Differential and Integral CalculusLaajuus (3 ECTS)
Course unit code: TG00AB45
General information
- Credits
- 3 ECTS
Objective
The student can explain what is meant by a limit of a function, and determine limits of functions. The student can explain what is meant by a derivative of a function, both geometrically and algebraically. The student can differentiate functions numerically and analytically, and by using mathematical software. The student can solve equations and systems of equations numerically using derivative (or gradient) based methods. The student can explain geometrically what is meant by a definite integral of a function. The student can explain the concept of an integral function and recognizes the link between definite integrals and integral functions. The student can integrate functions numerically and analytically, and by using mathematical software. The student can apply derivatives and integrals in physics, chemistry and environmental engineering. The student understands the concept of a gradient and knows its typical applications. The student can use mathematical software, e.g. Excel and Matlab, in applications of differential and integral calculus.
Content
1. The concept of a limit of a function, and limits of typical functions appearing in science and in environmental engineering.
2. Derivative, numerical differentiation the use of differentiation rules.
3. Newton’s method for equations.
4. The integral function and the concept of an integral and its relation to the integral function.
5. Numerical integration methods.
6. Applications of derivatives and integrals in science and environmental engineering.
7. The concept of a gradient.
8 .Using mathematical software in differential and integral calculus.
Qualifications
Equations and Matrices
Vectors and Analytical Geometry
Assessment criteria, satisfactory (1)
1. The concept of a limit of a function, and limits of typical functions appearing in science and in environmental engineering.
2. Derivative, numerical differentiation the use of differentiation rules.
3. Newton’s method for equations.
4. The integral function and the concept of an integral and its relation to the integral function.
5. Numerical integration methods.
6. Applications of derivatives and integrals in science and environmental engineering.
7. The concept of a gradient.
8. Using mathematical software in differential and integral calculus.
Assessment criteria, good (3)
1. The student can find out limits of rational functions.
2. The student can explain the derivative of a function in algebraic terms and can approximate derivatives using forward or symmetric difference quotient.
3. The student can use Newton’s method for solving simple equations that don’t have analytical solutions.
4. The student can explain the integral of a function as a limit. The student can determine integral functions of typical functions appearing in environmental engineering.
5. The student can apply several numerical integration techniques.
6. The student can use derivatives and integrals in simple engineering or science problems, e.g. in optimization.
7. --
8. The student shows ability to use mathematical software in calculus problems.
Assessment criteria, excellent (5)
1. --
2. The student knows techniques for differentiating data that are given in tabular form, e.g. spectra.
3. The student can use Newton’s method for solving equations that don’t have analytical solutions
4. --
5. The student can integrate data that are given in tabular form, e.g. spectra.
6. The student can use derivatives and integrals engineering problems, e.g. in in problems of related rates.
7. The can explain how gradients can be used in optimization of functions of several variables.
8. The student shows ability write programs in Matlab or in some other Mathematical software.