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KEF/BMS


Matematický seminář sticky icon

Course: Seminar in Mathematics

Department/Abbreviation: KEF/BMS

Year: 2016 2017

Guarantee: 'Mgr. Jan Říha, Ph.D.'

Annotation:

  • Introduction to vector algebra
    • Scalar and vector physical quantities, their properties
    • Definition of a vector, vector space
    • Arithmetical and geometrical definition of a vector
    • Linear combinations of vectors, linearly-dependent and independent system vectors, bases and dimensions of vector space
    • Operation with vectors - scalar, vector and mixed product of vectors
    • Transformations of vector coordinates in curvilinear systems of coordinates used in physics
    • Use of vector calculus in physics


  • Introduction to tensor calculus
    • Anisotropic media, tensor physical quantities, their properties
    • Definition of a tensor
    • Algebraic operations with tensors
    • Transformations of tensor components
    • Tensors in physics


  • Differential calculus of a function with one variable
    • Real function of one real variable, basic types of functions, their properties
    • Limit of a function, basic rules for calculation of function limits
    • Differentiation of a function, its physical and geometrical interpretation
    • Differential of a function, its physical and geometrical interpretation
    • Differentiations of higher orders, physical interpretation of the second differentiation


  • Differential calculus of a function with two and more variables
    • Real function of more real variables
    • Partial differentiation of the first order and higher orders
    • Total differential of the first order and higher orders


  • Integral calculus of a function with one variable
    • Primitive function, indefinite integral
    • Basic methods and rules of integration
    • Definite integral and its calculation
    • Use of definite integral in geometry and physics


  • Introduction to solving of differential equations
    • Definition of differential equation
    • Solving of basic types of the first-order differential equations - equations with separable variables, homogeneous equations, linear equations
    • Solving of the second-order differential equations with constant coefficients


  • Integral calculus of a function with two and more variables
    • Double integral and its calculation
    • Triple integral and its calculation

Course review:

  • Introduction to vector algebra
    • Scalar and vector physical quantities, their properties
    • Definition of a vector, vector space
    • Arithmetical and geometrical definition of a vector
    • Linear combinations of vectors, linearly-dependent and independent system vectors, bases and dimensions of vector space
    • Operation with vectors - scalar, vector and mixed product of vectors
    • Transformations of vector coordinates in curvilinear systems of coordinates used in physics
    • Use of vector calculus in physics


  • Introduction to tensor calculus
    • Anisotropic media, tensor physical quantities, their properties
    • Definition of a tensor
    • Algebraic operations with tensors
    • Transformations of tensor components
    • Tensors in physics


  • Differential calculus of a function with one variable
    • Real function of one real variable, basic types of functions, their properties
    • Limit of a function, basic rules for calculation of function limits
    • Differentiation of a function, its physical and geometrical interpretation
    • Differential of a function, its physical and geometrical interpretation
    • Differentiations of higher orders, physical interpretation of the second differentiation


  • Differential calculus of a function with two and more variables
    • Real function of more real variables
    • Partial differentiation of the first order and higher orders
    • Total differential of the first order and higher orders


  • Integral calculus of a function with one variable
    • Primitive function, indefinite integral
    • Basic methods and rules of integration
    • Definite integral and its calculation
    • Use of definite integral in geometry and physics


  • Introduction to solving of differential equations
    • Definition of differential equation
    • Solving of basic types of the first-order differential equations - equations with separable variables, homogeneous equations, linear equations
    • Solving of the second-order differential equations with constant coefficients


  • Integral calculus of a function with two and more variables
    • Double integral and its calculation
    • Triple integral and its calculation

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