Compulsory 1 Chapter 1 Meaning and Representation of Sets 1 Basic Operation of Sets 3. 1 Intersection and Union of Sets 3.2 Complete Sets and Complements of Sets Chapter 2 Functions 1 Variables in Life 2 Further Understanding of Functions 2. 1 Function Concept 2.2 Representation of Functions 2.3 Mapping 3 Monotonicity 4 of Functions Image of kloc-0/ quadratic function 4.2 Properties of quadratic function 5 Simple income tax Chapter III Exponential function and logarithmic function 1 positive integer exponential function 2 Exponential expansion and its operational properties 2. 1 Exponential concept 2.2 Exponential operational properties 3. 1 Exponential function concept 3.2 Image and properties of exponential function sum 3.3 Exponential function 4 Logarithmic 4./ Kloc-0/ Logarithm and its Operation 4.2 Conversion Formula 5 Logarithm Function 5. 1 Logarithm Function Concept 5.2 y=log2x Image and Logarithm Function Image with Property 5.3 Comparison of Exponential Function, Power Function and Logarithm Function Growth Chapter 4 Function Application 1 Function and Equation 1 Judging the Existence of Equation Solution by Function Property 1 .2 Finding Approximate Solution of Equation by Dichotomy 2 Functional Modeling of Practical Problems 2. 1 Functional Characterization of Practical Problems 2.2 Solving Practical Problems by Using Functional Models 2.3 Cases Required for Functional Modeling 2 1 A Preliminary Study of Solid Geometry. Step 1 simple geometry 1. 1 simple rotator 1.2 simple polyhedron 2 direct view 3. 1 simple assembly 3.2 restore from three views to object 4. Basic relation and axiom of spatial graph 4. 1 understanding of basic relation of spatial graph 4. Determination of Plane Relation 5.2 Nature of Parallel Relation 6 Vertical Relation 6.66 Geometry 7. 1 lateral area of Simple Geometry 7.2 Prism, Pyramid, Prism, Cylinder and Cone, Study on the Shape of Cube Section in Truncated Cone Volume Chapter II Preliminary Analytic Geometric Equation of Lines and Lines 1. 1 Inclination and Slope Equation of Lines 1 .2 Position equation of two straight lines 1.3 Intersection point of two straight lines 1.4 Distance formula in plane Cartesian coordinate system 2 Equation 2. 1 Standard equation of circle 2.2 General equation of circle 2.3 Straight line and circle, Position relationship between circles 3 Establishment of spatial rectangular coordinate system 3. 1 3.2 Coordinates of midpoint in spatial rectangular coordinate system 3.3 Distance formula between two points in space required 3 Chapter 1 Statistics 1 Sampling method from census to sampling 2. 1 Simple random sampling 2.2 Hierarchical sampling and systematic sampling 3 Digital characteristics of data 4.6543 8+0 mean, median, mode and range. Variance 4.2 standard deviation 5 Estimate the distribution of the population with samples 5. 1 Estimate the numerical characteristics of the population 6 Statistical activities: the change of marriage age 7 correlation 8 least squares estimation Chapter II Basic idea of algorithm 1 algorithm 1 case study of algorithm/sorting problem and diversity of algorithm 2. 1 Sequence Structure and Selection Structure 2.2 Variables and Assignments 2.3 Cyclic Structure 3 Basic Statements 3.66 Conditional Statements 3.2 Cyclic Statements Chapter 3 Probability 1 Probability of Random Events 1 Frequency and Probability 1.2 Probability in Life 2 Classical Probability 2.6558. +0 Classical Probability Characteristics and Probability Calculation Formula 2.2 Establishing Probability Model 2.3 mutually exclusive events 3 Simulation Method —— Applying Probability Essentials 4 Chapter 1 Trigonometric Function 1 Periodic Phenomena 2 Extension of Angle Concept 3 Curvature System 4 Definition and Inductive Formula of Sinusoidal Function and Cosine Function 4. 1 Sinusoidal Function at any angle, Definition of cosine function 4.2 Unit circle and periodicity 4.3 Unit circle and inductive formula 5 Properties and images of sine function 5. 