# Introduction to Mathematical Analysis I

## Dublin Core

### Description

The lecture notes contain topics of real analysis usually covered in a 10-week course: the completeness axiom, sequences and convergence, continuity, and differentiation. The lecture notes also contain many well-selected exercises of various levels. Although these topics are written in a more abstract way compared with those available in some textbooks, teachers can choose to simplify them depending on the background of the students. For instance, rather than introducing the topology of the real line to students, related topological concepts can be replaced by more familiar concepts

such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds.

such as open and closed intervals. Some other topics such as lower and upper semicontinuity, differentiation of convex functions, and generalized differentiation of non-differentiable convex functions can be used as optional mathematical projects. In this way, the lecture notes are suitable for teaching students of different backgrounds.

### Creator

Beatriz Lafferriere

Gerardo Lafferriere

Nguyen Mau Nam

### Publisher

Portland State University Library

Portland,

Portland,

### Rights

Creative Commons

### Files

### Collection

### Citation

Beatriz Lafferriere, Gerardo Lafferriere, and Nguyen Mau Nam, “Introduction to Mathematical Analysis I,”

*Open Educational Resource (OER)*, accessed January 28, 2022, http://oer.iain-padangsidimpuan.ac.id/items/show/73.