The first chapter is the limit of unary function.
1. 1 function
First, about the inverse function.
Second, odd function, even function
Third, the periodic function
Four, several commonly used inequalities
Fifth, find the general term of recursive sequence.
1.2 Prove the existence of limit by definition
First, prove the limit by definition.
Second, prove the limit with Cauchy criterion
Third, negative form.
4. Prove the existence of limit by monotone boundedness principle.
Fifth, the limit relationship between sequence and subsequence, function and sequence.
VI. Restrictions on the operability of symbols
The first chapter is the limit of unary function.
1. 1 function
First, about the inverse function.
Second, odd function, even function
Third, the periodic function
Four, several commonly used inequalities
Fifth, find the general term of recursive sequence.
1.2 Prove the existence of limit by definition
First, prove the limit by definition.
Second, prove the limit with Cauchy criterion
Third, negative form.
4. Prove the existence of limit by monotone boundedness principle.
Fifth, the limit relationship between sequence and subsequence, function and sequence.
Sixth, the operational nature of limit.
Several methods to find the limit value in 1.3
First of all, use equivalent substitution and elementary deformation to find the limit.
A. Equivalent substitution
B. Using elementary deformation to find the limit
Second, using known limits
Third, use variable substitution to find the limit.
Fourth, the two-sided attack rule
Fifthly, the generalized form of double-sided clamping rule.
Six, other commonly used methods to find the limit
A. Hospital (usually translated as L'H?pital) rules.
B. Find the limit with Taylor formula
C. Find the limit with integral definition
D. Using series to solve limit problems
E. using continuity to find the limit
F. Comprehensive examples
1.4O.Stolz formula
First, the situation of the series
Second, the situation of functional limits
Recursive form of 1.5 limit
First, use existence to seek the limit.
Second, write the general term of limit.
Third, displacement and deformation.
Fourth, the graphic method
Generalization of fixed point method of verb (abbreviation of verb)
Sixth, the application of stolz formula.
Upper and lower bounds of 1.6 sequence
1. Describe the upper and lower limits in ε-N language.
Second, the upper and lower bounds are described by the limit of the sub-column.
Third, the upper and lower bounds are described by the limit of the supremum.
Fourthly, the upper and lower bounds are used to study the limit of sequence.
5. Operational properties of upper and lower limits
Upper and lower bounds of 1.7 function
Definition and equivalent description of upper and lower bounds of 1. function
Second, the unilateral upper and lower limits
Three. Inequalities of upper and lower bounds of functions
1.8 real number and its basic theorem
First, introduce real numbers.
Second, the basic theorem of real numbers
Chapter II Continuity of Univariate Functions
Chapter III One-dimensional Calculus
The fourth chapter is the integral of unary function.
The fifth chapter series
Chapter VI Differential of Multivariate Functions
Chapter VII Multivariate Integral calculus