Knowledge of advanced mathematics, knowledge points of advanced mathematics

Seek guidance y first'=2x+1, this should be, after finding it, substitute x=3 to get the slope 7 at x=3, and then substitute the point (3,13), use the point slope method to get the tangent equation y-13=7(x-3), you can also simplify it, it is y=7x+8;The product of the slope of the normal and the slope of the tangent is minus one, according to which the slope of the normal is -1 7, and the normal equation y-13=-1 7 (x-3) is substituted

The first thing to know is the tangent formula (x-x')/1=(y-y'y is about the derivative of x.

The derivative of this question is 7, so y=7x-8

In there is to know the normal plane formula (x-x')+dy/dx(y-y')=0 can be brought in y-13=-1 7(x-3).

Tangent: The derivative is 2x=6,k2, bring x=3 in, y=12, and the tangent should pass through (3,12) tangent y=2x+6

Normal: k 1 2, the normal also passes through (3,12) normal y=

y'=2*x+1

The tangent equation at the point x=3 y-13=7 (x-3).

The normal equation y-13=-1 7(x-3).

It's a complete computational problem, it's not interesting, as long as you have a preliminary knowledge of analytic geometry, you can do it!

The knowledge points of advanced mathematics are as follows: the scope of indefinite integral knowledge, the definition of original functions and indefinite integrals, and the existence of theorems in original functions. Basic integral formula.

The commutation integral method, the first commutation method (the commutation differential method), and the second commutation method. Divisional Integral Law Cover Activation. Integrals of some simple rational functions.

It is required to understand the concept and relationship between the original function and the indefinite integral, grasp the properties of the indefinite integral, and understand the existence theorem of the original function. Proficient in the basic formula of indefinite integrals, proficient in the first commutation method of indefinite integrals, and master the second commutation method (limited to triangular substitution and simple radical substitution).

Proficient in the partial integration method of indefinite integrals. will find the indefinite integral of a simple rational function. Vector algebra, scope of knowledge, concept of vectors, definition of vectors, modulo of vectors, unit vectors, projection of vectors on coordinate axes, coordinate notation of vectors, directional cosine of vectors, linear operations of vectors, addition of vectors, subtraction of vectors, number multiplication of vectors.

The quantity product of the vector is the angle between the two vectors, the sufficient necessary conditions for the perpendicularity of the two vectors, the vector product of the two vectors, and the sufficient necessary conditions for the parallelism of the two vectors, which require an understanding of the concept of vectors, a grasp of the coordinate representation of vectors, and the projection of unit vectors, direction cosine, and vectors on the coordinate axis.

Proficient in linear operation of vectors, calculation methods of quantity product and vector product of vectors. Proficiency in the sufficient and necessary conditions for parallel and perpendicular binary vectors.

Functions and Limits.

1.Understand the concept of functions and master the representation of functions.

2.Functional relations in simple application problems are established.

3.Learn about parity, monotonicity, periodicity, and boundedness of functions.

4.Understand the properties and graphs of basic elementary functions.

5.Understand the concepts of composite functions and piecewise functions, and understand the concepts of inverse functions and implicit functions. Derivatives and differentiation.

1.Understand the concept of derivatives and differentiation, understand the relationship between derivatives and differentiation, understand the geometric meaning of derivatives, find tangent equations and normal equations for plane curves, understand the physical meaning of derivatives, describe some physical quantities with derivatives, and understand the relationship between derivability and continuity of functions.

2.Master the four rules of operation of derivatives and the derivation rules of composite functions, master the derivative formulas of elementary functions, understand the four rules of operation of differentiation and the invariance of first-order differential forms, and be able to find elementary functions. Differential calculus.

3.The derivatives of the functions determined by the implicit and parametric equations and the inverse functions are found.

4.Able to find the derivatives of piecewise functions, understand the concept of higher-order derivatives, and find higher-order derivatives of simple functions.

Application of the differential median theorem and derivatives.

1.Proficient in using the differential median theorem to prove simple propositions.

2.Proficient in using Robida's Law and Taylor's Formula to find limits and prove propositions.

3.Learn about the charting steps of function graphs. Learn about two ways to approximate solutions to equations: the dichotomy and the tangent method.

4.The function will find monotonic intervals, convex and concave intervals, extremums, inflection points, progressive lines, and curvatures.

Antiderivative. 1.Understand the concepts of primitive functions and indefinite integrals, and master the basic formulas and properties of indefinite integrals.

