Mathematics for Economists I
| Date | Contents | Problems |
|---|---|---|
| 20.9. | Lecture: Introduction, practical stuff. I. First encounter with functions. Real numbers and variables. Set R, intervals, logical operations, quantifiers, set operations. Seminar: Linear equations and inequalities, equations with absolute value, inequalities with rational functions (=fractions of polynomials). |
Problems1 |
| 27.9. | Lecture: Absolute value of a real number. Powers and power roots, domain of definition, fractional and negative exponent. Seminar: Graphs of simple functions in cartesian coordinates: Linear functions, meaning of the coefficients of a linear function (intercept with the y-axis, slope of the line, increasing/decreasing line). Quadratic functions, meaning of coefficients (convexity, concavity). Calculation and representation of the vertex of the parabola. |
Problems2 |
| 4.10. | Lecture: Exponentials, logarithms. Domain of definition. Seminar: Linear fractional function, center and asymptotes of the hyperbola. Equations with exponentials and logarithms. Domain of definition. |
Problems3 Problems4 |
| 11.10. | Lecture: Limit of a sequence. Seminar: Limit of a sequence - practical computation. |
Problems5 |
| 18.10. | Lecture: Limit of a function. Seminar: Limit of a function - practical computation. |
Problems6 |
| 25.10. | Lecture: Derivative of a function. Seminar: Practical differentiaion. |
Problems7 |
| 1.11. | Lecture: Tangent to the graph. L'Hospital's rule. Seminar: Computing tangents, using the l'Hospital's rule. |
Problems8 Problems9 |
| 8.11. | Week of innovations - no classes. | Scored HW |
| 15.11. | Lecture: Monotony, extremes of a function. Seminar: Course of the function (domain, limits, derivative, monotony, extremes, graph). |
Problems10 |
| 22.11. | Lecture: Preparation for midterm test Seminar: Midterm test |
-- |
| 29.11. | Lecture: Asymptotes, convexity, concavity Seminar: Asymptotes, convexity, concavity |
Problems11 |
| 6.12. | Lecture: Functions of several variables, partial derivatives, stationary points, free and constrained extremes, substitution method Seminar: Partial derivatives, stationary points, free and constrained extremes, substitution method |
Problems12 |
| 13.12. | Lecture: Lagrange multipliers method Seminar: Lagrange multipliers method |
Problems13 |
Midterm test
Sample midterm test available here
Final test
Sample final test available here
Sample final test with solutions available here
Mini-tests on seminars
| Date | Week number | Minitest contents |
|---|---|---|
| 27.9. | 2 | Equations and inequalities with absolute value and with rational functions (=fractions of polynomials) |
| 4.10. | 3 | Graph of a quadratic function (intercepts with axes, vertex) |
| 11.10. | 4 | Equations with exponentials and logarithms |
| 18.10. | 5 | Limit of a sequence |
| 25.10. | 6 | Limit of a function |
| 1.11. | 7 | Derivative of a function |
| 8.11. | 8 | Week of innovations - no classes. |
| 15.11. | 9 | Tangent to the graph |
| 22.11. | 10 | Midterm test - no minitest |
| 29.11. | 11 | Intervals of monotony |
| 6.12. | 12 | Convexity, concavity |
| 13.12. | 13 | Stationary points for functions of two variables |