- supremum and infimum of a set of real numbers
- limit of a sequence
- limit of a function
- continuity of a function at a point
- derivative of a function at a point

- open ball
- open set
- closed set
- convergence of a sequence in
**R**^{n} - function continuous on a set
- compact set
- maximum/minimum of a function on a set
- local maximum/minimum of a function with respect to a set
- partial derivative
- function of class
*C*^{1} - convex set
- concave function
- antiderivative

- the Euclidean metric
- interior point of a set
- interior of a set
- boundary point of a set
- boundary of a set
- closure of a set
- bounded set
- a function continuous with respect to a set
- a function continuous at a point
- strict maximum/minimum of a function on a set
- strict local maximum/minimum of a function with respect to a set
- local maximum/minimum
- strict local maximum/minimum
- limit of a function at a point
- tangent hyperplane
- gradient of a function
- critical point of a function
- partial derivative of the second order
- function of class
*C*and^{k}*C*^{∞} - convex function
- strictly concave/convex function
- quasiconcave/quasiconvex function
- strictly quasiconcave/quasiconvex function
- rational function
- Riemann integral

- properties of the Euclidean metric
- properties of open sets
- characterisation of convergence of sequences in
**R**^{n} - characterisation of closed sets
- properties of closed sets
- boundedness of the closure
- continuity and level sets
- necessary condition for a local extremum
- continuity of functions of class
*C*^{1} - super-level sets of concave functions
- extremum of a concave function of class
*C*^{1} - uniqueness of an extremum
- super-level sets of quasi-concave functions
- structure of the set ∫f(x)dx
- linearity of antiderivative
- integration by substitution
- integration by parts

- Heine theorem
- characterisation of compact sets in
**R**^{n}(proof in**R**^{2}) - on attaining extrema of functions
- weak Lagrange theorem
- tangent hyperplane theorem
- implicit function theorem
- Lagrange multipliers theorem in
**R**^{2} - integral with variable upper limit

- properties of the interior and the closure
- continuity and arithmetic operations
- continuity and composition of functions
- derivative of a compound function
- interchanging of partial derivatives
- implicit functions theorem
- Lagrange multipliers theorem with more constraints
- relation of concavity and continuity
- characterisation of concave functions of class
*C*^{1} - existence of an antiderivative
- existence of the Riemann integral
- Riemann integral over subintervals
- linearity of the Riemann integral
- Riemann integral and inequalities
- Newton-Leibniz formula