Introduction
"Methods for Solving Equations and Equations" is published by Anhui Normal University Press.
Book catalog
Foreword
General introduction
1 factorial method
2 substitution method
p>1. Single-type conversion method
2. Difference and constant conversion method
3. Mean value conversion method
Four. Cycle conversion Element Method
3 Proportional Nature Method
4 Non-negativity Method
1. Apply the non-negativity of even-order arithmetic roots
2. Use the nonnegativity of absolute value
3. Use the nonnegativity of even power or even root of real numbers
5 inequality method
1. Using mean inequalities
2. Using inequalities to determine or define the roots of equations (groups)
6 Basic solutions for elementary transcendental equations
1. Exponential equation
2. Logarithmic equation
3. Power function equation of irrational exponent
4. The simplest triangle equation
5. The simplest equation of inverse trigonometric function
7Using the root and coefficient relationship method
8 matching method
9Constructing auxiliary formula or auxiliary equation (group) method
1. Conjugate factor method
2. Apply the same solution theorem to construct auxiliary equations
3. Use square method to construct auxiliary equations
Four. Construct the auxiliary equation from the consistency of the equation structure
Five. Construct the auxiliary equation from the symmetry of the equation (set)
VI. Construct the auxiliary equation from the given conditions and functions The nature of the construction of auxiliary equations
Seven, the use of triangular duality to construct auxiliary equations (sets)
10 discriminant method
11 formula method
< p>1. Formula method for root extraction2. Formula method for root finding
3. Inverse usage of formula for root finding
Four. Formula method for multiplication
p>5. Cramer formula method
12 multiplication method
13 uniqueness method
1. Using irrational number expression form Uniqueness
2. When using complex numbers to be equal, the uniqueness of the corresponding equal parts of the real and imaginary parts
3. The uniqueness of using fractions to transform into continued fractions
< p>Four. Use the same number of powers to equal the sum of isomorphic terms, and the uniqueness of the corresponding exponentsFive. Use the same number of fractional isomorphic terms to equal the sum, the numerators correspond to the same, and the uniqueness of the denominator
The rational root method of 14 rational coefficient equations
15 triangle substitution method
16 fraction equation deformation method
1. True Fraction method
Two. Multiplying common denominator and rounding method
Three. Reduction method
Four. Substitution method
Five , Proportion Method
Six. Discussion Method
Seven. Partial Fraction Method
8. Subsection Method Method of division
Nine. Determinant method
17 Zero point subsection method
18 Constant and variable interchange method
19 Equation group Elimination method
1. Substitution elimination method
2. Comparative elimination method
3. Addition and subtraction elimination method
4. Gaussian Elimination Method
Auxiliary Angle Method of 20 Triangular Equations
21 Accumulation and Multiplication
22 Resultant Method
23 Solving method of symmetric equation system
1. Solving method of first kind of symmetric equation system
2. Solving method of second kind of symmetric equation system
24 division method< /p>
25 reciprocal equation solutions
1. Types and properties of reciprocal equations
2. Reciprocal equation solutions
26 open methods< /p>
27 definition domain and value range discussion method
28 function monotonicity method
29 geometry method
30 indefinite equation solution
p>One, two-variable first-degree indeterminate equations
Second, multiple-variable first-degree indefinite equations and equations
Three. Pell equation solution
Four. The solution of the Pythagorean equation
Five. The rational ratio method for solving the indefinite equation xy =22
VI. The solution form is ay2 = x(x+1) quadratic indefinite The recursive method of the equation
Seven. The parity analysis method for solving the multivariate high-order indeterminate equation
31 The method of solving linear congruence equations
1. Congruence The concept and properties of the formula
2. Residual class and complete residual system
3. Simplified residual system
4. Euler theorem, Fermat theorem, Wilson theorem< /p>
Five. The solution of linear congruence equations
VI. The solution of first-order congruence equations
Conclusion