GATE Naval Architecture and Marine Engineering (NM)

Your mathematics is two paragraphs with no sub-headings, and it is close to the whole engineering list. Determinants, matrices, linear systems and eigenvalues are the Linear Algebra chapter; "functions" and "definite and indefinite integrals" are the borrowed calculus chapters; chain rules, partial and directional derivatives and the whole of vector calculus with Stokes, Gauss and Green are Multivariable Calculus and Vector Calculus. Your differential equations are "linear, non-linear, first and higher order, ordinary and partial", with separation of variables: the borrowed first-order chapter and the Differential Equations chapter, which also carries your Laplace transformation. Analytic functions and complex analysis are named, so the Complex Variables chapter is yours in full. Your syllabus names Fourier series but no Fourier or z-transform, so read the first section of the Transforms chapter and stop there. Numerical integration and probability and statistics are in the shared chapters. Two of your sub-items are in a chapter written for this paper alone, because no shared chapter teaches them: numerical methods for differentiation (difference formulas, their errors and Richardson extrapolation) and the non-linear first-order equations — exact equations with integrating factors, and the Bernoulli equation. All four of this paper’s discipline sections are written too, two chapters each — Applied Mechanics and Structures, Fluid Mechanics and Marine Hydrodynamics, Naval Architecture and Ocean Engineering, and Thermodynamics and Marine Engineering — so the whole NM paper is covered and the full 65-question paper is available in the mock.