【独家资料】多伦多大学topology and multi-variable calculus自编全套讲义。内容非常充实完整，是很系统的高级微积分教材。用来参考和自学都非常合适。从拓扑学入手，利用拓扑学和多维空间去阐述微积分，既侧重理论及证明，又有对运算的练习。书内有讲解以及例题。还有每一课时配套的练习，非常有难度，很值得一做。以下是目录，好资源分享给需要的小伙伴~

Topology and Multi-variable calculus

Tyler Holden

James Mracek

Department of Mathematics

University of Toronto

Contents

1 Basic Set Theory

2 Topology of Rn

3 Sequences

4 Continuity

5 Compactess

6 Connectedness

7 Parameterized curves and surfaces

8 Dierentiability

9 Taylor's theorem

10 Optimization

11 Manifolds in Rn

11.1 The Implicit and Inverse Function Theorems

11.2 Curves and Surfaces

12 Integration of R-valued functions 14

12.1 Integration on the Line

12.2 Multivariable Integration

12.3 Iterated Integrals

12.4 Change of Variables

13 Vector eld integration

13.1 Vector Derivatives

13.2 Line Integrals

13.3 Green's Theorem

13.4 Surface Integrals and the Divergence Theorem

13.5 Stokes Theorem

13.6 Dierential Form