Introduction to Calculus
Course code
old course code
Course title in Estonian
Diferentsiaal- ja integraalarvutuse algkursus
Course title in English
Introduction to Calculus
ECTS credits
Assessment form
lecturer of 2023/2024 Spring semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
lecturer of 2024/2025 Autumn semester
Not opened for teaching. Click the study programme link below to see the nominal division schedule.
Course aims
To offer to the students an overview of terms and notions of diferential and integral calculus, which are useful for those who choose to teach mathematics at the first and the secondary school level.
Brief description of the course
The set of real numbers. The concept of a function. Function composition. Inverse function. Graph sketching using simple transformations. The exponential and logarithmic function. Trigonometric functions. Sequences. Limit of a sequences. Limit of a function, its properties and conditions for existence. Continuous functions, their properties. Functions continuous on a closed interval. Derivative of a function, its properties, interpretations and conditions for existence. Differentiability and differential of a function. Higher-order derivatives and differentials. Mean value theorems in differential calculus, their applications to the finding of limits and treating of functions. Applications in geometry. Indefinite integral, its properties, changing the variable of integration. Definite integral, its properties, geometric interpretation. Newton-Leibniz formula. Measurable sets on the plane, their areas. Geometric and physical applications of definite integrals.
Attending lectures is a prerequisite of the learning process.
Learning outcomes in the course
Upon completing the course the student:
- knows main notions of differential and integral calculus;
- is familiar with the main properties, relations, theorems and some simplest proof methods of this course;
- is able to use and apply methods taught in a subject in order to solve exercises.
lekt Anna Šeletski