1 Viewing properties of sine function from unit circle 5.2 Images of sine function 5.3 Properties of sine function 6 Properties and images 6.2 Properties of sine function 7 Tangent function 7. 1 Definition of tangent function. 7.2 Images and Properties of Tangent Function 7.2 Inductive Formula of Tangent Function 8 Images of Function y=Asin 9 Simple Application of Trigonometric Function Chapter 2 Plane Vector 1 From Displacement, Velocity and Force to Vector 1 Displacement, Velocity and Force Concept 1.2 Vector 2 From Synthesis of Displacement to Addition of Vector 2. 1 Vector 2.2 from vector subtraction 3 from multiple of speed to multiplication vector 3. 1 multiplication vector 3.2 basic theorem of plane vector 4. 1 coordinate representation of plane vector 4.2 coordinate representation of plane vector linear operation 4.3 vector flattening. The coordinates of the line indicate the work done by 5 forces on the product of vectors, and the coordinates of the product of 6 plane vectors. Vector application example 7. 1 distance from point to straight line formula 7.2 Application example of vectors. Chapter III Constant deformation of triangles 1 basic relation of trigonometric function with the same angle 2 and trigonometric function of difference 2. 1 cosine function of sum and difference of two angles 2.2 Sine of sum and difference of two angles. Cosine Function 2.3 Tangent Function of Sum and Difference of Two Angles 3 Trigonometric Function of Two Angles Must Learn 5 Chapter 1 Series 1 Series 1 .2 Series Function Features 2 arithmetic progression 2. 1 arithmetic progression 2.2 arithmetic progression's First N Term and 3 geometric progression 3.65438' s First N Term and 4 Series Applications in Daily Economic Life. Chapter 2 Solving Sine Theorem of Triangle 1 and Cosine Theorem 1. 1 Sine Theorem 1.2 Cosine Theorem 2 Solving Geometric Calculation in Triangle 3 Solving Practical Application Examples of Triangle Chapter 3 Inequality 1 Inequality Relation 1.65438+ 8+0.2 Solution of quadratic inequality in one variable 2.2 Application of quadratic inequality in one variable 3 Basic inequality 3 and plane region 4.2 Simple linear programming 4.3 Revised version of Simple linear programming 1- 1 Chapter 1 Common logical terms 1 proposition 2 Sufficient and necessary conditions 2. 1 Sufficient and necessary conditions 2.3 Full name quantifiers and existential quantifiers 3./kloc All-name quantifiers and all-name propositions 3.3 Denying all-name propositions and special propositions 4 Logical conjunction "Fei" 4. 1 Logical conjunction of its standard equation 1.2 Simple properties of ellipse 2 Parabola 2.65438+ 3. 1 Hyperbola and its standard equation 3.2 Simple properties of hyperbola Chapter 3 Change rate and derivative 1 The concept of rate of change and its derivative and its geometric meaning 2. 1 the concept of derivative 2.2 the geometric meaning of derivative 3 four algorithms for calculating derivative 4. 1 the addition and subtraction of derivative 4.2 the multiplication and division rule of derivative 1 the value of function 1. 1 the derivative and monotonicity of function/kloc-. .2 Application of extreme value of function 2 derivative in practical problems 2. Significance of1derivative in practical problems 2.2 Maximum value, Minimum Problem Elective 1-2 Chapter 1 Statistical Cases 1 Regression Analysis 1 Regression Analysis 1.2 Correlation Coefficient 1.3 Linearizable Regression Analysis 2 Independence Test 2. 1 Conditional Probability and Independent Events 2.2 Independence Test 2.3 Basic Ideas of Independence Test 2.4 Flow chart 2 Structure chart Chapter III Reasoning and Proof 1 Induction and Analogy 65438 and Reduction to absurdity Chapter IV Promotion and Introduction of Number System 1. 1 Extension of the concept of complex number 1.2 Related concepts of complex number 2 Four operations of complex number 2. 1 addition and subtraction of complex number 2.2 Multiplication and division of complex number Kloc-0/ Common logical terms 1 Proposition 2 Sufficient conditions and necessary conditions 2.6666666 and pan-proposition 3.2 Existence of quantifiers and special propositions 3.3 Denying pan-proposition and special proposition 4 Logical conjunctions are even or costly 4. 