Mathematics 2

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(tylko po angielsku) The teaching methods applied to the course include lecture, discussion, solving exercises and problems, presentations, and e-learning via Moodle.

(tylko po angielsku) Based on the point system.

Practice class:

- activity during classes and quizzes at the e-learning platform(+/-10 points),

- attendance at all classes and lectures is obligatory (two unjustified absences are acceptable), the third and subsequent absence from the lessons = 2 points are taken away,

- homework: a set of problems for each class.

- TEST. The test consists of 10 open-ended practical exercises (50 points).

The final exam has a form of up to 30 closed-ended and open-ended questions (50 points).

The sufficient condition to receive the credit for

- the practical classes (tutorials) is to collect at least 25 points (TEST, activity, attendance)

- the course is to pass the practical classes and collect at least 50 points from the final exam and tutorials.

Make-up exams:

You can retake the test twice during the winter exam session.

In addition to participation in lectures and classes, students are obliged to conduct their self-studies (55 hours):

- the current study is estimated at 15 hours in the case of lectures and 15 hours for classes,

- preparing for two tests and the final exam: 25 hours.

(tylko po angielsku) 1. Rank of matrix, the matrix in the row echelon form, and Gaussian elimination.

2. Linear systems, solutions to square and rectangular systems, basic solutions.

3. Quadratic forms and matric definiteness.

4. Functions of two variables: domain, graphs, level curves and contour plots.

5. Partial derivatives, gradient, the Hessian matrix.

6. Approximation formula: tangent planes, quadratic approximation.

7. Optimization problems. Least-squares problem. Second derivative test for minima, maxima and saddle points.

8. Optimization with constraints. The Lagrange multipliers and constrained differentials.

9. Application of differential calculus in economics

T

T

(tylko po angielsku) The teaching methods applied to the course include lecture, discussion, solving exercises and problems, presentations, and e-learning via Moodle.

(tylko po angielsku) Based on the point system.

Practice class:

- activity during classes and quizzes at the e-learning platform(+/-10 points),

- attendance at all classes and lectures is obligatory (two unjustified absences are acceptable), the third and subsequent absence from the lessons = 2 points are taken away,

- homework: a set of problems for each class.

- TEST. The test consists of 10 open-ended practical exercises (50 points).

The final exam has a form of up to 30 closed-ended and open-ended questions (50 points).

The sufficient condition to receive the credit for

- the practical classes (tutorials) is to collect at least 25 points (TEST, activity, attendance)

- the course is to pass the practical classes and collect at least 50 points from the final exam and tutorials.

Make-up exams:

You can retake the test twice during the winter exam session.

In addition to participation in lectures and classes, students are obliged to conduct their self-studies (55 hours):

- the current study is estimated at 15 hours in the case of lectures and 15 hours for classes,

- preparing for two tests and the final exam: 25 hours.

(tylko po angielsku) 1. Rank of matrix, the matrix in the row echelon form, and Gaussian elimination.

2. Linear systems, solutions to square and rectangular systems, basic solutions.

3. Quadratic forms and matric definiteness.

4. Functions of two variables: domain, graphs, level curves and contour plots.

5. Partial derivatives, gradient, the Hessian matrix.

6. Approximation formula: tangent planes, quadratic approximation.

7. Optimization problems. Least-squares problem. Second derivative test for minima, maxima and saddle points.

8. Optimization with constraints. The Lagrange multipliers and constrained differentials.

9. Application of differential calculus in economics

T

T

T

(tylko po angielsku) The teaching methods applied to the course include lecture, discussion, solving exercises and problems, presentations, and e-learning via Moodle.

(tylko po angielsku) Based on the point system.

Practice class:

- activity during classes and quizzes at the e-learning platform(+/-10 points),

- attendance at all classes and lectures is obligatory (two unjustified absences are acceptable), the third and subsequent absence from the lessons = 2 points are taken away,

- homework: a set of problems for each class.

- TEST. The test consists of 10 open-ended practical exercises (50 points).

The final exam has a form of up to 30 closed-ended and open-ended questions (50 points).

The sufficient condition to receive the credit for

- the practical classes (tutorials) is to collect at least 25 points (TEST, activity, attendance)

- the course is to pass the practical classes and collect at least 50 points from the final exam and tutorials.

Make-up exams:

You can retake the test twice during the winter exam session.

In addition to participation in lectures and classes, students are obliged to conduct their self-studies (55 hours):

- the current study is estimated at 15 hours in the case of lectures and 15 hours for classes,

- preparing for two tests and the final exam: 25 hours.

(tylko po angielsku) 1. Rank of matrix, the matrix in the row echelon form, and Gaussian elimination.

2. Linear systems, solutions to square and rectangular systems, basic solutions.

3. Quadratic forms and matric definiteness.

4. Functions of two variables: domain, graphs, level curves and contour plots.

5. Partial derivatives, gradient, the Hessian matrix.

6. Approximation formula: tangent planes, quadratic approximation.

7. Optimization problems. Least-squares problem. Second derivative test for minima, maxima and saddle points.

8. Optimization with constraints. The Lagrange multipliers and constrained differentials.

9. Application of differential calculus in economics

T

T

(tylko po angielsku) The teaching methods applied to the course include lecture, discussion, solving exercises and problems, presentations, and e-learning via Moodle.

