Math and Science Basics 3 (5 cr)

Objective

The student understands the meaning of the derivative and the integral of a function graphically and algebraically on own fields applications.
The student is able to apply elementary differentiation and integration rules to simple functions and calculate numerical derivatives and integrals. The computational skills of the student are enhanced in mandatory computer labs.
The student is able to use differential and integral calculus in his or hers subsequent studies in physics, chemistry, biology and professional studies, and in subsequent courses in mathematics.
The students become familiar with the physical exploration of thermodynamics phenomena and learn the necessary fundamentals for advanced professional studies. The students develop their studying and problem solving skills required in learning of natural sciences. The students learn the analysis of thermal phenomena in nature based on physical theories.
Student knows the physical laws in the background of the technology systems, and is able to present reasoned solutions to problems.

Content

1. Limits
2. Differential calculus
3. Integral
4. Numerical differentiation and numerical integration
5. Applications of differential and integral calculus in student’s own field of specialization.
6. Computer aided mathematics
7. Thermal expansion
8. Thermal energy
9. Humidity
10. The electric field and its applications
11. DC-circuits

Materials

Mathematics: Tuomenlehto et al. Insinöörin matematiikka, EDITA
Physics: material given by the teacher

Teaching methods

Mathematics: Lessons, excercises, Excel-excercises
Physics: Lessons, exercices

Employer connections

N/A

Exam schedules

Mathematics: 22.4.2024 ( 29.4.2024 ja 8.5.2024)
Physics: to be agreed later

International connections

N/A

Completion alternatives

N/A

Student workload

Physics:
Lessons: 28 h
Exam: 2 h
Homework assignments: 15 h
Self study: 10 h

Mathematics:
Lessons: 39 h
Exam: 3 h
Homework: 25 h
Excel-exercises: 4 h
Self study: 10 h

Content scheduling

Physics:
Basis of heat
Basics of electricity

Mathematics:
Limits and Continuity
Differentiation
Integration

Evaluation scale

0-5

Assessment criteria, satisfactory (1)

The student is able to use numerical methods in differentiation and integration
The student is able to apply the basic rules of differentiation and integration to simple functions. The student is able to interpret the derivative and the integral of a function graphically.
The student takes part in the computer classes and carries out the given exercises acceptably.
Student knows underlying physical laws of thermal expansion and is able to solve simple thermal expansion problems
Student knows qualitatively the concepts of thermal energy and be able to explain the energies of the phase transformation
Student can explain underlying physical laws of concepts of humidity.
Knows basic concepts of electric field and is able to solve simple problems
Knows basic concepts of DC circuit and is able to solve simple problems

Assessment criteria, good (3)

The student is able to apply integrals and differentiating in simple problems of his or hers own field. The student is also able to assess the sensibility and correctness of a result obtained by him or her. The student is able to recognize derivatives and integrals appearing in physical, chemical or biological phenomena.
Able to apply formulas of the thermal energy and calculate the heat of transformations in different phase changes
Able to calculate the humidity conditions in a given situation
Able to apply the theory of electric field to solve problems and can explain how it is applied in the various technology systems
Able to apply the theory of DC circuit to solve problems and can explain how it is applied in the various technology systems

Assessment criteria, excellent (5)

The student is able to model phenomenon in which is deeded derivative and integral calculus.
Able to apply fluently formulas of the thermal energy and critically evaluate results
Able to create and solve mathematical model of electric field and critically evaluate results
Able to create and solve mathematical model of DC circuit and critically evaluate results

Assessment criteria, approved/failed

The student is able to use numerical methods in differentiation and integration
The student is able to apply the basic rules of differentiation and integration to simple functions. The student is able to interpret the derivative and the integral of a function graphically.
The student takes part in the computer classes and carries out the given exercises acceptably.
Student knows underlying physical laws of thermal expansion and is able to solve simple thermal expansion problems
Student knows qualitatively the concepts of thermal energy and be able to explain the energies of the phase transformation
Student can explain underlying physical laws of concepts of humidity.
Knows basic concepts of electric field and is able to solve simple problems
Knows basic concepts of DC circuit and is able to solve simple problems

Assessment methods and criteria

Matematiikka: Tentti 100 %, laskuharjoitukset 10 % (lisäpisteitä)
Fysiikka: Tentti 100 %, kotiehtävistä lisäpisteitä

Kokonaisarvosana=(3*matematiikan arvosana+2*fysiikan arvosana)/5

Qualifications

Math and Science Basics 1 and 2

Qualifications

Math and Science Basics 1 and 2