# Mathematics 2

## Syllabus

1. Functions of more variables. Definition; limits; partial derivatives; Taylor's series.

2. Application of functions of more variables. Cobb-Douglas production function; marginal cost and marginal productivity; competitive and complementary products.

3. Maxima and minima. Hessian and its leading principal minors; critical point; saddle point; convex set.

4. Lagrange multipliers. Lagrange function; Lagrange multpliers; examples; budget constraint.

5. Kuhn-Tucker conditions. Kuhn-Tucker conditions; necessary conditions and sufficient conditions; examples.

6. Linear programming. Definition; graphical solution; types of solution; transformation of a problem to a canonical form.

7. Simplex algorithm. Initial simplex table; basic variables; pivots; optimality test; convex combination; general form of simplex algorithm; artifical variables; 2-phase method; degeneracy.

8. Application of linear programming. Planning a production; a diet problem; a work scheduling problem; a capital budgeting problem; blending problem; production process problems; dnamic problems.

9. Duality. A dual problem; finding a solution by solving a dual problem; dual simplex algorithm; shadow prices.

10. Sensitivity analysis. Notation; basic formulae; changing an objective function coefficient; changing a coefficient in the right-hand side; changing a coefficient in a nonbasic variable column.

11. Integer linear programming. Cutting plane algorithm; branch-and-bound method.

12. Repetition.

13. Repetition.

Keywords: Functions of more variables; partial derivatives; maxima and minima; Lagrange multipliers; Kuhn-Tucker conditions; linear programming; simplex algorithm; duality; sensitivity analysis; integer linear programming.