Authors: Xu Senlin, Xue Chunhua,

Pricing: 36 yuan

Publication date: 2005- 10- 1

Publishing House: Tsinghua University Publishing House, Volume 1 includes the limit of sequence, the limit and continuity of function, the derivative and differential mean value theorem of unary function, Taylor formula, indefinite integral and Riemann integral. There are a large number of typical examples in the book, and the exercises are divided into three levels: exercise questions, thinking questions and review questions.

This set of books can be used as teaching materials for mathematics majors in science and engineering universities or normal universities, especially for basic or experimental courses, and can also be used as reference books for university teachers and mathematicians. Preface 1

Chapter 1 series restrictions 1

The limit concept of 1. 1 sequence 1

Basic properties of 1.2 sequence 15 limit

1.3 real number theory, real number continuity proposition 26

Cauchy convergence criterion (principle) of 1.4, limit of monotone sequence, number e=limn→+∞ 1+ 1nn42.

1.5 upper and lower limits 59

1.6 Stoertz formula 70

Review questions 176

Chapter II Function Limit and Continuity 8 1

2. The concept of1function limit 8 1

2.2 Nature of Functional Limitations 99

2.3 Infinitesimal (large) quantity of order of magnitude 1 15

2.4 Continuity of functions, discontinuous point sets of monotone functions and continuity of elementary functions 123

2.5 Properties of continuous functions on bounded closed interval [a, b] 135

Review question 2 150

Chapter III Derivative and Differential Mean Value Theorem of Univariate Functions 153

3. 1 derivative and its algorithm 153

3.2 Leibniz formula 17 1 For higher-order derivatives, derivatives and derivatives of parametric functions.

3.3 Differential Mean Value Theorem 185

3.4L Hospital Rules 198

3.5 Study one of the derivative functions: monotonicity, extremum, maximum value 206.

3.6 Study the quadratic function with derivative: concavity and convexity, as shown in Figure 22 1.

Review question 324 1

Chapter 4 Taylor formula 245

4. 1 Taylor formula with various residuals 245

4.2 Taylor formula application 265

Review question 4279

The fifth chapter indefinite integral 282

5. 1 primitive function, indefinite integral 282

5.2 Alternative integration method, integration by parts 293

5.3 The indefinite integral of rational function can be changed into the indefinite integral of rational function 3 1 1

Review question 5326

Chapter VI Riemann Integral 328

6. The concept of1Riemannian integral, the necessary and sufficient condition of Riemannian integrability 328

6.2 Properties of Riemann Integral, First and Second Mean Value Theorems of Integral 353

6.3 Basic Theorem and Formula of Calculus 37 1

6.4 Substitution of Riemann Integral and Partial Integral 386

6.5 Generalized Integral 399

6.6 Application of Riemann Integral and Generalized Integral 427

Review question 6444

Reference 449