This book is divided into twelve chapters, which respectively mark the requirements for the first, second and third examinations of mathematics, and is suitable for different types of examinees. The whole book systematically summarizes the basic theories of each chapter, and the key question types and comprehensive question types of each part are given in the key question type explanation part, so that the examinees can better adapt to the requirements of the exam and lay a solid foundation for taking the exam. It has the following characteristics: 1. Comprehensive coverage of examination sites. This book contains all the knowledge points examined by the postgraduate entrance examination in advanced mathematics. It is well detailed and appropriate, suitable for candidates to prepare for exercises, break through key points and eliminate weaknesses. 2. The investigation requirements are clear. The examination requirements of the outline are listed at the beginning of each sheet, so that students can test the review effect by themselves. 3. The summary of the questions is detailed. At the end of each chapter, the book summarizes and sorts out the common test questions according to the contents of this chapter, with appropriate examples, and combines learning with practice to help candidates master the solutions to common test questions.
Bibliography
Chapter I Limit and Continuity
Section 1 Functions
Section II Limit
Section 3 Continuity and discontinuity
Chapter 2 Derivative and Differential
Section 1 Basic concepts of derivative and differential
Section 2 Derivation Formulas and Rules
Section 3 Derivation of implicit function and function determined by parametric equation
Chapter 3 Application of Differential Calculus of One Variable Function
Section 1 Mean value theorem
Section II Monotonicity and extreme value, concavity and convexity and inflection point, function drawing
Chapter IV Indefinite Integral
Section 1 Concept and basic properties of indefinite integral
Section 2 Basic Formula and Integral Method of Indefinite Integral
Section 3 Indefinite integral of two important functions
——Rational Function and Triangular Rational Function (not required by Mathematics III)
Chapter V Definite Integral and Its Application
Section 1 Concept and basic properties of definite integral
Section II Basic Theory
Section 3 Generalized Integral
Section 4 Application of Definite Integral
Chapter VI Differential Calculus of Multivariate Functions
Section 1 Basic concepts of differential calculus of multivariate functions
Section 2 Basic Theory of Multivariate Function
Section 3 Application of Differential Calculus of Multivariate Functions
Section 4 Physical and Geometric Applications of Differential Calculus of Multivariate Functions (Mathematics II and III are not required)
Chapter 7 Differential Equations
Section 1 Basic concepts of differential equations
Section 2 Types and Solutions of First Order Differential Equations
Section 3 Higher order differential equations that can be reduced (not required for Math III)
Section 4 High order differential equation
Chapter VIII Multiple Integral
Section 1 Double integral
Section II Triple integral (not required for mathematics II and III)
Chapter IX Series (not required for Math II)
Section 1 Series of constant terms
Section 2 Power Series
Section 3 Fourier Series (not required for Math III)
Chapter 10 Space Analytic Geometry (Mathematics II and III are not required)
Section 1 Theory of space analytic geometry
Section 2 Application of Vector
Chapter 11 Curve Integral and Surface Integral (not required for Mathematics II and III)
Section I Curve integral
Section 2 Surface integral
Section III Preliminary Field Theory
Chapter 12 Economic Application of Mathematics (Mathematics I and II are not required)
Section 1 Difference equation
Section 2 Marginality and elasticity
Section 3 Present Value and Interest
