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  • University of Illinois at Urbana-Champaign
Basic Analysis: Introduction to Real Analysis
Conditional Remix & Share Permitted
CC BY-NC-SA
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This free online textbook is a one semester course in basic analysis. These were my lecture notes for teaching Math 444 at the University of Illinois at Urbana-Champaign (UIUC) in fall 2009. The course is a first course in mathematical analysis aimed at students who do not necessarily wish to continue a graduate study in mathematics. A Sample Darboux sums prerequisite for the course is a basic proof course. The course does not cover topics such as metric spaces, which a more advanced course would. It should be possible to use these notes for a beginning of a more advanced course, but further material should be added.

Access also available here: https://www.jirka.org/ra/

Table of Contents
Introduction
1 Real Numbers
2 Sequences and Series
3 Continuous Functions
4 The Derivative
5 The Riemann Integral
6 Sequences of Functions
7 Metric Spaces

Subject:
Mathematics
Material Type:
Textbook
Provider:
University of Illinois at Urbana-Champaign
Author:
Jiří Lebl
Date Added:
04/24/2019
Notes on Diffy Qs: Differential Equations for Engineers
Conditional Remix & Share Permitted
CC BY-NC-SA
Rating

A first one-semester course on differential equations aimed at engineers.

Table of Contents
First order ODEs
Higher order linear ODEs
Systems of ODEs
Fourier series and PDEs
Eigenvalue problems
The Laplace transform
Power series methods
Nonlinear systems

Reviews available here: https://open.umn.edu/opentextbooks/textbooks/notes-on-diffy-qs-differential-equations-for-engineers

Subject:
Engineering
Calculus
Material Type:
Full Course
Textbook
Provider:
University of Illinois at Urbana-Champaign
Provider Set:
Individual Authors
Author:
Jiri Lebl
Date Added:
04/24/2019