Hafta 114–20 Eyl
Fizik için linear algebra tekrarı
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
inner productorthogonalityeigenvalueArfken Bölüm 2, 5 ve 6
Hafta 221–27 Eyl
Linear operatörler ve eigenvalue problemleri
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
diagonalizationnormal modesJordan canonical formself-adjoint operators
Hafta 328 Eyl – 4 Eki
Koordinat sistemleri, Jacobian ve curvilinear koordinatlar
Coordinate systems and transformations. Jacobians and metric factors. Orthogonal curvilinear coordinates and physical interpretation. Arfken: Chapter 3
coordinate transformationJacobianorthogonal curvilinear coordinatesArfken Bölüm 3
Hafta 45–11 Eki
Curvilinear koordinatlarda vector calculus
Vector calculus in curvilinear coordinates. Gradient, divergence, curl, and Laplacian operators. Integral theorems and physical meaning. Arfken: Chapter 3
curvilinear coordinatesgradient, divergence, curlLaplacian operatorArfken Bölüm 3
Hafta 512–18 Eki
Partial differential equation sınıflandırması ve sınır koşulları
Classification of partial differential equations. Boundary and initial conditions. Physical examples from diffusion, waves, and electrostatics. Arfken: Chapter 9
partial differential equationsboundary conditionsinitial conditionsArfken Bölüm 9
Hafta 619–25 Eki
Eigenvalue problemi olarak değişkenlerine ayırma
Separation of variables as an eigenvalue problem. Orthogonality and completeness of modes. Fourier series in bounded domains. Arfken: Chapters 8, 9, and 19
eigenvalue problemorthogonality ve completenessFourier seriesArfken Bölüm 8, 9, 19
Hafta 726 Eki – 1 Kas
Integral transform'lar, convolution ve Parseval; Arfken Bölüm 20
Fourier transforms and integral transforms. Convolution theorem and Parseval’s identity. Physical applications to wave and diffusion equations. Arfken: Chapter 20
Fourier transformconvolution theoremParseval's identitywave and diffusion equations
Hafta 82–8 Kas
Sturm-Liouville teorisi ve özfonksiyon açılımları
Sturm-Liouville theory. Weight functions, eigenfunction expansions, and physical boundary-value problems. Arfken: Chapter 8
Sturm-Liouville theoryweight functioneigenfunction expansionboundary-value problem
Hafta 99–15 Kas
Green's Functions ve Linear Response Teorisi
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
Green's functions for ODE ve PDEoperator inversionlinear response theoryconformal mapping (2D Laplace)
Hafta 1016–22 Kas
Bessel functions ve silindirik geometriler (Arfken Bölüm 14)
Bessel functions*. Radial equations arising from separation of variables in cylindrical geometries. Zeros and orthogonality. Applications to waveguides and circular membranes. Arfken: Chapter 14
Bessel functionsseparation of variablesorthogonalitywaveguides
Hafta 1123–29 Kas
Legendre polynomials ve spherical harmonics
Legendre polynomials and associated Legendre functions*. Spherical harmonics and angular eigenvalue problems. Arfken: Chapter 15
Legendre polynomialsassociated Legendre functionsspherical harmonicsArfken Bölüm 15
Hafta 1230 Kas – 6 Ara
Hermite polynomials ve harmonic oscillator
Hermite polynomials and Hermite functions*. Harmonic oscillator and Gaussian weight functions. Arfken: Chapter 18
Hermite polynomialsHermite functionsharmonic oscillatorArfken Bölüm 18
Hafta 137–13 Ara
Laguerre polinomları ve radyal kuantum problemleri
Laguerre and associated Laguerre polynomials*. Radial problems and applications to quantum systems. Arfken: Chapter 18
Laguerre polynomialsassociated Laguerreradyal problemlerArfken Bölüm 18
Hafta 1414–20 Ara
Boundary-value problemlerinin operator ve spectral formülasyonu
Common operator-based and spectral formulation of boundary-value problems in classical and quantum physics. Synthesis of Arfken Chapters 6-10 and 14-20
boundary-value problemsspectral formulationArfken Bölüm 6-10Arfken Bölüm 14-20