The better version of the general university liberal arts advanced mathematics recommendation 10

The National People's Congress Edition, "Calculus" by Zhao Shuyan

Chapter 1 Functions.

Gather. Set of real numbers.

Functional relationships. Piecewise functions.

Example of establishing a functional relationship.

Several simple properties of functions.

Inverse and composite functions.

Elementary functions. Simple combinations and transformations of function graphs.

Exercise 1. Chapter 2 Limits and Continuity.

The limits of the sequence.

The limits of the function.

The limits of the variable.

Infinitely large and infinitesimal quantities.

The algorithm of the limit.

Two important limits.

The limit is found using the equivalent infinitesimal substitution.

Continuity of functions.

Exercise 2. Chapter 3 Derivatives and Differentiation.

An example problem that leads to the concept of derivatives.

Derivative concept. The basic formulas and algorithms of derivatives.

Higher-order derivatives. Differential calculus. Exercise 3. Chapter 4 The Median Theorem and the Application of Derivatives.

Median value theorem. Lobida's Law.

The increment or decrease of functions.

The extreme value of the function.

The application of maximum and minimum values, extreme values.

The concave direction and inflection point of the curve.

How to do it with function graphs.

Application of the Rate of Change and the Relative Rate of Change in the Economy: An Introduction to Marginal Analysis and Elasticity Analysis.

Exercise 4. Chapter 5 Indefinite Integrals.

The concept of indefinite integrals.

The nature of indefinite integrals.

Basic integral formula.

Commutation integral method.

Fractional integral method.

Comprehensive miscellaneous examples. Exercise 5. Chapter 6 Definite Integrals ......

Chapter 7 Infinite Series ......

Chapter 8 Multivariate Functions ......

Chapter 9 Introduction to Differential Equations and Difference Equations ......

Question 1: How many books do you need to learn in high school mathematics and liberal arts? 7 books.

Compulsory 1 (Chapter 1: *Chapter 2: Functions Chapter 3: Exponential and Logarithmic Functions Chapter 4: Applications of Functions).

Compulsory 2 (Chapter 1: Elementary Solid Geometry Chapter 2: Preliminary Analytic Geometry) Compulsory 3 (Chapter 1: Statistics Chapter 2: Preliminary Algorithms Chapter 3: Probability).

Core 4 (Chapter 1: Trigonometric Functions, Chapter 2: Plane Vectors, Chapter 3: Trigonometric Identity Deformation).

Compulsory 5 (Chapter 1: Number Sequence, Chapter 2: Solving Triangles, Chapter 3: Inequality).

Elective 2 1 (Chapter 1: Common Logical Terms, Chapter 2: Space Vectors and Solid Geometry, Chapter 3: Conic Curves and Equations).

Elective 2 2 (Chapter 1: Reasoning and Proof Chapter 2: Rate of Change and Derivatives Chapter 3: Applications of Derivatives Chapter 4: Definite Integrals).

Question 2: Which books do you study for high school mathematics and liberal arts and science in the A version of Renjiao? Compulsory courses 1 to 5, both arts and sciences must be studied.

Liberal Arts Electives 1-1, 1-2. Science electives 2-1, 2-2, 2-3. There are also elective 4-work, 4-2, 4-4, 4-5.

Generally, each school chooses two out of four books.

Question 3: What is the difference between liberal arts and science in the college entrance examination? What books are tested in mathematics? Liberal Arts Mathematics: Compulsory 1---5, Elective 1--1, 1---2, 4--4 or 4--5

Science and Mathematics: Compulsory 1---5, Elective 2--1, 2---2, 2---3, 4--4 or 4--5.

Question 4: Which mathematics books do liberal arts students learn Compulsory 1-5, Elective 1-1, Elective 1-2, Elective 4-1, Elective 4-4, Elective 4-5

Question 5: What electives should high school mathematics and liberal arts students take? High School Mathematics (Liberal Arts):

Compulsory Parts: Compulsory 1, Compulsory 2, Compulsory 3, Compulsory 4, Compulsory 5, Elective 1-1, Elective 1-2; Elective part: Elective 4-1 (Selected Lectures on Geometric Proofs), Elective 4-2 (Matrices and Transformations), Elective 4-4 (Coordinate Systems and Parametric Equations), Elective 4-5 (Selected Inequalities).

Note: The compulsory part of the college entrance examination is a compulsory question, and the optional part is an optional question (choose one of the three).

Question 6: How many books are there on mathematics for liberal arts students in the Shenzhen college entrance examination? Which ones are they? Liberal Arts is compulsory 1-5, elective 1-1, 1-2, and elective 4-series.

The People's Education Publishing House uses version A.

Question 7: Which books are elective books for high school Chinese mathematics! Thank you o( o thank you Compulsory 1, Compulsory 2, Compulsory 3, Compulsory 4, Compulsory 5;

Elective 1-1, Elective 1-2;

Elective 4-1, Elective 4-4, and Elective 4-5 are all studied in each high school. In each of the three books, students choose only one question according to their own situation.

