数学分析
Workshop, China University of Petroleum at Beijing, Science, 2019
These are notes and test papers about real analysis.
Table of Contents
In mathematics, real analysis is the branch of mathematical analysis that studies the behavior of real numbers, sequence and series of real numbers, and real functions. Some particular properties of real valued sequences and functions that real analysis studies include convergence, limits, continuity, smoothness, differentiability and integrability.
Real Analysis I
Lecture Notes
- 📖Introduction
- 📖Limit of Sequence
- 📖Continuity
- 📖Mean Value Theorem
- 📖Derivative
- 📖Primitive
- 📖Definite Integral
- 📖Improper Integral
Homework
- 📝Homework of Introduction
- 📝Homework of Limits
- 📝Homework of Continuity.
- 📝Homework of Mean Value Theorem.
- 📝Homework of Derivative.
- 📝homework of Primitive.
- 📝Homework of Integral.
Test
- ✏️Test of Limits.
- ✏️Test of Continuity.
- ✏️Test of Mean Value Theorem.
- ✏️Test of Derivative.
- ✏️Test of Primitive.
List
Real Analysis II
Lecture Notes
- 📖Multi-variable Function.
- 📖Differential of Multi-variable Function.
- 📖Multiple Integral.
- 📖Line and Surface Integral.
Homework
Test
- ✏️Test for differential of multi-variable function
- ✏️Test of multiple integral
- ✏️Test of line ans surface integral
- ✏️Final Test: 18-19-2-final-test
Real Analysis III
Lecture Notes
Homework
- 📝Homework of Parameter Integral
- 📝Homework of Series
- 📝Homework of Functional Series
- 📝Homework of Power Series
- 📝Homework of Fourier Series
List
Test
References:
[1]. V. A. Zorich. Mathematical Analysis I, 2nd ed. 2015, Springer.
[2]. V. A. Zorich. Mathematical Analysis II, 2nd ed. 2015, Springer.
[3]. 陈纪修,於崇华. 数学分析上下册, 2006, 高等教育出版社.
[4]. 华东师范大学. 数学分析上下册, 2010, 高等教育出版社.
[5]. 裴礼文. 数学分析中的典型问题与方法, 2015, 高等教育出版社.
Calculus and its Visualization: an Introduction
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