GATE Metallurgical Engineering (MT)

Your linear algebra is matrices, determinants, linear systems and eigenvalues, so the Linear Algebra chapter is yours and the vector-space chapter is not. Your Calculus heading ends with Fourier series, so read the first section of the Transforms chapter and stop there — this paper names no transform, Laplace or Fourier. There is no complex-variables heading at all, so the Complex Variables chapter is not on your list. Your vector calculus (gradient, divergence, curl, line, surface and volume integrals, Gauss) is the Vector Calculus chapter. Your Differential Equations heading opens with first-order ODEs, linear and non-linear, which are in the borrowed first-order chapter; the constant-coefficient higher-order ODEs, Cauchy’s and Euler’s equations and the one-dimensional heat and wave equations are in the Differential Equations chapter, whose Laplace-transform section goes beyond your list. Four of your sub-items are in a chapter written for this paper alone, because no shared chapter teaches them: sequences and series with tests for convergence, the analysis of experimental data, the linear least squares method, and numerical differentiation by Taylor series. All seven of this paper’s discipline sections are written too — Metallurgical Thermodynamics, Transport Phenomena and Rate Processes, Mineral Processing and Extractive Metallurgy, Physical Metallurgy, Mechanical Behaviour of Materials, Manufacturing Processes, and Materials Science and Non-Metallic Materials — so the whole MT paper is covered and the full 65-question paper is available in the mock.