Mathematics 1

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(tylko po angielsku) The teaching methods applied to the course include lectures, discussions, 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) are 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.

(tylko po angielsku) Methods to verify the achievement of the assumed learning outcomes include:

- practice class: student activity during lessons, quizzes at the e-learning platform, and one written test (which consists of up to 8 open-ended practical exercises)

- the final exam consists of two parts: the written part has up to 30 closed-ended or open-ended questions, and the oral exam consists of two open-ended questions.

The method of assessment is based on a point system. The sufficient condition to receive the credit for

- the practical class 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.

(tylko po angielsku) Unit 1 Precalculus:

1. Properties of single-variable functions: domain, range, zeroes, monotonicity, extreme points, convexity, concavity, inflection points, the composition of two functions, shifting and reflecting graphs, inverse functions.

2. Limits, continuity and asymptotes.

Unit 2 Differentiation

1. Derivative and its geometrical and physical interpretations.

2. Derivatives of the sum, product and quotient.

3. The chain rule, implicit differentiation, derivatives of inverse functions.

4. Higher-order derivatives.

Unit 3 Application of Differentiation

1. The L’Hospital rule.

2. Testing for monotonicity and local extreme points.

3. Testing for convexity, concavity and inflection points.

4. Polynomial approximation: the Taylor formula.

5. Application of differentiation in economics: marginal functions and elasticities.

Unit 4 Integration and its applications

1. Antiderivatives and indefinite integrals.

2. Techniques of integration: integration by substitution and by parts.

3. Definite integrals and Fundamental Theorem of Calculus.

4. Applications of the integral calculus: areas between two functions, average values of functions, finding total cost and revenue functions, consumer’s and producer’s surplus.

5. Differential equations: separable and linear equations.

Unit 5 Vectors, matrices and linear equations

1. Vectors, dot products, vector length, and angles between vectors.

2. Determinants, area of parallelograms and volume of parallelepipeds.

3. Equations of lines and planes.

4. Matrix operations: multiplication by a scalar, addition, transposition, multiplication; matrix inverses.

5. The rank of a matrix, a matrix in the row echelon form, and the Gaussian elimination.

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

T

T

(tylko po angielsku) The teaching methods applied to the course include lectures, discussions, 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) are 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.

(tylko po angielsku) Methods to verify the achievement of the assumed learning outcomes include:

- practice class: student activity during lessons, quizzes at the e-learning platform, and one written test (which consists of up to 8 open-ended practical exercises)

- the final exam consists of two parts: the written part has up to 30 closed-ended or open-ended questions, and the oral exam consists of two open-ended questions.

The method of assessment is based on a point system. The sufficient condition to receive the credit for

- the practical class 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.

(tylko po angielsku) Unit 1 Precalculus:

1. Properties of single-variable functions: domain, range, zeroes, monotonicity, extreme points, convexity, concavity, inflection points, the composition of two functions, shifting and reflecting graphs, inverse functions.

2. Limits, continuity and asymptotes.

Unit 2 Differentiation

1. Derivative and its geometrical and physical interpretations.

2. Derivatives of the sum, product and quotient.

3. The chain rule, implicit differentiation, derivatives of inverse functions.

4. Higher-order derivatives.

Unit 3 Application of Differentiation

1. The L’Hospital rule.

2. Testing for monotonicity and local extreme points.

3. Testing for convexity, concavity and inflection points.

4. Polynomial approximation: the Taylor formula.

5. Application of differentiation in economics: marginal functions and elasticities.

Unit 4 Integration and its applications

1. Antiderivatives and indefinite integrals.

2. Techniques of integration: integration by substitution and by parts.

3. Definite integrals and Fundamental Theorem of Calculus.

4. Applications of the integral calculus: areas between two functions, average values of functions, finding total cost and revenue functions, consumer’s and producer’s surplus.

5. Differential equations: separable and linear equations.

Unit 5 Vectors, matrices and linear equations

1. Vectors, dot products, vector length, and angles between vectors.

2. Determinants, area of parallelograms and volume of parallelepipeds.

3. Equations of lines and planes.

4. Matrix operations: multiplication by a scalar, addition, transposition, multiplication; matrix inverses.

5. The rank of a matrix, a matrix in the row echelon form, and the Gaussian elimination.

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

T

T

(tylko po angielsku) The teaching methods applied to the course include lectures, discussions, 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) are 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.

(tylko po angielsku) Unit 1 Precalculus:

1. Properties of single-variable functions: domain, range, zeroes, monotonicity, extreme points, convexity, concavity, inflection points, the composition of two functions, shifting and reflecting graphs, inverse functions.

