32 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.

Derive binary channel capacities from mutual information, calculate a repetition code's rate and residual error, and understand the conditions behind the coding theorem and Gaussian capacity formulas.

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

Solve a two-variable quadratic program, check its active constraints and KKT multipliers, and certify optimality with a primal–dual gap.

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.

Work through eigenvalues and rectangular SVD, reconstruct a matrix, calculate low-rank error, and connect singular values to PCA, identifiability, and conditioning.

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

Use runnable examples of binary representation, rounding, cancellation and summation to understand conditioning, backward stability and justified tolerances.

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.

Compare Euler, RK4, implicit and symplectic integration with runnable decay and oscillator examples, and check step size, error and long-term energy behavior.

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.