Candidates can get Best University Physics Books 2018 also a Top List of Main Study Materials for 2017-2018 entrance exam in India.
- university physics with modern physics by Hugh D. Young 13th edition
1. Complex variables Recapitulation : Complex numbers, triangular inequalities, Schwarz inequality. Function of a complex variable — single and multiple-valued function, limit and continuity; Differentiation — CauchyRiemann equations and their applications; Analytic and harmonic function; Complex integrals, Cauchy’s theorem (elementary proof only), converse of Cauchy’s theorem, Cauchys Integral Formula and its corollaries; Series — Taylor and Laurent expansion; Classification of singularities; Branch point and branch cut; Residue theorem and evaluation of some typical real integrals using this theorem.
2. Theory of second order linear homogeneous differential equations Singular points — regular and irregular singular points; Frobenius method; Fuch’s theorem; Linear independence of solutions — Wronskian, second solution. Sturm-Liouville theory; Hermitian operators; Completeness.
3. Inhomogeneous differential equations : Green’s functions
4. Special functions Basic properties (recurrence and orthogonality relations, series expansion) of Bessel, Legendre, Hermite and Laguerre functions.
5. Integral transforms Fourier and Laplace transforms and their inverse transforms, Bromwich integral [use of partial fractions in calculating inverse Laplace transforms]; Transform of derivative and integral of a function; Solution of differential equations using integral transforms.
6. Vector space and matrices Vector space: Axiomatic definition, linear independence, bases, dimensionality, inner product; GramSchmidt orthogonalisation. Matrices: Representation of linear transformations and change of base; Eigenvalues and eigenvectors; Functions of a matrix; Cayley-Hamilton theorem; Commuting matrices with degenerate eigenvalues; Orthonormality of eigenvectors.
7. Group theory Definitions; Multiplication table; Rearrangement theorem; Isomorphism and homomorphism; Illustrations with point symmetry groups; Group representations : faithful and unfaithful representations, reducible and irreducible representations; Lie groups and Lie algebra with SU as an example.