Advanced Mathematics notes (2)

1) differential: dy =. DX, meaning: For the Function Y = f (x), the incremental dx in X is enough hours, and the incremental dy in the function value y can be approximately equal to. DX, where A is a constant irrelevant to DX.
2) f (x) is a sufficient and necessary condition for the function f (x) to be able to be exported at x0;
3) derivative, also known as derivative: derivative formula dy/dx = f' (x) => differential formula DY = f' (x) dx
4) geometric significance of differentiation: Local Linearity of nonlinear functions (replacing curve segments with linear segments ).
5) The differential formula can be easily introduced based on the derivation formula;
6) Differential Form immutability.
7) ferma's theorem: in plain words, the derivative of the maximum or minimum values within the range defined by X is 0;
8) on-site and critical point;
9) Rolle Theorem (Rolle); Laplace mean value theorem (differential mean value definition F (B)-f (a) = f (k) (B-);
10) finite Increment Theorem DY = f' (x + ADX) * dx (0 <A <1); Mean Value Theorem of kernel;
11) Law of lobida: under certain conditions, the limit at which the ratio of the two functions is located can be converted to the limit at which the ratio of the derivative of the two functions is located. (a method is provided to calculate the limit value of a function by downgrading the denominator ). [uncertain limit)
12) n-order Taylor formula, n-th Taylor Polynomial, Laplace remainder, pealo type remainder, and mclaulin Formula
13) use the reciprocal size of the function to determine the monotonicity of the curve function; increase greater than 0 and decrease less than zero.
14) determine the concave and convex of the curve function based on the size of the second derivative. If the value is greater than 0 concave, the value is smaller than 0 convex;
15) Extreme Values, maximum values, and minimum values;
16) curvature, curvature radius: P = 1/K
17) indefinite points: indefinite points, integral functions, product functions, product expressions, and integral variables;
18) Basic integral table

19) the nature of indefinite points:
A)The sum of the functions is equal to the sum of the indefinite credits of each function;
B) When an indefinite integral is obtained, the constant factor not zero in the product function can be mentioned outside the integral number;
20) Indefinite Integral Method: direct method, substitution method, Division integral method; Rational Function integral; query integral table method;
21) definite points; Newton-levenitz formula; basic calculus formula;

22: Application of points determination:
A) area of a plane image;
B) volume (volume of the rotating body, etc );
C) The Arc Length of the plane curve;

... Gravity, work, etc.

PS: It's big. It's coming to an end.