Mathematics for Engineers 2Laajuus (5 cr)

Objectives

After completing this course student is able to

- understand the concept of a function and recognizes the characteristic properties of different basic functions
- solve equations involving basic functions, recognize graphs of basic functions, perform basic calculations with matrices and apply them in practical problems
- apply the concepts of limit and derivative when solving practical problems,
- determine the derivative using graphical, and construct error estimates using the differential method
- to understand basics of integral calculus

Content

Functions: polynomial, rational, power, exponential, logarithmic, trigonometric); graphs of basic functions, equations. Limit, Derivative, Applications of Derivative, Error Estimation with Differential. Integral Function

Assessment criteria, satisfactory (1-2)

Has a basic understanding of the concept of a function and recognizes the properties of basic functions. Can solve simple equations involving basic functions and recognizes their graphs. Understands elementary matrix calculations and can apply them to straightforward practical problems. Grasps the basic concepts of limit and derivative and can apply them in simple practical problems. Knows the basics of integral calculus at a fundamental level.

Assessment criteria, good (3-4)

Demonstrates a clear understanding of the concept of a function and can identify the characteristic properties of different basic functions. Can solve equations involving basic functions, accurately recognizes graphs of basic functions, and performs calculations with matrices in more complex practical problems. Effectively applies the concepts of limit and derivative in solving practical problems, determines the derivative using graphical methods, and constructs error estimates using the differential method. Has a solid understanding of the fundamentals of integral calculus.

Assessment criteria, excellent (5)

Exhibits a comprehensive and in-depth understanding of functions and recognizes the characteristic properties of various basic functions. Solves complex equations involving basic functions, recognizes and interprets graphs of basic functions, and performs advanced calculations with matrices, applying them to solve sophisticated practical problems. Demonstrates a thorough understanding of limit and derivative concepts, applies them effectively in practical problem-solving, accurately determines derivatives using graphical methods, and constructs precise error estimates using the differential method. Possesses a solid understanding of integral calculus and applies it in a range of contexts.