Department of Mathematics Syllabus
This syllabus is advisory only. For details on a particular instructor's syllabus (including books), consult the instructor's course page. For a list of what courses are being taught each quarter, refer to the Courses page.
MAT 125B: Real Analysis
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Lecture(s) 
Sections 
Comments/Topics 
Chapter 5 
Riemann integration 

2 
1 
Definition of Riemann integral 
2 
2 
Riemann’s definition; properties 
2 
3 
Fundamental theorem of calculus 
2 
4 
Improper integrals 
Chapter 11 
Multivariate differentiation 

2 
1 
Restricting to one variable 
Chapter 8 

1 
2 
Linear transformations 
Chapter 11 
Multivariate differentiation (continued) 

2 
2 
Differentiability 
1 
3 
Relations to univariate concepts 
2 
4 
Chain rule 
2 
5 
Multivariate MVT and Taylor’s theorem 
2 
6 
Inverse function theorem 
Chapter 12 
Multivariate integration 

2 
1 
Integrating indicator functions 
2 
2 
Multivariate Riemann integral 
2 
3 
Iterated integrals 
2 
4 
Change of variables 