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Mathematical concepts I


  • Vectors
    • Why vectors?
    • Scalar product
    • Component representation in cartesian coordinate system
    • Rotation of coordinate systems
    • Vector product
  • Calculus
    • Why do we need differentiation and integration?
    • Basic techniques of differentiation and integration
    • Taylor series
    • Differentiation of vectors
    • Gradient
    • Line integral
    • Multidimensional integrals
  • Differential equations
    • Typology of differential equations
    • Homogeneous first-order differential equations
    • Homogeneous second-order differential equations
      • Linear differential equations with constant coefficients
      • First integral
    • Inhomogeneous linear differential equation
    • Green functions
  • Linear algebra
    • Dyadic product
    • Determinants
    • Systems of linear equations
    • Eigenvalue problems
    • Linear systems of differential equations