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Calculus & Optimization

Calculus and Optimization in GATE DA is about functions of a single variable: limits, continuity, derivatives, Taylor series and finding maxima and minima. These lessons work through each idea with examples, and check every limit, derivative and optimum numerically with small programs.

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1Single-Variable Calculus

  1. Functions, Limits, Continuity and DifferentiabilityFunctions of a single variable, limits and one-sided limits, standard limits, indeterminate forms and L'Hôpital's rule, continuity and types of discontinuity, and differentiability (with |x| as the classic counterexample), for GATE DA.
  2. Derivatives, Mean Value Theorem and Taylor SeriesRules of differentiation, the chain rule, derivatives of common functions, higher derivatives, Rolle's theorem and the mean value theorem, and Taylor and Maclaurin series with the error of a Taylor approximation, for GATE DA.

2Optimization

  1. Maxima and MinimaLocal and global extrema, critical points, the first and second derivative tests, finding the absolute maximum and minimum on a closed interval, convex functions and why their local minima are global, for GATE DA.
  2. Single-Variable Optimization MethodsSolving optimization word problems, gradient descent in one dimension and the effect of the learning rate, Newton's method for minimisation and root finding, and bisection and golden-section search, for GATE DA.

3GATE Practice

  1. Calculus and Optimization GATE Practice SetMixed GATE DA style questions on limits, continuity, differentiability, derivatives, Taylor series, maxima and minima, convexity and numerical optimization, with answers and explanations.