29 docs tagged with "calculus"

Forward- and reverse-mode automatic differentiation through computational graphs, illustrated with JAX transformations.

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 SymPy guide to symbolic differentiation, integration, limits, series expansion, and differential equations.

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.

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.

How derivatives support critical-point analysis, monotonicity, concavity, implicit differentiation, and Newton's method.

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.

The gradient as local direction and rate of change, with applications to multidimensional optimization and regression.

The one-variable gradient-descent update, learning-rate trade-offs, local minima, and a compact implementation example.

Extending gradient descent to two parameters through partial derivatives, vector updates, and convergence considerations.

Convergence tests for improper integrals and practical midpoint, trapezoid, and Simpson approximation rules.

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.

An introduction to multivariable functions, coordinate slices, partial derivatives, and tangent-plane construction.

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

A calculus-based optimization workflow connecting objective functions, extrema, constraints, and applied modeling examples.

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

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