27 docs tagged with "mathematics"

A compact derivative table for powers, exponentials, logarithms, trigonometric functions, and chain-rule variants.

Core differentiation rules for sums, products, quotients, compositions, exponentials, logarithms, and inverse functions.

A map from limits and derivatives through integration, gradients, optimization, automatic differentiation, and symbolic computation.

A map from limits and derivatives to integration, gradients, and optimization.

A compact reference for standard limits of powers, exponentials, logarithms, and polynomials at infinity.

Pointwise and interval continuity, one-sided endpoint conditions, composition, and the intermediate value theorem.

A foundation map for convex sets, convex functions, duality, and optimization problems with global guarantees.

The derivative as a limit, tangent slope, instantaneous rate of change, and motion-related quantity.

A map of derivatives from their limit definition to rules, critical points, and curve analysis.

A foundation map for logic, proof, counting, discrete structures, and probability in computer science.

A decision-oriented guide to substitution, algebraic simplification, one-sided analysis, asymptotics, and L'Hôpital's rule.

The two parts of the Fundamental Theorem connecting accumulation functions, derivatives, and definite integrals.

A foundation map for measuring uncertainty, information, compression limits, and distributional difference.

The definite integral as accumulated signed area and the indefinite integral as a family of antiderivatives.

A reference for linearity, interval properties, inequalities, and standard antiderivatives of common functions.

A map of antiderivatives, definite integrals, the fundamental theorem, and standard integration techniques.

Worked techniques for integration by parts, trigonometric substitution, and partial-fraction decomposition.

Formal and intuitive definitions for finite limits, one-sided limits, limits at infinity, and infinite limits.

Algebraic laws for combining existing finite limits, including the conditions required for quotients, powers, and roots.

Definitions, one-sided limits, continuity, limit laws, and practical evaluation techniques.

A foundation map for vectors, linear transformations, matrix factorization, and data-oriented applications.

Mathematical foundations for reasoning, modeling, computer science, and machine learning.

A foundation map for approximation, error, stability, and reliable computation with finite precision.

A bridge from calculus-based extrema to objective functions and machine-learning loss.

A practical guide to substitution and trigonometric identities for transforming integrals into standard forms.

A map from probability models and random variables to sampling, estimation, and statistical decisions.

How matching left- and right-hand limits determine whether a two-sided limit exists.