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

Information for Mathematical Methods in Physics

BMETE11AP58, 2024 Fall Semester

 

Lectures

 

Wednesdays, Room F29

rapid test: 08:15-8:25

lecture: 8:25-09:55 

13 lectures from Sep. 4. to Dec. 4., except Oct. 23. 

Lecturer: Gergely Zaránd

 

Practice Sessions

 

Thursday 12:15-13:45 

14 Practice Sessions from Sep. 5. to Dec. 5, except Nov. 21.

Extra Practice Session on November 26 16:15-17:45, location KF81

Group Instructor Room
T1 Dr. Dániel Varjas KF87
T2 Dr. Márton Kormos T601/2

 

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. Public holiday, no lecture on Oct. 23. 

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

  10. 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) 

  11. 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) 

  12. 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) 

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

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

 

Course Requirements

 

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. 5-7 points / test) to the final score.

There will be a retake opportunity on Dec. 11 14:15-14:45 in room E505 when you can retake at most two mini tests to improve your score.

 

Attendance

 

Attending at least 70% of the lectures AND 70% of practice sessions is necessary for signature. The mini tests also serve to monitor lecture attendance.

 

Midterm exams

 

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

Test Time Place Max. Score
Test 1 Oct. 15. 16:00-18:00 K155 100
Test 2 Nov. 28. 12:15-14:00 K155 100

 

There will be opportunity to retake each of the tests:

Test Time Place Max. Score
Test 1 Retake Nov. 5 16:00-17:40 KM34 100
Test 2 Retake Dec. 11 15:00-17:00 E505 100

 

Homework

 

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

 

 

Condition for signature

 

Attending at least 70% of Lectures and practices + passing both midterm exams separately (individual threshold: 40 points).

 

Final exam

 

  • The exam (both written and oral) starts with an entry question from the published list. Only those who answer correctly can commence to the rest of the exam.
  • Written exam on Dec. 18 14:00-17:00 in room K275. Max score: 200 points
  • 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.
  • Students must register for the written theory test(s) and the optional oral exams in the Neptun system.

 

Evaluation

 

The threshold for passing the final test is 80 points (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

 

Last edit: 2024.12.01.