diff --git a/source/calculus/notations.rst b/source/calculus/notations.rst index b603eab..45cf572 100644 --- a/source/calculus/notations.rst +++ b/source/calculus/notations.rst @@ -5,17 +5,27 @@ Differentiation Notations Leibniz's Notation ------------------- -The derivative of a function :math:`f` at :math:`x` is given -by :math:`\lim\limits_{h\to0} \frac{f(x+h)-f(x)}{h}`. - +The derivative of a function :math:`f` at :math:`x` is given by :math:`\lim\limits_{h\to0} \frac{f(x+h)-f(x)}{h}`. The Leibniz's notation expresses the derivative of :math:`f` as :math:`\frac{dy}{dx}` with :math:`y=f(x)`. - More details `here `__. .. note:: The following :math:`\frac{dx}{dt}` means :math:`x` is a function of :math:`t` such as :math:`x=f(t)`. See explanations `here `__. +:math:`\frac{d}{dx}` is an operator not a quotient! +Although it behaves like a quotient. In fact it is a limit: + +.. math:: + + \lim\limits_{h\to0} \frac{f(x+h)-f(x)}{h} \ne \frac{\lim\limits_{h\to0} \left(f(x+h)-f(x)\right)}{\lim\limits_{h\to0} h} + +See, we cannot express this limit-of-a-quotient as a-quotient-of-the-limits, then the derivative is not a quotient. +More details `here `__. + +Can we perform operation without relying on this assumption? +The answer is yes! Using the chain rule. + Lagrange's Notation ------------------- Also cal prime notation diff --git a/source/electronics/maxwell/gauss.rst b/source/electronics/maxwell/gauss.rst new file mode 100644 index 0000000..14804bf --- /dev/null +++ b/source/electronics/maxwell/gauss.rst @@ -0,0 +1,2 @@ +Gauss's Law +============ diff --git a/source/electronics/maxwell/index.rst b/source/electronics/maxwell/index.rst new file mode 100644 index 0000000..6a824f8 --- /dev/null +++ b/source/electronics/maxwell/index.rst @@ -0,0 +1,8 @@ +The Maxwell's Equations +======================================== + +.. toctree:: + :maxdepth: 2 + :caption: First equation + + gauss.rst diff --git a/source/index.rst b/source/index.rst index 1b6d9a8..a9f0728 100644 --- a/source/index.rst +++ b/source/index.rst @@ -33,6 +33,7 @@ Welcome to ScienceNotes's documentation! :numbered: :caption: Electronics + electronics/maxwell/index.rst electronics/metrics.rst electronics/components.rst electronics/kirchhoff.rst