1 Logical conjunctions are even or costly 4.3 Logical conjunctions are even. 38+0 Operation of Space Vector from Plane Vector to Space Vector 2 3 Coordinate Representation and Fundamental Theorem of Space Vector 3. 1 Standard Orthogonal Decomposition and Coordinate Representation of Space Vector 3.2 Fundamental Theorem of Space Vector 3.3 Coordinate Representation Operation of Space Vector 4 Discussion on Calculation of Vertical and Parallel Angles of Vector 5. 1 Angle between straight lines 5.2 Angle between straight lines 5.3 Calculation of angle with plane Chapter III Conic curve and equation 1 ellipse/ellipse and its standard equation 1 .2 Simple properties of ellipse 2 parabola 2. 1 parabola and its standard equation 2.2 Simple properties of parabola 3 hyperbola 3. 1 Hyperbola and its standard equation 3.2 Simple property 4 curve and equation 4. 1 curve and equation 4.2 Conic curve * * * 4.3 Intersection of straight line and conic curve with the same property 2-2 Chapter 1 Reasoning and proof 1 induction and analogy 1 .2 Analogical reasoning 2 Comprehensive method and analysis method 2./kloc Comprehensive method 2.2 Analysis method 3 Reduction method 4 Mathematical induction method Chapter 2 Change rate and derivative method 65438 2 Concept of derivative and its geometric meaning 2. 1 Concept of derivative 2.2 Geometric meaning of derivative 3 Four algorithms for addition and subtraction of derivative 4.2 Multiplication and division rule 5 Derivation rule of simple compound function Chapter 3 Monotonicity and extreme application of derivative 1 Rule of derivative and 0./ Monotonicity of kloc-0/ function/application of extreme value 2 derivative of kloc-0/.2 function in practical problems 2./meaning of kloc-0/derivative in practical problems 2.2 maximum and minimum problems chapter 4 concept of definite integral 1 definite integral 1 background of definite integral- .2 Definite Integral 2 Basic Theorem of Calculus 3 Simple Application of Definite Integral 3. 1 Area of Plane Figure 3.2 Volume of Simple Geometry Chapter 5 Expansion of Number System and Introduction of Complex Number 65438+ Introduction and Popularization of the Concept of Number 1.6538 Complex Number 2. 1 Addition and subtraction of Complex Number 2.2 Multiplication and division of Complex Number 2-3 Electives of Chapter 1 Counting Principles/. Counting principle of 8+0.2-step multiplication 2 permutation 3 combination 4 simple counting problem 5 binomial theorem 5. 1 binomial theorem 5.2 properties of binomial coefficient chapter 2 probability 1 discrete random variables and their distribution list 2 hypergeometric distribution 3 conditional probability and independent events 4 binomial distribution 5 mean and variance 6 normal distribution. +0 Continuous Random Variables 6.2 Normal Distribution Chapter III Statistical Cases 1 Regression Analysis 1 Regression Analysis 1.2 Correlation Coefficient 1.3 Linearizable Regression Analysis 2 Independence Test 2.2 Basic Ideas of Independence Test 2.3 Application of Independence Test Elective Course 3-65438 Lecture on History Chapter I Overview of Mathematical Development/Kloc From the origin of mathematics, Early Development to the Formation of Elementary Mathematics 2 From Variable Mathematics to Modern Mathematics Chapter 2 Representation of Numbers and Symbols 1 and Expansion of Decimal Numbers 2 3 Mathematical Symbols Chapter 3 History of Geometry Development from Empirical Geometry to Deductive Geometry 2 Projection Geometry 3 Analytic Geometry Chapter 4 Monument in the History of Mathematics-Calculus 1 Origin of Integral Thought Chapter 5 Infinity of Calculus 1 Began to know the cardinality set of infinite 2 real numbers. Chapter VI Appreciation of Explicit Problems 1 Fermat's Last Theorem 2 Seven Bridges in the Koenigsberg Problem 3 Higher-order Equation 4 China Remainder Theorem 5 Goldbach conjecture 3-3 Geometry on Sphere May 2007 2nd Edition 5th Printing May 2009 Chapter I Basic Properties of Sphere. Position relation between plane and sphere 2 Distance between straight line and sphere Chapter II Triangle on sphere 1 spherical triangle1./intersection angle of two straight lines on sphere 1.2 Symmetry on sphere 1.3 Spherical triangle 1.4 Basic properties of spherical triangle/kloc. 3 Angular relation of spherical triangle 3. 