Question 8: What books are tested in the college entrance examination for high school Chinese mathematics? All compulsory exams are required, and elective 1-1 and 1-2 are compulsory; Elective 4-1, 4-2, 4-5 are optional questions, choose one of the three, but it is recommended that you learn them all, and look at that and write that simply during the college entrance examination.

1. Function, limit, continuous.

2. Differential calculus of unary functions.

3. Integral science of unary functions.

4. Calculus of Multivariate Functions.

5. Infinite series.

6. Ordinary differential equations and difference equations.

The first chapter of the book covers all the knowledge points in the first chapter of the syllabus.

The second chapter of the book is read in its entirety, and the third chapter only looks at the first six sections, which basically covers the knowledge points of the second chapter of the outline. The economic significance of the missing derivative and the asymptote of the function graph are two points that make up by themselves.

The fourth chapter of the book is read in its entirety, the fifth chapter is read in its entirety, and the sixth chapter is read in the first and second sections of the first and second sections (three are not read), which basically covers the knowledge points of the third chapter of the outline. Although the fifth section of chapter 5 is marked with an asterisk, it is similar to the judgment of infinite series, which can be seen. In the application of missing integrals, there is a point about simple economic application problems, and you can make up for it yourself.

Chapter 8 of the book looks at sections 1, 2, 3, 4, 5, and 8, and chapter 9 looks at sections 1 and 2 (3 do not read), which basically covers the knowledge points of chapter 4 of the outline. Leak the point of simple anomalous double integration on the unbounded region, and make up for it yourself.

Chapter 11 of the book looks at the first four sections, covering all the knowledge points in chapter 5 of the outline.

Chapter 12 of the book looks at sections 1, 2, 3, 4, 7, 8, and 9, barely covering the knowledge points of Chapter 6 of the outline. The concept of leakage difference and difference equations, the general and special solutions of difference equations, linear difference equations with constant coefficients of the first order, and the simple application of differential equations are four points, which are completed by themselves.

Note: The above chapters contain a very small number of super-outline points, which are beneficial and harmless to the postgraduate entrance examination, but it is okay to read it.

If anyone has a sixth edition, please check it as well.

Look at Tongji's textbooks.

It's not much different! Different schools use different versions, but the point is that they all have calculus!! The idea of integration runs through the entire science and engineering class, which is very important and must be learned well

College liberal arts mathematics will be relatively less content.

Specific chapters: Functions and Limits, Derivatives and Differentiation of Unary Functions, Differential Median Theorem and Applications of Derivatives, Indefinite Integrals, Definite Integrals.

The main thing is that differentiation, limits, derivatives and a small number of integrals are simple.

Nowadays, many universities use Tongji (6th Edition):

Table of Contents: Volume I, Chapter 1, Functions and Limits.

Section 1 Mappings and Functions.

Section 2 The Limits of the Sequence.

Section 3 Limits of Functions.

Section 4 Infinity and Infinitesimal.

Section 5 Limit Algorithms.

Section 6 Criterion for the Existence of Limits Two important limits.

Section 7 Infinitesimal Comparisons.

Section 8 Continuity and Break Points of Functions.

Chapter 2 Derivatives and Differentiation.

Chapter 3 The Differential Median Theorem and Applications of Derivatives.

Chapter 4 Indefinite Integrals.

Chapter 5 Definite Integrals.

Chapter 6 Application of Definite Integrals.

Chapter 7 Differential Equations.

Volume II, Chapter 8, Spatial Analytic Geometry and Vector Algebra.

Chapter 9 Multivariate Function Differentiation and Its Applications.

Chapter 10 Re-integral.

Chapter 11 Curve Integrals and Surface Integrals.

Chapter 12: Infinite Series.

Such as the bright picture of the cherry blossom skin ode chop.

The differential equation also needs to be multiplied by a dx

The liberal arts have low requirements for advanced mathematics, while the sciences have high requirements for advanced mathematics, and the content of higher mathematics in the liberal arts is appropriately reduced compared with that of science.

The specific situation of each university is different, and the teaching plan of the university is not uniform across the country.

Finance majors are generally expected to study advanced mathematics in the sciences, which is not a choice for you, so there is no need for you to ask this question.

Derivation. y'=6x+2, let y'=0, then x=-(1 3) because y'At negative infinity to -(1 3) <0, at -(1 3) to positive infinity "0, so y decreases at negative infinity to -(1 3) and increases at -(1 3) to positive infinity;

y'=x 2+2x-3, let y'=0, then y=1 or y=-3 because y'at negative infinity to -3>0, at -3 to 1<0, at 1 to positive infinity", so y increases at negative infinity to -3, decreases at -3 to 1, and increases at 1 to positive infinity.