GATE Petroleum Engineering (PE)

Your linear algebra is matrix algebra, linear systems and eigenvalues, so the Linear Algebra chapter is yours and the vector-space chapter is not. Your Calculus heading runs from single-variable calculus through partial and total derivatives, maxima and minima and the whole of vector calculus (gradient, divergence, curl, identities, directional derivatives, line, surface and volume integrals, Stokes, Gauss and Green), so the borrowed calculus chapters, Multivariable Calculus and Vector Calculus are yours; it names no Fourier series, so the Transforms chapter is not on your list. Careful with complex variables: your heading is only "complex number; polar form of complex number; triangle inequality", which is the borrowed complex-numbers chapter, not the analytic-functions chapter. Your Differential Equations heading opens with first-order equations, linear and nonlinear, which are in the borrowed first-order chapter; the higher-order, Cauchy-Euler, initial- and boundary-value and Laplace-transform items are in the Differential Equations chapter. The sampling theorems your Probability heading names are in the Probability and Statistics chapter. Four of your sub-items are in a chapter written for this paper alone, because no shared chapter teaches them at your paper’s depth: the Taylor series of a function of one variable, the numerical solution of linear algebraic equations (Gauss elimination, Jacobi and Gauss-Seidel), linear regression analysis, and the solution of the one-dimensional diffusivity and Laplace equations. All ten of this paper’s discipline sections are written too — Petroleum Exploration, Drilling Technology, Reservoir Engineering, Production Operations, Offshore Drilling and Production, Formation Evaluation, Well Testing, Health Safety and Environment, Enhanced Oil Recovery, and Latest Trends — so the whole PE paper is covered and the full 65-question paper is available in the mock.