(tylko po angielsku) Based on the point system.

Practice class:

- activity during classes and quizzes at the e-learning platform(+/-10 points),

- attendance at all classes and lectures is obligatory (two unjustified absences are acceptable), the third and subsequent absence from the lessons = 2 points are taken away,

- homework: a set of problems for each class.

- TEST. The test consists of 10 open-ended practical exercises (50 points).

The final exam has a form of up to 30 closed-ended and open-ended questions (50 points).

The sufficient condition to receive the credit for

- the practical classes (tutorials) is to collect at least 25 points (TEST, activity, attendance)

- the course is to pass the practical classes and collect at least 50 points from the final exam and tutorials.

Make-up exams:

You can retake the test twice during the winter exam session.

In addition to participation in lectures and classes, students are obliged to conduct their self-studies (55 hours):

- the current study is estimated at 15 hours in the case of lectures and 15 hours for classes,

- preparing for two tests and the final exam: 25 hours.

(tylko po angielsku) 1. Rank of matrix, the matrix in the row echelon form, and Gaussian elimination.

2. Linear systems, solutions to square and rectangular systems, basic solutions.

3. Quadratic forms and matric definiteness.

4. Functions of two variables: domain, graphs, level curves and contour plots.

5. Partial derivatives, gradient, the Hessian matrix.

6. Approximation formula: tangent planes, quadratic approximation.

7. Optimization problems. Least-squares problem. Second derivative test for minima, maxima and saddle points.

8. Optimization with constraints. The Lagrange multipliers and constrained differentials.

9. Application of differential calculus in economics

T

T

(tylko po angielsku) The teaching methods applied to the course include lecture, discussion, solving exercises and problems, presentations.

(tylko po angielsku) Based on the point system.

Practice class:

- activity during classes and quizzes at the e-learning platform(+/-10 points),

- attendance at all classes and lectures is obligatory (two unjustified absences are acceptable), the third and subsequent absence from the lessons = 2 points are taken away,

- homework: a set of problems for each class.

- TEST. The test consists of 10 open-ended practical exercises (50 points).

The final exam has a form of up to 30 closed-ended and open-ended questions (50 points).

The sufficient condition to receive the credit for

- the practical classes (tutorials) is to collect at least 25 points (TEST, activity, attendance)

- the course is to pass the practical classes and collect at least 50 points from the final exam and tutorials.

Make-up exams:

You can retake the test twice during the winter exam session.

In addition to participation in lectures and classes, students are obliged to conduct their self-studies (55 hours):

- the current study is estimated at 15 hours in the case of lectures and 15 hours for classes,

- preparing for two tests and the final exam: 25 hours.

(tylko po angielsku) Functions of two variables, tangent approximation and optimization

1. Functions of two variables: domain, graphs, level curves and contour plots.

2. Partial derivatives, gradient, the Hessian matrix.

3. Approximation formula: tangent planes.

4. Optimization problems. Least-squares problem. Second derivative test for minima, maxima and saddle points.

5. Optimization with constraints. The Lagrange multipliers and constrained differentials.

6. Application of differential calculus in economics.

T

T

(tylko po angielsku) The teaching methods applied to the course include lecture, discussion, solving exercises and problems, presentations.

(tylko po angielsku) Based on the point system.

Practice class:

- activity during classes and quizzes at the e-learning platform(+/-10 points),

- attendance at all classes and lectures is obligatory (two unjustified absences are acceptable), the third and subsequent absence from the lessons = 2 points are taken away,

- homework: a set of problems for each class.

- TEST. The test consists of 10 open-ended practical exercises (50 points).

The final exam has a form of up to 30 closed-ended and open-ended questions (50 points).

The sufficient condition to receive the credit for

- the practical classes (tutorials) is to collect at least 25 points (TEST, activity, attendance)

- the course is to pass the practical classes and collect at least 50 points from the final exam and tutorials.

Make-up exams:

You can retake the test twice during the winter exam session.

In addition to participation in lectures and classes, students are obliged to conduct their self-studies (55 hours):

- the current study is estimated at 15 hours in the case of lectures and 15 hours for classes,

- preparing for two tests and the final exam: 25 hours.

(tylko po angielsku) 1. Rank of matrix, the matrix in the row echelon form, and Gaussian elimination.

2. Linear systems, solutions to square and rectangular systems, basic solutions.

3. Quadratic forms and matric definiteness.

4. Functions of two variables: domain, graphs, level curves and contour plots.

5. Partial derivatives, gradient, the Hessian matrix.

6. Approximation formula: tangent planes, quadratic approximation.

7. Optimization problems. Least-squares problem. Second derivative test for minima, maxima and saddle points.

8. Optimization with constraints. The Lagrange multipliers and constrained differentials.

9. Application of differential calculus in economics