∑GATE DA Atlas
GATE DA / Section 3

Calculus and Optimization

Functions of a single variable, limits and continuity, differentiability and the mean value theorems, Taylor series, maxima and minima, single-variable optimisation (including gradient descent and Newton's method), and the integration you need for probability.

5 topics49 practice questions≈ 8 marksPractise this section →

Calculus has carried about 8 marks in both GATE DA papers analysed so far (third-party analyses). The syllabus is deliberately narrow — single-variable functions only — so the questions are usually quick if you know the standard limits, the derivative rules, the Maclaurin series by heart and the first/second derivative tests.

What the syllabus lists: functions of a single variable, limit, continuity and differentiability, Taylor series, maxima and minima, optimisation involving a single variable.

Topics

Read in order — later topics build on earlier ones
01Functions of a Single Variable and LimitsFunctions, domain and range, composition and inverses, even/odd and monotone functions, the meaning of a limit, one-sided limits, limit laws, the standard limits you must memorise, indeterminate forms, L'Hôpital's rule, the squeeze theorem, limits at infinity and asymptotes.0/10 solved02Continuity, Differentiability and the Mean Value TheoremsContinuity at a point and on an interval, the kinds of discontinuity, the intermediate and extreme value theorems, the derivative as a limit, differentiability vs continuity, derivative rules (product, quotient, chain, implicit, logarithmic), derivatives of the functions used in ML, Rolle's theorem and the mean value theorem.0/10 solved03Taylor and Maclaurin SeriesBuilding polynomial approximations from derivatives, the Taylor and Maclaurin formulas, the standard series you must know, manipulating series (substitution, multiplication, differentiation, integration), the remainder and error bounds, radius of convergence, and how Taylor expansions power limits, numerical approximation and optimisation algorithms.0/9 solved04Maxima, Minima and Single-Variable OptimizationCritical points, the first, second and higher-order derivative tests, global extrema on closed intervals, concavity, convexity and inflection points, why convexity guarantees global optima, applied optimisation problems, and the algorithms of data science — gradient descent (with learning-rate analysis), Newton's method and bracketing methods — plus maximum likelihood as an optimisation problem.0/11 solved05Integration Essentials (for Probability and ML)A supporting topic not listed separately in the syllabus but needed everywhere in it — antiderivatives and the fundamental theorem of calculus, substitution and integration by parts, definite integrals as areas and expectations, improper integrals and convergence, the Gamma function and the Gaussian integral, and numerical integration.0/9 solved