Sampson Michael. Introduction to Mathematical Economics. Part 1

5th edition. — Loglinear Publishing, 2015. — 274 p.Guides economics students in the use of calculus and linear algebra, up to and including multivariate calculus and Lagrangians. Some exposure to calculus is helpful but not necessary. Suitable for a one-semester course, self-study, or as a reference.The mathematical method:
Definitions.
Difference between 'equal' and 'identical'
Implication.
Negation.
Proof by contradiction.
Necessary versus sufficient conditions.
Necessary AND sufficient conditions.
'Or' and 'And'
The quantifiers
Proof by cont-example.
Proof by induction.
Functions.Univariative calculus:
Derivatives.
Second derivatives.
Maximization and minimization.
Econometrics.
Ordinal and cardinal properties.
Exponential functions and logarithms.
Technical issues.Matrix algebra:
Matrix additions and obstructions.
Matrix multiplication.
The transpose of the matrix.
The inverse of the matrix.
The determinant of the matrix.
The trace of the matrix.
Higher dimensional space.
Solving systems of equations.
Eigenvalues and eigenvectors.
Linear and quadratic functions in R(n+1).
Idempotent matrices.Multivariate calculus:
Function of many variables.
Partial derivatives.
Second-order partial derivatives.
Unconstrained optimization.
Quasi-concavity and Quasi-convexity.
Constrained optimization.
Econometrics.