2.Indefinite integrals of rational functions, trigonometric functions, rational expressions, and simple irrational functions are found.

3.Master the step-by-step integration method of indefinite integrals.

4.Master the commutation integral method of indefinite integrals.

Application of definite integrals.

1.Master the calculation of some physical quantities (work, gravity, pressure) with definite integrals.

2.Master the expression and calculation of some geometric quantities (the area of a plane figure, the arc length of a plane curve, the volume and side area of a rotating body, the area of a parallel cross-section is a known solid volume) and the average value of functions.

Differential equation. 1.Understand differential equations and their solutions, orders, general solutions, initial conditions, and special solutions.

2.Able to solve odd differential equations, and can solve some differential equations by substitution of simple variables.

3.Master the differential equations of separable variables, and use simple variables to substitute the solution of certain differential equations.

4.Master the method of solving homogeneous differential equations with constant coefficients of the second order, and be able to solve some homogeneous differential equations with constant coefficients higher than the second order.

5.Master the solution of first-order linear differential equations, and be able to solve Bernoulli's equations.

6.The following differential equations will be solved using the reduced-order method.

y''=f(x，y').

7.Solve nonhomogeneous linear differential equations with free terms as polynomials, exponential functions, sine functions, cosine functions, and their sums and products.

8.Will solve Euler's equations.

Topics include: sequences, limits, calculus, spatial analytic geometry and linear algebra, series, and ordinary differential equations. It is the basic subject of the graduate examination of engineering, science, and finance. Compared with elementary mathematics, the objects and methods of mathematics are more complicated.

Broadly speaking, mathematics other than elementary mathematics is advanced mathematics, and there are also those that refer to the more in-depth algebra, geometry, and simple set theory and logic as intermediate mathematics, as a transition between elementary mathematics at the primary and secondary school levels and advanced mathematics at the university level.

It is generally believed that advanced mathematics is a fundamental discipline formed by calculus, more advanced algebra, geometry, and the intersection between them.

Summary. Let the bottom side of the rectangle be x and the height y, then there is x y = advanced mathematical foundation.

Please send me the question** to see!

Good! Please wait a minute, I'm calculating.

And then wait, there's this.

Anxious teacher. Thank you, teacher.

Let the bottom side of the rectangle be long x and high y, then there is x y = the surface area of the cuboid of the manuscript is s, then s = x + 4xy = x + 54 x ,s'=2x-54 x, when x=3, s obtains the minimum value of the search limb, so the bottom side length is 3 meters, and the height is the most economical material.

If it is self-taught, the requirements are not too high, don't learn any mathematical analysis, engineering mathematical analysis, it is more difficult; Mathematical analysis is generally anthropological in the Department of Mathematics.

Advanced Mathematics and Linear Algebra are generally separate from each other.

The content of Higher Mathematics is as follows:

1.The limit and continuity of a univariate function. Theoretical proofs such as -n, -x, -do not need to be learned; The clamping theorem and monotonous boundedness are quite important, and some equivalent substitutions need to be mastered; The continuity of functions is easy to learn, not difficult.

2.Differential calculus of unary functions. You must learn the derivation well, otherwise you will be miserable when you learn the integral; The essence of differentiation is derivation; The fundamental theorem of differential calculus, the lagrange median theorem must be studied hard, and the proof problem basically depends on it; l'The hospital is quite important; Taylor's formula is commonly used in proof questions.

3.Integral science of unary functions. Let's learn the variable limit function; Let's also learn the division integration method and the commutation integration method; There will be a lot of practical problems in this section.

4.Ordinary differential equation. I won't talk about the specific content, it's not difficult anyway, but it's very annoying and annoying, just memorize the formula.

5.Multivariate Differential Calculus. It's not just diversity, it's a lot of content. The complex variable function is out.

6.Multivariate Function Integral. The double and triple integrals are out, which involve the calculation of the first type of curve and surface.

7.Integration of vector functions. Involves the calculation of type 2 curves and surfaces.

8.Integration of complex variable functions. Cauchy's integral theorem is the foundation is the key, and LZ will look at it.

9.A series of constant terms.

10.The series of function items.

lz, linear algebra must be learned, otherwise you will have a hard time learning the content behind high numbers; However, linear algebra is also very annoying, because there are too many contents, but they are not very deep, and basically revolve around three points: solving equations with matrices, explaining quadratic forms with matrices, eigenvalues and their transformations (orthogonal transformations are important).

Hope all help LZ.