defter / katalog / PHYS 242

PHYS 242

Advanced Calculus for Applications in Physics

PHYS 242 is where the math you've been doing starts to look like the language physics actually speaks: linear operators, eigenvalue problems, and special functions as the natural machinery for solving boundary-value problems in classical and quantum systems. You'll spend the semester separating variables, expanding solutions in orthogonal bases (Fourier, Bessel, Legendre, Hermite, Laguerre), and building Green's functions, with weekly quizzes keeping the problem-solving muscles sharp alongside two midterms and a final. Coming off freshman calculus and linear algebra, this is the toolkit you'll lean on constantly in quantum mechanics, electrodynamics, and statistical physics.

Credit3ECTS5FacultyFaculty of ScienceBölümPhysicsPreMATH 241MüfredatY2 Bahar

→ STARS müfredatı (resmi syllabus)

Değerlendirme 100% — 4 adım

25%

35%

15%

Midterm Midterm-I, Midterm-II 50%

Final Final 35%

Quiz Quiz or take home assignments 15%

Önerilen kaynaklar 5 kitap

📕

Zorunlu

Mathematical Methods for Physicists

G. B. Arfken, H. J. Weber

and F. E. Harris · 7th edition

📖

Önerilen

Mathematical Methods in the Physical Sciences

M. L. Boas, Wiley

📖

Önerilen

Mathematical Physics: A Modern Introduction to Its Foundations

S. Hassani, Springer

📖

Önerilen

Mathematical Methods for Physics and Engineering

K. F. Riley, M. P. Hobson

and S. J. Bence · Cambridge University Press

📖

Önerilen

Mathematical Methods for Physicists : A concise introduction

Tai L. Chow, Cambridge University Press

Haftalık müfredat 14 hafta

Hafta 1

Review of linear algebra for physics: inner products, norms, orthogonality, and projections. Eigenvalues and eigenvectors as tools for decoupling physical systems. Arfken: Chapters 2, 5, and 6

Hafta 2

Linear operators and eigenvalue problems. Diagonalization and normal modes. Degeneracy and simultaneous diagonalizability of commuting operators. Defective operators and Jordan canonical form. Physical consequences of non-diagonalizability. Self-adjoint operators and reality of spectra. Arfken: Chapters 5 and 6

Hafta 3

Coordinate systems and transformations. Jacobians and metric factors. Orthogonal curvilinear coordinates and physical interpretation. Arfken: Chapter 3

Hafta 4

Vector calculus in curvilinear coordinates. Gradient, divergence, curl, and Laplacian operators. Integral theorems and physical meaning. Arfken: Chapter 3

Hafta 5

Classification of partial differential equations. Boundary and initial conditions. Physical examples from diffusion, waves, and electrostatics. Arfken: Chapter 9

Hafta 6

Separation of variables as an eigenvalue problem. Orthogonality and completeness of modes. Fourier series in bounded domains. Arfken: Chapters 8, 9, and 19

Hafta 7

Fourier transforms and integral transforms. Convolution theorem and Parseval’s identity. Physical applications to wave and diffusion equations. Arfken: Chapter 20

Hafta 8

Sturm–Liouville theory. Weight functions, eigenfunction expansions, and physical boundary-value problems. Arfken: Chapter 8

Hafta 9

Green’s functions for ordinary and partial differential equations. Operator inversion and physical response functions. Linear response theory*. Conformal mapping methods for two-dimensional Laplace problems*. Arfken: Chapter 10

Hafta 10

Bessel functions*. Radial equations arising from separation of variables in cylindrical geometries. Zeros and orthogonality. Applications to waveguides and circular membranes. Arfken: Chapter 14

Hafta 11

Legendre polynomials and associated Legendre functions*. Spherical harmonics and angular eigenvalue problems. Arfken: Chapter 15

Hafta 12

Hermite polynomials and Hermite functions*. Harmonic oscillator and Gaussian weight functions. Arfken: Chapter 18

Hafta 13

Laguerre and associated Laguerre polynomials*. Radial problems and applications to quantum systems. Arfken: Chapter 18

Hafta 14

Common operator-based and spectral formulation of boundary-value problems in classical and quantum physics. Synthesis of Arfken Chapters 6–10 and 14–20

🤖 GenAI politikası

Same as in http://www.fen.bilkent.edu.tr/~phys102/ GenAI_Policy.pdf.

Ders — defter ekibinin ders notları

PHYS 242 için ders notları hazır.

14 bölüm · 372 KB. Defter ekibinin öğrencilerin paylaştığı materyallerden, müfredattan ve hocanın slaytlarından AI ile sentezlediği tek tutarlı ders kitabı.

Notları aç →

↑ daha iyi olması için: notların / çözümlerin / sınavların varsa "+ materyal paylaş" — bir sonraki güncellemede sentezde yerini alır.

Geçmiş GPA dağılımı 13 dönem · ort. 2.21

Dönem	Course CPA
2024-2025 Spring	1.91	1 sec · 55 öğr
2023-2024 Spring	2.11	1 sec · 51 öğr
2022-2023 Spring	1.94	1 sec · 39 öğr
2021-2022 Spring	2.37	1 sec · 38 öğr
2020-2021 Spring	2.23	1 sec · 35 öğr
2019-2020 Spring	2.12	1 sec · 34 öğr
2018-2019 Spring	2.82	1 sec · 27 öğr
2017-2018 Spring	2.97	1 sec · 44 öğr
2016-2017 Spring	2.39	1 sec · 34 öğr
2015-2016 Spring	2.55	1 sec · 36 öğr

Aggregate course GPA — Bilkent STARS'tan public data. Hoca-bazlı per-section detayı için STARS evaluation report →. Öğrenci anket cevapları KVKK kapsamında defter'de tutulmaz.

⚠️ FZ engelleyen şartlar

ATTENDANCE RATE ABOVE 70%.

Hocalar 1 bu dönem · 4 geçmiş

Bu dönem (2025-2026 Spring) · 1 section

Aydın Cem Keser

Geçmişte ders veren (4 kişi)

Şahin Büyükdağlı, Ali Ulvi Yılmazer, Atilla Erçelebi, Tahsin Tuğrul Hakioğlu