The main objects of the course are the differential and integral calculation of real functions of a real variable. Analytically: Introduction to real numbers. Sequences and Series. Limits and continuity of functions. Inverse trigonometric functions. Hyperbolic functions. Differential calculus (Taylor’s theorem). Integral calculus (definitions, integration techniques). Applications of definite integral. General integral. Differential equations of first and second order with constant coefficients.
- Teacher: Ιωάννης Γάσπαρης
ECTS : 5
Language : el
Learning Outcomes : Upon successful completion of the course, the student will be able to: • have understood the concept of convergence of a sequence of real numbers. • have understood the concept of convergence of a series of real numbers. • be able to apply appropriate criteria and evaluate whether a sequence or a series of numbers converges. In some cases, they can calculate the exact value of the limit or sum. • calculate limiting values of real functions. • have understood the concept of derivative. • be able to calculate derivatives of composite functions. • be able to apply Differential Calculus methods to optimization problems. • be able to develop a function into a power series and calculate the interval and speed of convergence. • have understood the concept of the definite and indefinite Riemann integral. • have understood the basic theorems of Differential and Integral Calculus. • be able to apply a variety of integration techniques and calculate the indefinite integral of almost any elementary function. • be able to calculate the derivative and the indefinite integral of a power series. • have understood the concept of a generalized integral. • be able to apply appropriate criteria and decide on the convergence of a generalized integral. In some cases, they can calculate the exact value of this integral. • be able to correlate the generalized integral with an appropriate series of numbers. • be able to correlate the derivative and the integral with concepts of Geometry and Physics. • be able to calculate the area of a planar region. The volume of a solid of revolution. The length of a curve. The area of a surface of revolution. • be able to apply the theory to calculate values of physical quantities such as mass, moment of inertia, charge distribution.