BMETE11AP58

Course data
Course name: Mathematical Methods in Physics
Neptun ID: BMETE11AP58
Responsible teacher: Titusz Fehér
Programme: Physicist-Engineer BSC
Course data sheet: BMETE11AP58
Requirements, Information

The course page may not be up to date!

For technical reasons we will stop updating this page. Check the associated Teams page for the latest information. In case of disagreement, the information on Teams is considered accurate!

[Last edit: 2025/08/25]

 

Information for Mathematical Methods in Physics

BMETE11AP58, 2025 Fall Semester

 

Lectures

 

Wednesdays, Room F29

rapid test: 08:15-8:25

lecture: 8:25-09:55 

13 lectures from September 10. to December 10., except November 19 (TDK conference)

Lecturer: Gergely Zaránd

 

Practice Sessions

Thursday 12:15-13:45 

13 Practice sessions from September 11. to December 11., except October 23. (public holiday)

Group Instructor Room
T1 Dr. Dániel Varjas TBD
T2 Dr. Márton Kormos TBD
T3 Mihály Bodócs TBD

Course contents 

 

The aim of the course is to introduce mathematical methods and concepts that play an important role in advanced physics (e.g. electrodynamics, quantum mechanics) in more detail than taught in general mathematics. The focus is not on rigorous proofs of theorems, but on their illustration and applications to practical problems. 

Recommended reading  

 

  • Erwin Kreyszig: Advanced Engineering Mathematics (Wiley Global Education 2010) 
  • Supplementary notes 

Teams Access

 

The course has an associated team in the institutional Microsoft Teams, for which the access code is distributed to registered students via the Neptun system. We communicate via Neptun and Teams, and you can access most resources (lecture notes, homeworks) here .

 

Moodle

 

The course has a page on the institute Moodle.  Those who took the course on Neptun have been automatically added, contact the instructors if you don't have access. This is where we communicate test and exam results.

 

Lecture plan (approximate) 

(numbers refer to sections in the Kreyszig textbook) 

 

  1. Fourier series, Even and Odd Functions, Half-Range Expansions (11.1, 11.2), Supplementary: Approximation by Trigonometric Polynomials (11.4) 

  2. Revision: Complex numbers and algebra (13.1, 13.2), Complex Fourier series, Sturm–Liouville Problems. Orthogonal Functions, Orthogonal Series, Generalized Fourier Series (lecture notes, 11.5, 11.6) 

  3. Fourier Integral, Fourier Cosine and Sine Transforms, Fourier Transform (11.7, 11.9. 11.10) 

  4. Discrete and Fast Fourier Transforms (11.9), Laplace transform (6.1-6.3) 

  5. Ordinary differential equations: Basic Concepts, Geometric Meaning, direction Fields, Euler’s Method, Separable ODEs, Linear ODEs, Population Dynamics, Existence and Uniqueness of Solutions for Initial Value problems (1.1, 1.2, 1.3, 1.5, 1.7) 

  6. Homogeneous Linear ODEs of second order, Homogeneous Linear ODEs with Constant Coefficients, Nonhomogeneous Linear ODEs, Forced oscillations, resonance (2.1, 2.2, 2.4, 2.7, 2.8) 

  7. Higher order linear ODEs (3.1-3.3) 

  8. Systems of ODE’s, Phase plane, Qualitative methods (4.1-4.6) 

  9. Partial differential equations: Basic Concepts, Modeling: Vibrating String, Wave Equation, Solution by Separating Variables, Use of Fourier Series, D’Alembert’s Solution of the Wave Equation, Characteristics (12.1-12.4) 

  10. Modeling: Heat Flow from a Body in Space. Heat Equation: Solution by Fourier Series, Steady Two-Dimensional Heat Problems, Dirichlet Problem, Heat Equation: Modeling Very Long Bars, Solution by Fourier Integrals and Transforms, Modeling: Membrane, Two-Dimensional Wave Equation (12.5-12.8) 

  11. Rectangular Membrane, Double Fourier Series, Laplacian in Polar Coordinates. Circular Membrane, Fourier–Bessel Series , Laplace’s Equation in Cylindrical and Spherical Coordinates, Potential, Solution of PDEs by Laplace Transforms (12.9-12.12) 

  12. Complex differentiation, Analytic functions, Complex exponential, trigonometric functions, logarithm (13.3-13.7) 

  13. Complex line integrals, Cauchy integral theorem, Laurent series (14.1-14.2, 16.1) 

 

Course Requirements

 

Your score is based upon the midterm tests (2x100 points) and the final written exam (200 points + bonus points from mini-tests) 

Mini tests

 

There will be a 10-minute mini test at the start of every lecture from the material of the previous lecture. Those who get over 60% of the total score, automatically pass the entry question of the final exam (see below) AND we add their total mini-test score (max. 5 points / test) to the final score.

Attendance

 

Attending at least 70%  of practice sessions is necessary for signature, i.e., to go for the exam. 

Midterm exams

 

There are two written problem-solving tests during the semester, each for 100 points:

Test Time Place Max. Score
Test 1 TBD TBD 100
Test 2 TBD TBD 100

There will be opportunity to retake each of the tests. There will be an opportunity to re-retake one of the midterms, this requires registering on Neptun and paying a fee.

Test Time Place Max. Score
Test 1 Retake TBD TBD 100
Test 2 Retake TBD TBD 100
Re-Retake TBD (retake week) TBD 100

 

Homework

 

There will be no graded homework. We will give homework for recommended self-study, and at least one problem in each midterm will be chosen from the homework problems.

Condition for signature

 

Attending at least 70% of practices + passing both midterm tests separately (individual threshold: 40%).

Final exam

 

  • The exam starts with an entry question from the published list. Only those who answer correctly can commence the rest of the exam.
  • Those who fail the written exam, can take an oral repeat exam. The oral exam consists of two of the published exam questions / subjects, satisfactory knowledge of both is required to pass. In this case the grade is an average of the grade you got based on the written modterm tests and the oral exam. Mini-test bonus decides if your average is rounded upwards or downwards. 
  • Students must register for the written theory test(s) and the optional oral exams in the Neptun system.
Test Time Place Max. Score
Written final exam TBA (first week of January) TBA 200
Written final exam retake TBA TBA 200
 

 

Evaluation

 

The threshold for passing the final test is (40%).

The end result is computed from the total score (two problem solving tests, one final test, possible mini-test extra, max. 400 points total), graded using the following percentage limits:

Score (%) Evaluation Grade
  0-39.9 % fail 1
40-54.9 % pass 2
55-69.9 % average 3
70-84.9 % good 4
85- % excellent 5