math
Tsinghua University 2010-2011 Final Volume of Advanced Mathematics
Papers made 2 years ago, self-evaluation. This set of papers is relatively average, in line with the difficulty of 10 years ago, but now the papers are getting more and more difficult!
Summarize
Limits
Limits are one of the core concepts in calculus and require mastery of the following:
Symbols and definitions
of limits Basic properties of limits: uniqueness, local boundedness, number-preserving and four arithmetic rules
Important theorems of limits: clamping theorem, monotone bounded principle, L'Hopital's rule
Derivatives
(also known as derivatives) ) is a tool to describe the local rate of change of a function, which needs to strengthen the following knowledge:
The definition and graphic meaning
of derivatives The basic properties of derivatives: derivable must be continuous, the derivation rules of derivable functions, the geometric meaning and physical meaning of derivable functions The concept and calculation method of higher
order
derivatives
Another important content in calculus requires the following knowledge:
Definition of definite integral and indefinite integral and their relationship
Basic formula of integral and application of integral with substitution and integral by parts
Physical and geometrical application of integral: mass, center of gravity, area, arc length, etc.