Mathematical Methods in Physics - BMETE11AP58

Mathematical Methods in Physics

BMETE11AP58, 2026 Fall Semester

Lectures

Wednesdays, Room F29

rapid test: 08:15-8:25

lecture: 8:25-09:55

13 lectures from September 9. to December 9., except November 18 (TDK day)

Lecturer: Dániel Varjas

Practice Sessions

Thursdays 12:15-13:45

14 Practice sessions from September 10. to December 10.

Group	Instructor	Room
T1	Márton Kormos	F31SEM
T2	Mihály Bodócs	E501
T3	Miklós Tóth	E502

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.

Lecture plan (approximate)

(numbers refer to sections in the Kreyszig textbook)

Fourier series, Even and Odd Functions, Half-Range Expansions (11.1, 11.2), Supplementary: Approximation by Trigonometric Polynomials (11.4)
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)
Fourier Integral, Fourier Cosine and Sine Transforms, Fourier Transform (11.7, 11.9. 11.10)
Discrete and Fast Fourier Transforms (11.9), Laplace transform (6.1-6.3)
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)
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)
Higher order linear ODEs (3.1-3.3)
Public holiday, no lecture on Oct. 23.
Systems of ODE’s, Phase plane, Qualitative methods (4.1-4.6)
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)
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)
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)
Complex differentiation, Analytic functions, Complex exponential, trigonometric functions, logarithm (13.3-13.7)
Complex line integrals, Cauchy integral theorem, Laurent series (14.1-14.2, 16.1)

Course Requirements

Attendance and conditions for signature

Attending at least 70% of practice sessions (10 out of 14) and passing both midterm exams separately (individual threshold: 40%) is necessary for signature. If you can't attend practice for a good reason (illness, other important unforeseen event) please let us know in advance, or as soon as possible, so we can credit your attendance.

Midterm exams

There are two written problem-solving tests during the semester, each for 50 points:

Test	Time	Place	Max. Score
Test 1	TBA (7th week)	TBA	50
Test 2	TBA (13th week)	TBA	50

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	TBA (9th week)	TBA	50
Test 2 Retake	TBA (14th week)	TBA	50
Re-Retake	TBA (retake week)	TBA	50

Mini tests (bonus points)

There is a 5-minute mini test at the start of the lectures covering the material of the lectures and practice on the previous week. The grading is only based on the final answer on a correct/incorrect basis, 2 points per test. Bring a calculator! The maximum obtainable score is 20 points, the actual total may be higher depending on the number of tests (10-12 tests). The mini test score will be added to the midterm score as bonus, and those who score at least 60% (12 points) will be exempt from the entry question of the exam, and will get their final grade rounded up. See the Evaluation section for details. There will be no retakes for the mini tests!

Homework

There will be no graded homework, we will give homework for recommended self-study. Some of the homework problems will be on the mini tests and the midterms with modified numerical values.

Final exam

The exam (both written or oral) starts with an entry question from the published list. Only those who answer correctly can commence to the rest of the exam. Those with at least 60% mini test score pass the entry question automatically.
The written exam will consist of theoretical questions and practical problems.
The threshold for passing the written exam is 40%.
Those who fail the written exam, or want to improve their grade, can take a repeat oral exam.
The oral exam will cover randomly selected topics (1 main and 2 minor questions) from the published exam questions list. Satisfactory knowledge of all topics is required to pass.
Students must register for the exams in the Neptun system.

Test	Time	Place
Written final exam	TBA (1st week of January)	TBA
Oral final exam retake	TBA	TBA
Oral final exam retake	TBA	TBA
Oral final exam retake	TBA	TBA

Evaluation

Those who pass the midterms will get their mini test score added to the total of the midterms as bonus (max 50+50+20 points), and will receive a grade using the percentage limits in the table below. The mini test score is bonus, so the percentage is calculated with 100 points in the denominator.
The written exam is graded with the percentage limits below, the oral exam is graded at the discretion of the examiner.
The final grade is the average of the two grades (midterms and exam). We will round up if the result ends on .5 and the mini test score is at least 60%, and round down otherwise.

Score (%)	Evaluation	Grade
0-39.9 %	fail	1
40-59.9 %	pass	2
60-74.9 %	average	3
75-89.9 %	good	4
90- %	excellent	5

Course info