1 Cosine theorem and sine theorem of planar triangle 3.2 Cosine theorem of spherical triangle edge 3.3 Cosine theorem and sine theorem of spherical triangle angle 4. 1 spherical dihedral 4.2 Area of spherical triangle Chapter III Euler formula and non-euclidean geometry 1 Euler formula on sphere 1 .65438+0 Euler Formula on Sphere 1.2 Euler Formula on Sphere 1.3 Polyhedron 2.2 Comparison between Euclid Geometry and Sphere Geometry 3. 1 Difference and Connection between Euclid Geometry and Sphere Geometry 3.2 Another Non-Euclid Geometry Elective Course 4- 1 The third edition of the selected lecture notes on geometric proof was printed for the third time in May 2008. In May 2009, the first chapter was the congruence of straight lines, polygons and circles and the deformation-free transformation of similar figures1.2 translation, rotation, reflection 1.3 projection theorem similar to right triangle 1.5; Circle and straight line 2.1; Theorem of circle angle 2.2; Judgment and properties of the tangent of a circle 2.3; Tangent angle theorem 2.4; Tangent Theorem 2.5; Intersecting chord theorem 3; Circle and quadrilateral 3.65. 438+0 circle inscribed quadrilateral 3.2 Ptolemy Theorem Chapter II Conic curve 1 section appreciation 2 positional relationship between straight line and ball, plane and ball 2. 1 positional relationship between straight line and ball 2.2 relationship between plane and ball 3. 1 cylinder and plane 3.2 vertical section 3.3 general section 4 plane truncated cone 4. Cone 4.2 Vertical section 4.3 General section 5 Conical section 4-3 Calculation of quantity and vector 2 Equation of vector and vector representing straight line 3 Multiplication of second-order square matrix and plane vector Chapter 2 Geometric transformation and matrix 1 Some special matrix transformations Chapter 3 Synthesis of transformation and matrix multiplication Chapter 4 Synthesis of transformation and matrix multiplication Chapter 4 Inverse transformation and inverse matrix 1 Inverse transformation and inverse matrix 2 Elementary transformation and inverse matrix 3 Second-order determinant and inverse matrix 4 Reversible matrix and linear equations Chapter 5 Eigenvalues and eigenvectors of matrices 1 Simple application of eigenvectors and eigenvectors of matrix transformation in ecological models Choose 4-4 coordinate system and parametric equation Second edition May 2007 Fifth printing May 2009 Chapter 1 coordinate system 1 plane rectangular coordinate system. 1. 1 Plane Cartesian Coordinate System and Curve Equation 1.2 Telescopic Transformation in Plane Cartesian Coordinate System 2. 1 Concept of Polar Coordinates 2.2 Interaction between Polar Coordinates of Points and Cartesian Coordinates 2.3 Interaction between Polar Coordinates of Lines and Circles 2.4 Interaction between Polar Coordinates of Curves and Cartesian Coordinates 2.5 Polar Equations of Conical Curves 3 Cylindrical Coordinates and Spherical Coordinates Chapter II Parameter Equation 1 Concept 2 Parameter equation of straight line and conic curve 2 Parameter equation of straight line 2.2 Parameter equation of circle 2.3 Parameter equation of ellipse 2.4 Parameter equation of hyperbola 3 Parameter equation is transformed into ordinary equation 4 Flat cycloid and involute 4. 1 Flat Cycloid 4.2 Involute Elective Course 4-5 Inequalities Lecture Notes 2nd Edition May 2007 5th Printing May 2009 Chapter 1 Inequalities and Basic Inequalities 2 Equations with Absolute Value 3 Proof of Average Inequalities 4 Applications of Inequalities Chapter 2 Several Important Inequalities 1 Cauchy Inequalities 2 Sorting Inequalities 3 Mathematical Induction and Bernoulli Equation