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...University of waterloo faculty mathematics department applied amath calculus fall lecture notes e r vrscay introduction as written in the preface to course by j wainwright and g tenti this has two main themes vector elds fourier analysis therst theme which includes famous integral theorems associated with names green gauss stokes represents culmination traditional sequence material provides mathematical foundation for continuum mechanics uid dynamics electromagnetic theory phys is importance partial dierential equations second built on remarkable idea that a variety complicated functions can be synthesized from pure sine cosine mate rial signal image processing under development pdes quantum was when these were rst since time wavelets been oered several times instructor afew more remarks about major historically originally developed order un derstand number physical phenomena occurring nature ow electric magnetic gravitation note require concept eld exists space used explain their beha...