JAM Physics Syllabus

1. Mathematical Methods

• Calculus of single and multiple variables, Line, surface and volume integrals, Green’s, Stokes’ and Gauss’ theorems
• Linear algebra, matrices, Cayley-Hamilton Theorem, eigenvalue problems
• Fourier series, Fourier and Laplace transforms
• Differential equations: First order differential equation, Second order linear differential equations with constant coefficients
• Special functions (Hermite, Bessel, Laguerre and Legendre polynomials)
• Complex variables: Complex analytic functions, Cauchy’s integral theorem, Taylor and Laurent series, residue theorem
• Probability and statistics.

JAM Chemistry Syllabus

1. Physical Chemistry

• Basic Mathematical Concepts: Functions; maxima and minima; integrals; ordinary differential equations; vectors and matrices; probability.
• Atomic and Molecular Structure: Fundamental particles; Bohr’s theory of hydrogen-like atom; wave-mechanical model of atom; quantum numbers; Schrödinger equation; Heisenberg’s uncertainty principle; shapes of atomic orbitals; molecular orbital theory, hydrogen molecule ion; diatomic molecules; VSEPR theory and shapes of simple molecules.
• Theory of Gases: Equation of state for

JAM Mathematics Syllabus

1. Sequences and Series:

• Convergence of sequences and series
• Tests for convergence
• Power series
• Taylor and Maclaurin series.

2. Differential Calculus:

• Functions of one variable
• Limit, continuity, and differentiability
• Mean value theorem
• Taylor's theorem
• Indeterminate forms
• Maxima and minima.

3. Integral Calculus:

• Fundamental theorem of calculus
• Definite and indefinite integrals

JAM Economics Syllabus

1. Microeconomics

• Consumer theory: Utility maximization; demand analysis; consumer surplus; Slutsky equation.
• Production theory: Production functions; cost minimization; cost curves.
• Market structure: Perfect competition; monopoly; oligopoly; game theory.
• Welfare economics: Pareto optimality; social welfare functions.

2. Macroeconomics

• National income accounting: GDP; GNP; national income; expenditure