 2: Laguerre Polynomials

4 study hours
  • •Review Laguerre polynomials and their applications.
  • •Practice solving problems related to the hydrogen atom in quantum mechanics.
Week
13

Comprehensive Revision

6h

Final Revision

6 study hours
  • •Comprehensive review of all modules and units.
  • •Focus on key concepts and problem-solving techniques.
  • •Prepare for final examinations.

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

Focus on understanding the underlying principles of each mathematical method.

2

Practice solving a variety of problems from each unit to reinforce your understanding.

3

Create concept maps linking different mathematical methods and their applications.

4

Review all examples provided in the study units and attempt similar problems.

5

Allocate specific time slots for revision and problem-solving each week.

6

Prioritize understanding the applications of each method to real-world physics problems.

7

Practice past examination questions to familiarize yourself with the exam format and difficulty level.

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