Math3 Derivative and Integral (3 cr)

Evaluation scale

0-5

Content scheduling

Themes will be discussed in the following order (one week / theme):
1. Definition of the Derivative
2. Symbolic Differentiation
3. Applications of the Derivative
4. Definition of the Integral and Symbolic Integration
5. The Fundamental Theorem of Calculus
6. Applications of Integration

Objective

The object of the course
During this course you will learn the concepts needed to study continuous change and dynamic phenomena. With differential calculus you can study instantaneous rates of change and the slopes of curves. With integral calculus you can study accumulation of quantities and areas bounded by curves. During this course you learn how to use these concepts in applications.

Course competences

EUR-ACE: Knowledge and understanding 
You have the knowledge and understanding of mathematics and other basic sciences underlying your engineering specialisation, at a level necessary to achieve the other programme learning outcomes.

The learning objectives of the course
After completing this course you know the meaning of derivative and integral as tools for modeling dynamic phenomena. You know how to differentiate and integrate. You know how to use the derivative and integral in applications.

Content

In this course, you will learn to master the tools needed to study phenomena of change, such as the concepts of derivatives and integrals. You will understand the meaning of these concepts and be able to apply them in practice. You will learn to derive and integrate and solve applied problems using these methods. This course will give you a strong foundation in applying mathematical methods to engineering problems.

The derivative and its different interpretations. Rules of differentiation. Using differentiation in optimization problems and other applications involving the derivative such as estimation of error. The definite integral. Rules of integration. The applications of the integral. Using technology in calculations.

Location and time

This course is implemented 23.1.2023 - 2.4.2023 instead of the previously announced 9.1.2023 - 26.2.2023.

Lectures will be streamed online.

Guided exercises will be held at campus or online depending on the implementation of your degree programme.

Materials

Written material, video material and exercises prepared by teacher.

Appropriate textbooks in Finnish:
- Alestalo, S., Lehtola, P., Nieminen, T. & Rantakaulio, A. 2011. Tekninen matematiikka 1. 1. uusittu painos. Tampere: Tammertekniikka.
- Henttonen, J., Peltomäki, J. & Uusitalo, S. 2003. Tekniikan matematiikka: 1. Helsinki: Edita.

Teaching methods

Lectures, guided exercises, independent work, exams

Exam schedules

Exam to pass the course will be done independently during the course in e-exam studio or as a more traditional supervised exam during week 8, depending on the implementation of your degree programme.

The grade-determining exam will take place during week 8.

First resit 22.3.2023
Second resit 12.4.2023

Completion alternatives

Face-to-face and online implementations are available in spring and in autumn. It is also possible to attend the course online during summer 2023.

Student workload

For six weeks:

Lectures 2 * 45 min

Exercises (depending on programme): 3 * 45 min or 2 * 45 min


Additionally:

Exams approximately 4 h

Independent work approximately 55 - 60 h

Assessment criteria, satisfactory (1)

Sufficient 1
You know the concept of the derivative as the rate of change and as the slope of the tangent. Yo understand how to apply the derivative in optimization problems. You can differentiate and integrate polynomials without technology. You know the concept of the integral as accumulation of quantities and as area under a curve. You know the relation between integral and derivative.

Satisfactory 2
You have achieved the desired goals (look at the criteria of grade 1). You know many of the concepts and methods and how to apply them in familiar situations but your reasoning is sometimes deficient or you make mistakes in calculations.

Assessment criteria, good (3)

Good 3
You have achieved the desired goals(look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in familiar situations showing often the ability to reason completely and calculate flawlessly

Very good 4
You have achieved the desired goals (look at the criteria of grade 1). You know most of the concepts and methods and how to apply them in new situations showing in most cases the ability to reason completely and calculate flawlessly.

Assessment criteria, excellent (5)

You have achieved the desired goals (look at the criteria of grade 1). You know all the concepts and methods and how to apply them in new situations showing always the ability to combine things, reason completely and calculate flawlessly.

Qualifications

You know the concept of a limit value. You can work with polynomial, exponential, logarithmic and trigonometric functions.

Further information

Assessment is based on two-part final exam and exercises.