1. 1 integer

1.2 rational number system

1.3 rational number sequence

1.4 real number system

Brief introduction of 1.5 infinite decimal method

1.6 brief introduction of Dai Dejin district.

The supremum principle on 1.7 and the power of real exponent

Completeness and compactness of 1.8 real numbers

1.9 extension of real number to complex number

practise

Chapter II Sequence and Series

2. Limit of1sequence

2.2 Stoz Theorem and Its Application

2.3 Upper and Lower Limits

2.4 Real number series

2.5 Infinite product

2.6 Typical examples

Exercise 2

Chapter III Continuity

3. Limit and continuity of1function

3.2 Preliminary topology

3.3 Properties of continuous functions

3.4 discontinuity

3.5 Semi-continuous and bounded variogram

3.6p base

Exercise 3

Chapter IV Differential and Integral

4. 1 Differential and Mean Value Theorem

4.2 L'H?pital's Law and Taylor Formula

4.3 Lectures on Selected Typical Cases

4.4 Riemann-Stinger integral

4.5 Inequality

4.6 Convex function

4.7 numbers e and 7c

4.8 multivariate function

Exercise 4

Chapter V Uniform Convergence

5. Uniform Convergence of1Function Sequence

5.2 Properties of convergent sequences

5.3 Convergence of Series Sum of Function Terms

5.4 polynomial approximation

5.5 power series

5.6 Fourier series

5.7 Equal continuity

Exercise 5

Chapter VI Generalized Integral

6. Integral on1infinite interval

6.2 convergence criteria

6.3 defect integral

6.4 Generalized Integral and Series

6.5 Integral with Parameters on Finite Interval

6.6 Generalized Integral of Parameter Variables

6.7 Properties of Uniform Convergence Integral

6.8 Euler integral

Exercise 6

philology