Calculus II
Xia Zirui
February 22, 2025
Contents
1
Limit and continuity
1.1
Distance
1.2
Limit
1.3
Continuous mapping and function
1.4
Limit of mapping and function
1.5
O
and
o
2
Derivative and differential
2.1
Derivative of multiple variable function
2.2
Partial derivative
2.3
Gradient
2.4
High-order partial derivative
2.5
Implicit function theorem
2.6
Curve and surface
2.7
Taylor formula
2.8
Concavity and convexity
3
Integral depending on a parameter
3.1
Definite integral depending on a parameter
3.2
General integral depending on a parameter
3.3
Criterion for uniformly convergent
3.4
Applications of integral depending on a parameter
4
Multiple integral
4.1
The concept of multiple integral
4.2
The computation of multiple integral
4.3
Change of variable for multiple integral
4.4
Functional integral on curve and surface
4.5
Curve integral of the second kind
4.6
Surface integral of the second kind
4.7
Rotation and divergence of vector field
5
Series
5.1
Series
5.2
Convergence of series
5.3
Function sequence and function series
5.4
Power series
5.5
Fourier series
5.6
Convergence of Fourier series
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