2. Limits, continuity and asymptotes.

Unit 2 Differentiation

1. Derivative and its geometrical and physical interpretations.

2. Derivatives of the sum, product and quotient.

3. The chain rule, implicit differentiation, derivatives of inverse functions.

4. Higher-order derivatives.

Unit 3 Application of Differentiation

1. The L’Hospital rule.

2. Testing for monotonicity and local extreme points.

3. Testing for convexity, concavity and inflection points.

4. Polynomial approximation: the Taylor formula.

5. Application of differentiation in economics: marginal functions and elasticities.

Unit 4 Integration and its applications

1. Antiderivatives and indefinite integrals.

2. Techniques of integration: integration by substitution and by parts.

3. Definite integrals and Fundamental Theorem of Calculus.

4. Applications of the integral calculus: areas between two functions, average values of functions, finding total cost and revenue functions, consumer’s and producer’s surplus.

5. Differential equations: separable and linear equations.

Unit 5 Vectors, matrices and linear equations

1. Vectors, dot products, vector length, and angles between vectors.

2. Determinants, area of parallelograms and volume of parallelepipeds.

3. Equations of lines and planes.

4. Matrix operations: multiplication by a scalar, addition, transposition, multiplication; matrix inverses.

5. The rank of a matrix, a matrix in the row echelon form, and the Gaussian elimination.

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

T

T

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

(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.

(tylko po angielsku) Unit 1 Precalculus:

1. Properties of single-variable functions: domain, range, zeroes, monotonicity, extreme points, convexity, concavity, inflection points, the composition of two functions, shifting and reflecting graphs, inverse functions.

2. Limits, continuity and asymptotes.

Unit 2 Differentiation

1. Derivative and its geometrical and physical interpretations.

2. Derivatives of the sum, product and quotient.

3. The chain rule, implicit differentiation, derivatives of inverse functions.

4. Higher-order derivatives.

Unit 3 Application of Differentiation

1. The L’Hospital rule.

2. Testing for monotonicity and local extreme points.

3. Testing for convexity, concavity and inflection points.

4. Polynomial approximation: the Taylor formula.

5. Application of differentiation in economics: marginal functions and elasticities.

Unit 4 Integration and its applications

1. Antiderivatives and indefinite integrals.

2. Techniques of integration: integration by substitution and by parts.

3. Definite integrals and Fundamental Theorem of Calculus.

4. Applications of the integral calculus: areas between two functions, average values of functions, finding total cost and revenue functions, consumer’s and producer’s surplus.

5. Differential equations: separable and linear equations.

Unit 5 Vectors, matrices and linear equations

1. Vectors, dot products, vector length, and angles between vectors.

2. Determinants, area of parallelograms and volume of parallelepipeds.

3. Equations of lines and planes.

4. Matrix operations: multiplication by a scalar, addition, transposition, multiplication; matrix inverses.

5. The rank of a matrix, a matrix in the row echelon form, and the Gaussian elimination.

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

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) Point system

The assessment of the tutorials(classes) consists of three parts :

- 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,

- two 90 minutes tests, each test consisting of up to 10 open-ended questions or exercises (50 points for each test),

The sufficient condition to receive credit for the classes is to collect at least 50 points.

Final exam:

- the written exam has a form of multiple choice closed questions at the Moodle platform (50 points)

- oral exam (+/-5points).

The final grade is based on points from the written exam, practice classes, and oral exam.

In addition to participation in lectures and classes, students are obliged to conduct their self-studies (110 hours):

- the current study is estimated at 30 hours in the case of lectures and 30 hours for classes,

- preparing for two tests and the final exam: 50 hours.

(tylko po angielsku) Unit 1 Precalculus:

1. Properties of single-variable functions: domain, range, zeroes, monotonicity, extreme points, convexity, concavity, inflection points, the composition of two functions, shifting and reflecting graphs, inverse functions.

2. Limits, continuity and asymptotes.

Unit 2 Differentiation

1. Derivative and its geometrical and physical interpretations.

2. Derivatives of the sum, product and quotient.

3. The chain rule, implicit differentiation, derivatives of inverse functions.

4. Higher-order derivatives.

Unit 3 Application of Differentiation

1. The L’Hospital rule.

2. Testing for monotonicity and local extreme points.

3. Testing for convexity, concavity and inflection points.

4. Polynomial approximation: the Taylor formula.

5. Application of differentiation in economics: marginal functions and elasticities.

Unit 4 Integration and its applications

1. Antiderivatives and indefinite integrals.

2. Techniques of integration: integration by substitution and by parts.

3. Definite integrals and Fundamental Theorem of Calculus.

4. Applications of the integral calculus: areas between two functions, average values of functions, finding total cost and revenue functions, consumer’s and producer’s surplus.

5. Differential equations: separable and linear equations.

Unit 5 Vectors, matrices and linear equations

1. Vectors, dot products, vector length, and angles between vectors.

2. Determinants, area of parallelograms and volume of parallelepipeds.

3. Equations of lines and planes.

4. Matrix operations: multiplication by a scalar, addition, transposition, multiplication; matrix inverses.

5. The rank of a matrix, a matrix in the row echelon form, and the Gaussian elimination.

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