75376 - Calculus

Learning outcomes

At the end of the course the student has comprehensive, in-depth coverage of the topics required in a one-term course in advanced calculus and real analysis. The course is thought for students who have had a course in introductory algebra and undergraduate calculus. As for calculus, the student acquires a solid foundation in several variables calculus, vector analysis, linear algebra, systems of differential equations, vector fields, extremum problems.
Major emphasis will be given on differential equations, linear algebra and especially topics in real analysis.

Course contents

1 First Order Equations
2 Second Order Equations
3 Graphical and Numerical Methods
4 Linear Equations and Inverse Matrices
5 Vector Spaces and Subspaces
6 Eigenvalues and Eigenvectors
7 Applied Mathematics and ATA
8 Fourier and Laplace Transforms

9 Riemann Integral

10 Lebesgue Integral

11 Lebesgue Spaces

12 Absolute Continuity

13 Measure Theory

Readings/Bibliography

https://www.amazon.com/Real-Complex-Analysis-Higher-Mathematics/dp/0070542341/ref=sr_1_3?s=books&ie=UTF8&qid=1465802950&sr=1-3&keywords=rudin+analysis

 

https://www.amazon.com/Analysis-Probability-Cambridge-Advanced-Mathematics/dp/0521007542/ref=sr_1_1?s=books&ie=UTF8&qid=1465802977&sr=1-1&keywords=real+analysis+and+probability

Teaching methods

Regular blackboard lectures.

Assessment methods

Written and oral exams.

Teaching tools

Supplementary notes and material may be suggested and handed out during the course.

Office hours

See the website of Enrico Bernardi