Math and Science Basics 2 (5 cr)

Objective

Differential calculus
- On completion of the course the student can use the derivative when estimating the rate of change of a function and when studying the graph of a function.
Integral calculus
- On completion of the course the student knows the concept of a definite integral and is able to estimate the integral numerically.
- The student is able to form integral functions and to use them when calculating the value of an integral.
- The student is able to apply integrals in geometric and physical problems.

Physics Lab projects
On completion of the course the student can
- work safely in a laboratory
- carry out physical measurements
- identify sources of measurement uncertainty
- analyse measured data
- estimate the reliability and the meaning of the final results.

Content

1. Differential calculus
2. The derivative
3. Differential and error estimation
4. Extreme values
5. Higher derivatives
6. Newton’s method
7. Integral calculus
8. The concept of an integral
9. Calculating the approximation of an integral by using numerical methods
10. Calculating the integral with an integral function
11. The method of small differentials.

Physics Lab projects
- working in the physics lab in small groups
- analysing results.

Differential and Integral Calculus:
- manipulating expressions
- knowledge of functions.

Evaluation scale

0-5

Assessment criteria, satisfactory (1)

Differential calculus
- The student knows the definition of the derivative.
- The student can use basic rules of differentiation.
- The student understands an extreme value of a function and is able to find extreme values by means of the derivative.

Integral calculus
The student is able to form an approximate value of an integral as a sum.
The student is able to write down the expression of a definite integral and to calculate its value.
The student knows the definition of an integral function and is able to form integral functions in simple cases. The student is able to use integral functions when calculating the value of an integral.

Physics Lab projects
The student can
- carry out simple physical measurements
- calculate results with error margins.

Assessment criteria, good (3)

Differential calculus
In addition to the skills described above, the student is able to use the rules of differentiation fluently. The student can use the derivative when calculating the rate of change of a function and when finding the extreme values of a function.

Integral calculus
In addition to the skills described above, the student can use integrals when calculating various lengths, areas and volumes. The student can calculate moments and second moments in simple cases.

Physics Lab projects
The student can
- carry out physical measurements
- identify sources of measurement error
- work with measurement data
- estimate the reliability and the meaning of the final results.

Assessment criteria, excellent (5)

Differential and Integral Calculus
In addition to the skills listed above, the student can combine knowledge acquired during the course and apply it in a versatile manner.

Physics Lab projects
The student can
- carry out demanding physical measurements
- identify many different sources of measurement error
- work with measurement data
- estimate the reliability and the meaning of the final results.

Assessment criteria, approved/failed

Differential calculus
- The student knows the definition of the derivative.
- The student can use basic rules of differentiation.
- The student understands an extreme value of a function and is able to find extreme values by means of the derivative.

Integral calculus
The student is able to form an approximate value of an integral as a sum.
The student is able to write down the expression of a definite integral and to calculate its value.
The student knows the definition of an integral function and is able to form integral functions in simple cases. The student is able to use integral functions when calculating the value of an integral.

Physics Lab projects
The student can
- carry out simple physical measurements
- calculate results with error margins.

Qualifications

Basics of Mathematics
Fundamentals of Physics