UNSWMathematics Society
        (Higher) Several Variable Calculus
              Vector Calculus
           Presented by: Kabir Agrawal
               Term 1, 2020
   Vector Calculus                                                                        Fourier Series
    Table of contents
         1  Vector Calculus
               Vector Calculus Terminology and notation
               Scalar Integrals
               Vector Integrals
               Vector Integral Theorems
               Orthogonal Curvilinear Co-Ordinates
         2  Fourier Series
               Preliminaries
               Fourier Series
               Function Convergence
                                     Kabir Agrawal     MATH2011/2111    2 of 59
   Vector Calculus                                                                                             Fourier Series
                                                                                  Vector Calculus
                                              Kabir Agrawal         MATH2011/2111        3 of 59
   Vector Calculus                                                                                             Fourier Series
     Vector Fields I
          Definition 1
          Ascalar field/function is a function that maps a point to a value.
          Avector field is a function that maps a point to a vector.
          Example 1
              1   f (x,y) = x2 − y2
              2   F(x,y) = (2x −y,x +2y)
              3   F(x,y,z) = (−x,−y,−z)
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