Study Guide

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and mean values and square mean values of functions
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Evaluation scale

H-5

Qualifications

Precalculus course or skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and mean values and square mean values of functions
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Materials

1. Calculus (3rd edition), Fred Safier, SCHAUM’S outlines.
2. Engineering Mathematics (6th edition), K.A. Stroud [MACMILLAN PRESS LTD]
3. Formula book: Technical formulas

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding to use the derivatives to analyze functions, use differentials to approximate changes and errors, solve separable and linear first order differential equations, use integrals to calculate e.g. areas and mean values and square mean values of functions
and use relevant mathematical denotation correctly, moreover the students can use relevant mathematical denotation correctly.
The students will team up for a project work and writing reports on some current and relevant aspect of math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Student workload

Classroom activities: Classroom activities participation: 50 h
Homework: Working on homework sets 1-6: 30 h
Project work: Research, presentation material, presentation: 20h
Final exam: Preparing for the final exam : 25 h

Content scheduling

• Limits
• The derivative
• Differentials
• Antiderivatives and the definite integral
• Applications of differentiation and integration
• On differential equations

Further information

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in Optima.

Evaluation scale

H-5

Assessment methods and criteria

Homework sets 1-6: 30 %: Total of thirty homework exercises based on reading material and classroom notes: diagnostic/formative self / teacher evaluation
in connection with each homework set return session.
Project work, reports, presentations: 40 % : Each outcome of the project work is assessed independently (assessment criteria is specified in Optima): peer feedback summative teacher feedback at the end of the course.
Final exam: 30 %: A written exam (1,5 hrs) on specified material: Summative teacher evaluation at the end of the course

Assessment criteria, fail (0)

Fail in the final exam and not doing the assignments.

Assessment criteria, satisfactory (1-2)

Collect (50--60) points in the exam and doing 50% of the assignments.

Assessment criteria, good (3-4)

Collect (70--80) points in the exam and doing at least 75% of the assignments

Assessment criteria, excellent (5)

Collect (90--100) points in the exam and doing at least 90% of the assignments

Qualifications

Precalculus course or skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and mean values and square mean values of functions
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Content scheduling

•Limits
•The derivative
•Differentials
•Antiderivatives and the definite integral
•Applications of differentiation and integration
•On differential equations
Contact hours on weeks 2-17, c. 4h per week

Evaluation scale

H-5

Qualifications

Precalculus course or skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and mean values and square mean values of functions
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Evaluation scale

H-5

Qualifications

Precalculus course or skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and mean values and square mean values of functions
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Content scheduling

•Limits
•The derivative
•Differentials
•Antiderivatives and the definite integral
•Applications of differentiation and integration
•On differential equations
Contact hours on weeks 2-17, c. 4h per week

Evaluation scale

H-5

Qualifications

Precalculus course or skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and mean values and square mean values of functions
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Materials

1. Calculus (3rd edition), Fred Safier, SCHAUM’S outlines.
2. Engineering Mathematics (6th edition), K.A. Stroud [MACMILLAN PRESS LTD]
3. Formula book: Technical formulas

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding to use the derivatives to analyze functions, use differentials to approximate changes and errors, solve separable and linear first order differential equations, use integrals to calculate e.g. areas and mean values and square mean values of functions
and use relevant mathematical denotation correctly, moreover the students can use relevant mathematical denotation correctly.
The students will team up for a project work and writing reports on some current and relevant aspect of math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Student workload

Classroom activities: Classroom activities participation: 50 h
Homework: Working on homework sets 1-6: 30 h
Project work: Research, presentation material, presentation: 20h
Final exam: Preparing for the final exam : 25 h

Content scheduling

• Limits
• The derivative
• Differentials
• Antiderivatives and the definite integral
• Applications of differentiation and integration
• On differential equations

Further information

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in Optima.

Evaluation scale

H-5

Assessment methods and criteria

Homework sets 1-6: 30 %: Total of thirty homework exercises based on reading material and classroom notes: diagnostic/formative self / teacher evaluation
in connection with each homework set return session.
Project work, reports, presentations: 40 % : Each outcome of the project work is assessed independently (assessment criteria is specified in Optima): peer feedback summative teacher feedback at the end of the course.
Final exam: 30 %: A written exam (1,5 hrs) on specified material: Summative teacher evaluation at the end of the course

Assessment criteria, fail (0)

Fail in the final exam and not doing the assignments.

Assessment criteria, satisfactory (1-2)

Collect (50--60) points in the exam and doing 50% of the assignments.

Assessment criteria, good (3-4)

Collect (70--80) points in the exam and doing at least 75% of the assignments

Assessment criteria, excellent (5)

Collect (90--100) points in the exam and doing at least 90% of the assignments

Qualifications

Precalculus course or skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and mean values and square mean values of functions
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Materials

1. Calculus (3rd edition), Fred Safier, SCHAUM’S outlines.
2. Engineering Mathematics (6th edition), K.A. Stroud [MACMILLAN PRESS LTD]
3. Formula book: Technical formulas

Teaching methods

Teacher-directed classroom activities, group work and independent work; project work, reports, task-based (homework)

International connections

The contents of the course give understanding to use the derivatives to analyze functions, use differentials to approximate changes and errors, solve separable and linear first order differential equations, use integrals to calculate e.g. areas and mean values and square mean values of functions
and use relevant mathematical denotation correctly, moreover the students can use relevant mathematical denotation correctly.
The students will team up for a project work and writing reports on some current and relevant aspect of math, which gives everyone an opportunity to understand the topic; all students will develop their mathematical proficiency.
Task-based assessment supports learning and is continuous throughout the course. Studying in an international group develops students’ ability to intercultural communication and multicultural collaboration.

Student workload

Classroom activities: Classroom activities participation: 50 h
Homework: Working on homework sets 1-6: 30 h
Project work: Research, presentation material, presentation: 20h
Final exam: Preparing for the final exam : 25 h

Content scheduling

• Limits
• The derivative
• Differentials
• Antiderivatives and the definite integral
• Applications of differentiation and integration
• On differential equations

Further information

All practical information on timetables, project work, grading etc., as well as links to web materials are provided in Optima.

Evaluation scale

H-5

Assessment methods and criteria

Homework sets 1-6: 30 %: Total of thirty homework exercises based on reading material and classroom notes: diagnostic/formative self / teacher evaluation
in connection with each homework set return session.
Project work, reports, presentations: 40 % : Each outcome of the project work is assessed independently (assessment criteria is specified in Optima): peer feedback summative teacher feedback at the end of the course.
Final exam: 30 %: A written exam (1,5 hrs) on specified material: Summative teacher evaluation at the end of the course

Assessment criteria, fail (0)

Fail in the final exam and not doing the assignments.

Assessment criteria, satisfactory (1-2)

Collect (50--60) points in the exam and doing 50% of the assignments.

Assessment criteria, good (3-4)

Collect (70--80) points in the exam and doing at least 75% of the assignments

Assessment criteria, excellent (5)

Collect (90--100) points in the exam and doing at least 90% of the assignments

Qualifications

Precalculus course or skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and mean values and square mean values of functions
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Evaluation scale

H-5

Qualifications

Precalculus course or skills

Objective

After completing the course the student can
- use derivatives to analyze functions
- use differentials to approximate changes and errors
- use integrals to calculate e.g. areas and mean values and square mean values of functions
- use relevant mathematical denotation correctly

Content

- Limits
- The derivative
- Differentials
- Antiderivatives and the definite integral
- Applications of differentiation and integration
- On differential equations

Evaluation scale

H-5

Qualifications

Precalculus course or skills