Winter vacation mathematics study plan

The winter holiday is coming, have you planned for yourself? To fully enjoy this holiday, you will have a qualitative leap in your postgraduate review. I believe that leading education must be a correct choice. The following is a high-level review plan for leading education for 2012 graduate students. If you can follow this plan, you can achieve the desired results. But in the face of a very practical problem, students go home on holiday, can they make full use of the holidays, can they really complete the study tasks according to the plan? Therefore, leading the math training camp to launch a “win” plan during the winter vacation, help you to use the following plans as an outline, combine a large number of exercises, scientific tests and explanations, classify knowledge in higher mathematics, and teach problem-solving skills. In addition, the guidance of linear algebra will be started in advance.

First of all, the winter vacation is divided into eight stages, and then the following plans are carried out to complete the review of advanced mathematics.

1 First stage review plan:

Reviewing the first chapter of the high book, you need to achieve the following goals:

1. Understand the concept of a function, master the representation of a function, and establish a functional relationship that applies the problem.

2. Understand the boundedness, monotonicity, periodicity and parity of the function.

3. Understand the concepts of compound and segmentation functions, and understand the concepts of inverse and implicit functions.

4. Master the nature of the basic elementary function and its graphics, and understand the concept of elementary functions.

5. Understand the concept of the limit, understand the concept of the left and right limits of the function and the relationship between the existence of the limit and the left and right limits.

6. Master the nature of the limit and the four algorithms.

7. Master the two criteria of the existence of the limit, and use them to find the limit, master the method of using two important limits to find the limit.

8. Understand the concept of infinitesimal and infinitely large quantities, and master the infinitesimal comparison method, and use the equivalent infinitesimal quantity to find the limit.

9. Understand the concept of the continuity of the function, it will determine the type of the function breakpoint.

10. Understand the nature of continuous functions and the continuity of elementary functions, understand the properties of continuous functions on closed intervals, and apply these properties.

The main task at this stage is to grasp the boundedness, monotonicity, periodicity and parity of the function; the nature of the basic elementary function and its graph; the definition of the limit of the series and the limit of the function and its properties; the comparison of infinitesimal quantities; An important limit; the concept of continuous functions, the type of functional discontinuities; the nature of continuous functions on closed intervals.

2 second phase review plan:

Reviewing the second chapter of the high book, Chapters 1-3, you need to achieve the following goals:

1. Understand the concept of derivatives and differentials, understand the relationship between derivatives and differentials, understand the geometric meaning of derivatives, and find the tangent and normal equations of plane curves, understand the physical meaning of derivatives, and use derivatives to describe some physical quantities, understanding functions. The relationship between the conductivity and continuity.

2. Master the four arithmetic rules of derivative and the derivative rule of compound function, and master the derivative formula of basic elementary function. Understand the four arithmetic rules of differential and the invariance of first-order differential form, and find the differential of function.

3. Understand the concept of higher-order derivatives, and find the higher-order derivatives of simple functions.

The main task this week is to grasp the geometric meaning of the derivative; the relationship between the conductivity and continuity of the function; the tangent and normal of the plane curve; the derivative formula of the basic elementary function; the higher-order derivative is calculated by the recursion method .

3 The third phase review plan:

Review the second book of the high book, chapter 4-5, chapter 1-5. The following goals must be achieved:

1. Will find the derivative of the piecewise function, and will find the implicit function and the function determined by the parametric equation and the derivative of the inverse function.

2. Understand and use the Rolle theorem, the Lagrangian median theorem and the Cauchy median theorem.

3. Master the method of using the Lobita rule to find the limit of the infinitive.

4. Understand the concept of the extremum of the function, master the method of using the derivative to judge the monotonicity of the function and the extremum of the function, and grasp the method of finding the maximum and minimum values ​​of the function and its application.

5. The derivative of the function graph will be judged by the derivative. Will find the inflection point of the function graph and the horizontal, vertical and oblique asymptotes, which will depict the graph of the function.

The main task this week is to master the segmentation function, the inverse function, and the implicit function. The parametric equation determines the derivative of the function. The increase or decrease of the function is judged according to the derivative of the function at one point. Will use the differential mean value theorem proof. The limit will be determined according to the usage of Lobida's Law. Master the necessary conditions for the existence of extreme values, first and second sufficient conditions. The extreme and maximum values ​​of the function and the convexity and concavity of the function are calculated. The asymptote of the function is calculated. The set of questions related to the derivative [marginal, elastic, economic, and geometric problems] will be calculated.

4 Stage 4 review plan

Review the high number books, Chapter 4, Sections 1-3. The following goals must be achieved:

1. Understand the concept of the original function and understand the concept of indefinite integral.

2. Master the basic formula of indefinite integral, master the nature of indefinite integral, master the indefinite integral and the integral integral method, and find the indefinite integral of simple function.

This week's main task is to master the nature of indefinite integrals, the formula of indefinite integrals [remember that there are infinite numbers of primitive functions of a function, pay attention to +C], and use the first and second meta-methods to find the indefinite integrals of the functions. . Master the indefinite integral segment integral formula and apply it.

5 Stage 5 review plan

Review the high number books, Chapter 5, Sections 1-3. Achieve the following goals:

1. Understand the geometric meaning of the definite integral.

2. Master the nature of the definite integral and the mean value theorem of the definite integral.

3. Master the integral integral method and the definite integral generalized element method.

The main task of this week is to master the nature of indefinite points and to do the questions based on the nature of the indefinite points. In particular, the integral value of the integral upper and lower limits is changed to the opposite number. The definite integral is independent of the variable, and the integral can be calculated according to the parity of the function.

6 Stage 6 review plan

Review the fifth book, Chapter 4, Chapter 2, Section 2 of the high book. Achieve the following goals:

1. Master the function of the upper limit of the integral, and ask for its derivative and master the Newton-Leibnitz formula.

2. Master the definite integral method and the definite integral generalized element method. The definite integral of the piecewise function will be obtained.

3. Master the calculation of some geometric quantities with fixed integrals. Learn about generalized and infinite integrals.

The main task this week is to master the nature of the upper limit function, master the Newton-Leibnitz formula, and apply the definite integral method to determine the integral. The area of ​​the plane figure and the volume of the rotating body are calculated according to the geometric meaning of the definite integral.