Index
Definitions and theorems of Mathematics for Economics
The 103 definitions and 85 theorems of the theory of Mathematics for Economics, in the order of the topics. Each entry links to its box in the theory page.
Real functions and economic models
- Definition Sets and operations
- Definition Intervals
- Definition Real function of a real variable
- Definition Graph of a function
- Definition Increasing and decreasing functions
- Definition Injective function
- Definition Inverse function
- Definition Composite function
- Definition Linear function and slope
- Theorem Line through two points
- Theorem Vertex of the parabola
- Definition Exponential function
- Definition Logarithm
- Definition Natural domain
- Definition Demand and supply functions
- Definition Market equilibrium
- Definition Cost, revenue and profit
- Definition Break-even point
- Definition Average cost
Sequences, progressions and series
- Definition Sequence
- Definition Monotonic and bounded sequences
- Definition Arithmetic progression
- Theorem Sum of the terms of an arithmetic progression
- Definition Geometric progression
- Theorem Sum of the terms of a geometric progression
- Definition Limit of a sequence
- Theorem Rules for computing limits
- Theorem Monotone sequence theorem
- Theorem Limit of the geometric sequence
- Definition Numerical series
- Theorem Necessary condition for convergence
- Theorem Geometric series
- Theorem The number e
Limits and continuity
- Definition Finite limit at a point
- Definition Right-hand limit and left-hand limit
- Definition Infinite limits and limits at infinity
- Theorem Rules for computing limits
- Theorem Standard limits
- Theorem Comparison of infinities
- Definition Vertical, horizontal and oblique asymptotes
- Definition Continuous function
- Definition Points of discontinuity
- Theorem Intermediate zero theorem
- Theorem Intermediate value theorem
- Theorem Weierstrass theorem
Derivatives, marginal functions and elasticity
- Definition Derivative at a point
- Theorem Tangent line
- Theorem Differentiability and continuity
- Theorem Derivatives of elementary functions
- Theorem Differentiation rules
- Definition Higher-order derivatives
- Definition Marginal cost, revenue and profit
- Definition Elasticity
- Theorem Elasticity and revenue
- Theorem Fermat's theorem
- Theorem Rolle's and Lagrange's theorems
- Theorem Sign of the derivative and monotonicity
- Theorem De l'Hôpital's rule
- Theorem Linear approximation
Curve sketching and optimization
- Definition Absolute maximum and minimum
- Definition Relative maximum and minimum
- Theorem First derivative test
- Definition Convex function and concave function
- Theorem Sign of the second derivative and concavity
- Definition Inflection point
- Theorem Second derivative and inflections
- Theorem Second derivative test
- Definition Even and odd functions
- Theorem Absolute maximum and minimum on a closed interval
- Theorem Functions with a single stationary point
- Theorem Conditions for maximum profit
- Theorem Minimum average cost
Integral calculus and economic applications
- Definition Antiderivative
- Theorem Antiderivatives of the same function
- Definition Indefinite integral
- Theorem Basic integrals
- Theorem Basic integrals in composite form
- Theorem Integration by substitution
- Theorem Integration by parts
- Theorem Rational functions with a first-degree denominator
- Theorem Rational functions with a second-degree denominator
- Definition Riemann sums
- Definition Definite integral
- Theorem Properties of the definite integral
- Theorem Integral mean value theorem
- Definition Integral function
- Theorem Fundamental theorem of integral calculus
- Theorem Fundamental formula of integral calculus
- Theorem Area between two curves
- Definition Improper integral on a half-line
- Theorem Improper integral of powers
- Theorem Improper integral of the exponential
- Theorem Total cost from marginal cost
- Definition Average value of a quantity
- Definition Consumer and producer surplus
- Definition Present value of a continuous flow
Compounding, annuities and amortization
- Definition Principal, interest and accumulated value
- Definition Simple interest
- Definition Compound interest
- Theorem Comparison of the two regimes
- Definition Present value
- Definition Discount and discount rate
- Theorem Unknown time and rate
- Definition Equivalent rates
- Definition Nominal rate convertible k times
- Theorem Continuous compounding
- Definition Financial equivalence
- Theorem Independence of the valuation date
- Definition Average due date
- Theorem Average due date with commercial discount
- Definition Annuity
- Theorem Annuity immediate
- Theorem Annuity due
- Theorem Deferred annuity
- Theorem Perpetuity
- Definition Amortization schedule
- Theorem Outstanding balance
- Theorem French amortization
- Theorem Italian amortization
- Definition Net present value
- Definition Internal rate of return
- Theorem Existence and uniqueness of the IRR
Matrices, determinants and linear systems
- Definition Matrix
- Definition Sum and product by a scalar
- Definition Row-by-column product
- Theorem Properties of the product
- Definition Transpose matrix
- Definition Square matrix and identity matrix
- Definition Diagonal and triangular matrices
- Definition Symmetric matrix
- Definition Determinant of a 2 × 2 matrix
- Definition Complementary minor and cofactor
- Definition Determinant of a square matrix
- Theorem Sarrus's rule
- Theorem Laplace expansion
- Theorem Determinant of a triangular matrix
- Theorem Properties of the determinant
- Theorem Binet's theorem
- Definition Inverse matrix
- Theorem Existence and computation of the inverse
- Theorem Properties of the inverse
- Definition Minors and rank
- Theorem Bordered minors theorem
- Definition Echelon matrix
- Theorem Reduction to echelon form
- Definition Linear system in matrix form
- Theorem Cramer's rule
- Theorem Gaussian elimination method
- Theorem Rouché-Capelli theorem
- Definition Market equilibrium with two goods
- Definition Leontief input-output model
Functions of two variables
- Definition The plane ℝ²
- Definition Distance between two points
- Definition Circular neighborhood
- Definition Interior and boundary points
- Definition Open, closed and bounded sets
- Definition Function of two variables
- Definition Natural domain
- Definition Graph of a function of two variables
- Definition Level curves
- Definition Limit and continuity
- Theorem Weierstrass theorem in two variables
- Definition Partial derivatives
- Definition Gradient
- Definition Second partial derivatives
- Theorem Schwarz's theorem
- Definition Hessian matrix
- Definition Differentiable function
- Definition Tangent plane
- Theorem Differential and linear approximation
- Theorem Derivative along a curve
- Theorem Gradient and level curves
- Definition Cobb-Douglas function
- Definition Marginal productivities
- Definition Isoquants and indifference curves
- Theorem Marginal rate of substitution
- Definition Homogeneous functions
- Definition Returns to scale
- Theorem Euler's theorem
Unconstrained and constrained extrema
- Definition Relative and absolute maxima and minima
- Theorem Fermat's theorem in two variables
- Definition Stationary point
- Definition Saddle point
- Theorem Hessian test
- Definition Constrained extremum
- Theorem Lagrange multiplier theorem
- Definition Lagrangian function
- Definition Consumer's problem