Differential and Integral Calculus (3cr)

Objective

After completing the course, the student is able to define the derivative and integral of a single-variable function, perform differentiation and integration for the most common mathematical functions, and apply these concepts to professional subjects and practical problem-solving in working-life contexts.

Content

Derivative:

- geometric interpretation
- differentiation rules
- second derivative
- curvature
- spline and Bézier curves
- position–velocity–acceleration relationships
- extrema
- Taylor polynomial

Integral:
- definite integral
- integral function
- area and volume
- arc length
- acceleration–velocity–position relationships

Qualifications

Algebra and geometry, Vectors and matrices or similar knowledge

Assessment criteria, satisfactory (1)

The student knows and understands the basic concepts and methods of calculus to the extent that he/she is able to solve problems given in the course material independently but utilizing the material directly.

Assessment criteria, good (3)

The student is familiar with the concepts and methods of calculus, and is able to apply them to different types of problems given in the course material and also outside of it. The student is able to combine the accumulated knowledge and skills with previous experiences in the subject.

Assessment criteria, excellent (5)

The student is able to describe the concepts and methods of calculus flawlessly, and he/she is able to apply them to a variety of different problems that can be out of scope of the course material. The student has demonstrated creativity and innovation, and is able to find new meanings when applying what they have learned

Materials

To be announced at the beginning of the course