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If there is a ditch between calculus and advanced mathematics, and elementary mathematics, but in fact, once you have the basic principles limit and calculus, calculus and advanced mathematics is not difficult.
I put the syllabus developed as follows:
1 limit, find the limit is actually very simple, still use multiplication and division addition and subtraction elementary mathematics, Sanjiang teacher can be exemplified.
2 and the intuitive notion physical meaning of the derivative and the integral, the derivative is the slope for the curve, the derivative is a point slope, which is a limit, can be determined by the method of Limit.
It is to compute the integral curved edge shape and the area between the x-axis function, can specify the interval [x1, x2] determined to shape the area between the curved edge x1 ~ x2.
Triangle area in the physical sense, the most common example is uniformly accelerated motion, uniformly accelerated motion v = at, a proportional function, the function curve is a straight line, and this line is composed of the x-axis distance, i.e. distance integrating the speed v at time t.
3 Derivative find a quadratic function, with ⊿y / ⊿x, ⊿x -> 0, the request ⊿y / ⊿x way to limit the derivative.
Integrating the proportional function, a method using the triangle area seeking to integrate,
Acceleration of the movement and change process with a curved edge shape requirements to area integrating, by small rectangles + method to limit the number of columns integrating, provided a = kt, seeking v, s.
4 Fundamental Theorem of Calculus Newton - Leibniz formula
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With differential, derivative operation rules and the derivative formulas,
With differential, derivative, integral calculation rules and formulas quadrature.
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Stygian boat people apricot second home full scientific theoretical system of the Galaxy Academy of three Jiang Fangshi