ΠΕΡΙΓΡΑΜΜΑ ΜΑΘΗΜΑΤΟΣ

The course aims to introduce students to the concepts of Linear Algebra, Calculus (differential and integral calculus, differential equations)and Vector Calculus. Also, to the analysis and solution of applications within the scope of their specialty.

Educational objectives and expected skills

Upon the successful completion of this course a student will be able to:

• Implement the vector calculus to solve problems and make operations with vectors.
• Understand the meaning of the matrixes and be able to make matrix operations.
• Calculates determinants and know their properties.
• Calculates the inverse matrix.
• Recognizes a system of linear equations and describe all of its solutions.
• Recognizes the augmented matrix of a system.
• Uses operations between rows of a matrix in order to convert it to reduced echelon matrix.
• Knows of methods of solving linear systems.
• knows basic notations and definitions of a function.
• knows the basic operations of functions.
• Finds the limit of a function.
• Has understood the concept of continuity of a function and can prove that a function is continuous.
• Has understood the concept of derivative.
• Finds the derivative function.
• knows basic theorems of differential calculus.
• Studies the monotony of a function and find max and min values.
• Studies the curvature and find the turning points.
• Has understood the concept of the integral (indefinite, definite).
• Uses the fundamental theorem of integral calculus.
• Calculates integrals.
• Has understood the concept of the differential equation.
• Solves differential equations first order.
• knows basic notations and definitions of functions several variables.
• Finds the partial derivative of a function of several variables.
• Understand and use the mathematical dimensions that contain the problems of their specialty, to further studies program.

• Search, analysis and synthesis of data and information.
• Autonomous work.
• Teamwork.
• Production of free, creative and inductive thinking.

Elements of Vector Calculus:

• Definitions, vectors properties, applications.

Elements of Linear Algebra:

• Matrices (definitions, properties and operations). Determinant of a matrix. Linear systems.

Calculus:

• Functions (one real variable)
  Definition, function categories, periodic function, graphics, Limit and continuity of function: definitions, basic theorems, applications. Derivative of a function: definition, lateral derivatives, geometric interpretation, higher order derivatives, differential function, derivation rules, and theorems of the mean: applications in the study of functions. Indefinite integral: definition, integration rules, basic integration methods, approximate calculation using the formula of Taylor. Definite integral: definition, properties, theorems of average value, calculation of generalized integrals, applications in agricultural technology and oenology.
• Differential Equations
  Definition, form and types of differential equations, first order differential equation.
• Functions of several variables
  Definitions, limits, continuity, partial derivative and basic theorems on them, total differential, the concept of vector function, applications.