Mathematical Methods For Physics Ii
- Sciences
- 300 level
- 3 credit units
- 187 pages
- 12 units
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.
About this course
- Difficulty
- Advanced
- Study hours
- 120 hours
- Maths
- Advanced
- Content
- Theoretical, problem solving
- Practical work
- No
- Calculus I
- Calculus II
- Ordinary Differential Equations
- Assignments
- Tutor marked assignments
- Final examination
What you'll read
The real module and unit structure of PHY312, taken from the course material NOUN publishes.
One paragraph, so you can see how it reads
PHY312 · UNIT 1 PARTIAL DIFFERENTIAL EQUATIONS
This examination concludes the assessment for the course. It constitutes 70% of the whole course. You will be informed of the time of the examination. It may or may not coincide with the University Semester Examination.
What you should be able to do
- Solve linear second-order partial differential equations.
- Apply Fourier series to forced vibration problems.
- Utilize Fourier Integral for treating periodic functions.
- Apply half-range expansions to problem solutions.
- Derive and apply Legendre and Hermite polynomials.
- Evaluate Fourier coefficients.
- Apply Laplace transformation to solve initial and boundary value problems.
What it prepares you for
- Physicist
- Applied Mathematician
- Data Scientist
- Research Scientist
- Telecommunications
- Aerospace
- Medical Imaging
- Financial Modeling
- Acoustics
Where it gets hard
The units students slow down on, and what makes each one heavy.
- Module 2: Application of Fourier to PDEs (Legendre polynomials and Bessel Functions)
Unit 1: Legendre Polynomials
The complex derivations and applications of Legendre polynomials in quantum mechanics require a strong foundation in mathematical physics.
- Module 2: Application of Fourier to PDEs (Legendre polynomials and Bessel Functions)
Unit 2: Bessel Functions
Bessel functions involve intricate recurrence relations and integral representations, demanding advanced calculus skills.
A suggested way through it
13 weeks, about 54 hours in total. Yours will differ.
- Week 1Module 1: Partial Differential Equations with Applications in Physics
Unit 1: Partial Differential Equations · 4 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 2Module 1: Partial Differential Equations with Applications in Physics
Unit 2: Fourier Series · 4 hours
Learn about Fourier series and their properties.. Evaluate Fourier coefficients for different functions.. Solve problems involving Fourier series expansions..
- Week 3Module 2: Application of Fourier to PDEs (Legendre polynomials and Bessel Functions)
Unit 1: Legendre Polynomials · 4 hours
Study Legendre polynomials and their properties.. Solve Legendre's equation.. Practice using the generating function and Rodrigue's formula..
- Week 4Module 2: Application of Fourier to PDEs (Legendre polynomials and Bessel Functions)
Unit 2: Bessel Functions · 4 hours
Learn about Bessel functions and their properties.. Solve Bessel's differential equation.. Practice using recurrence relations and generating functions..
- Week 5Module 3: Application of Fourier to PDEs (Hermite Polynomials and Laguerre Polynomials)
Unit 1: Hermite Polynomials · 4 hours
Study Hermite polynomials and their properties.. Solve Hermite's differential equation.. Practice using the generating function and Rodrigues' formula..
- Week 6Module 3: Application of Fourier to PDEs (Hermite Polynomials and Laguerre Polynomials)
Unit 2: Laguerre Polynomials · 4 hours
Study Laguerre polynomials and their properties.. Solve Laguerre's differential equation.. Practice using the generating function and Rodrigues' formula..
- Week 7Module 1: Partial Differential Equations with Applications in Physics
Unit 1: Partial Differential Equations · 4 hours
Review partial differential equations and their applications.. Practice solving wave equations and heat conduction equations..
- Week 8Module 1: Partial Differential Equations with Applications in Physics
Unit 2: Fourier Series · 4 hours
Review Fourier series and their applications.. Practice evaluating Fourier coefficients and solving forced vibration problems..
- Week 9Module 2: Application of Fourier to PDEs (Legendre polynomials and Bessel Functions)
Unit 1: Legendre Polynomials · 4 hours
Review Legendre polynomials and their applications.. Practice solving problems related to angular momentum in quantum mechanics..
- Week 10Module 2: Application of Fourier to PDEs (Legendre polynomials and Bessel Functions)
Unit 2: Bessel Functions · 4 hours
Review Bessel functions and their applications.. Practice using recurrence relations and solving problems involving Bessel functions..
- Week 11Module 3: Application of Fourier to PDEs (Hermite Polynomials and Laguerre Polynomials)
Unit 1: Hermite Polynomials · 4 hours
Review Hermite polynomials and their applications.. Practice solving problems related to the harmonic oscillator in quantum mechanics..
- Week 12Module 3: Application of Fourier to PDEs (Hermite Polynomials and Laguerre Polynomials)
Unit 2: Laguerre Polynomials · 4 hours
Review Laguerre polynomials and their applications.. Practice solving problems related to the hydrogen atom in quantum mechanics..
- Week 13Comprehensive Revision
Final Revision · 6 hours
Comprehensive review of all modules and units.. Focus on key concepts and problem-solving techniques.. Prepare for final examinations..
Preparing for the exam
- Focus on understanding the underlying principles of each mathematical method.
- Practice solving a variety of problems from each unit to reinforce your understanding.
- Create concept maps linking different mathematical methods and their applications.
- Review all examples provided in the study units and attempt similar problems.
- Allocate specific time slots for revision and problem-solving each week.
- Prioritize understanding the applications of each method to real-world physics problems.
- Practice past examination questions to familiarize yourself with the exam format and difficulty level.
Questions students ask about this course
What is PHY312 about?
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.
How many units does PHY312 have?
PHY312, Mathematical Methods For Physics Ii, has 12 units across 3 modules, over 187 pages of course material. You can read it one unit at a time.
How many credit units is PHY312?
PHY312 carries 3 credit units, at 300 level in Sciences.
Is PHY312 hard?
PHY312 is rated advanced level, with advanced mathematical content. It is mostly theoretical and problem solving work.
How long does PHY312 take to study?
About 120 hours of study, spread across its 12 units.
How is PHY312 assessed?
PHY312 is assessed by assignments, tutor marked assignments and final examination.
What do I need before starting PHY312?
Calculus I Calculus II Ordinary Differential Equations
What can I do with PHY312?
Physicist, Applied Mathematician, Data Scientist and Research Scientist.