GATE Environmental Science and Engineering (ES)

Your Section 1 is called Mathematics Foundation, and it is shorter at the top and longer at the bottom than an engineering paper’s. Your Linear Algebra is determinants and matrices, linear systems and eigenvalues, so the Linear Algebra chapter is yours; the direct solution of a linear system by Gauss elimination and LU is in it. Your Calculus heading is single-variable calculus, partial and total derivatives, and first-order equations only — so the borrowed calculus chapters, the partial-derivative part of Multivariable Calculus and the borrowed first-order chapter are yours, and Vector Calculus, the second-order Differential Equations chapter, Complex Variables and Transforms are not on your list. Root finding, the trapezoidal and Simpson rules and the single- and multi-step ODE methods are in Numerical Methods; probability, Bayes’ theorem, the distributions and central tendency are in Probability and Statistics. Two chapters are written for this paper alone, because your syllabus names things no shared chapter teaches: tests for convergence, the Taylor series of one variable, volume by the definite integral, the exact and Bernoulli equations, approximation and errors, Newton and Lagrange interpolation, least squares and numerical differentiation in the first; dispersion, skewness and kurtosis, risk and reliability, correlation, single and multiple regression and the t, F and chi-square tests in the second. One gap, disclosed: your Numerical Methods heading names the numerical solution of linear equations, and the iterative Jacobi and Gauss–Seidel schemes are taught in no chapter you receive; elimination is. All eight of this paper’s discipline sections are written too — Environmental Chemistry, Environmental Microbiology, Water Resources and Environmental Hydraulics, Water & Wastewater Treatment and Management, Air and Noise Pollution, Solid and Hazardous Waste Management, Global and Regional Environmental Issues, and Environmental Management and Sustainable Development — so the whole ES paper is covered and the full 65-question paper is available in the mock.