1, square difference formula: x2? y=(x？ y)(x+y)^。 Complete square formula: (a+b) 2 = A2+2AB+B2. Law of derivation: (u v)' = u v', (UV)' = u v+UV', (u/v)' = (u v-UV')/v? . Integral formula: ∫(0, x)f(t)dt=F(x)-F(0), ∫(a, b)f(x)dx=(a, b)f(x)dx.
2. Taylor expansion: This formula is used to express a function as the sum of infinite terms, and each term is the derivative of the function at a certain point. For example, f (x) = f (a)+f' (a) (x-a)+f'' (a) (x-a)? /2! +...+f(n)(a)(x-a)^n/n！ +...。 Rule of Derivation: These formulas are used to calculate the derivative of a function. For example, (u v)' = u v', (UV)' = u v+UV'.
3. Integral formulas: These formulas are used to calculate definite integral and indefinite integral. For example, ∫(0, x)f(t)dt=F(x)-F(0), where F(x) is the original function of f(t); ∫(a, b)f(x)dx=(a, b)f(x)dx, where f(x) is the original function of (x).
4. Green's formula: Green's formula is an important integral formula, which is used to calculate the curve integral on the two-dimensional plane. Its general form is ∮ (ax+by) dx+(CX+dy) dy = (b-a) ∮ ADY+(c-d) ∮ BDX, where A and B are two infinitesimal curves with opposite directions to the integrand curve.
Application field of advanced mathematics
1, financial investment. The concepts of calculus and sequence in advanced mathematics can be applied to financial investment, such as calculating compound interest and return on investment. Physics. Higher numbers are widely used in physics, such as kinematics and mechanics. We can use the knowledge of high numbers to calculate the speed, acceleration and displacement of objects.
2. engineering. High number also has many application scenarios in engineering, such as circuit design and signal processing. We can use the knowledge of high numbers to analyze the parameters such as voltage, current and power in the circuit. Statistics. High numbers also have many applications in statistics, such as probability and statistical analysis. We can use the knowledge of high numbers to analyze statistical data and make probability prediction.