This two-semester course is designed as a basic analysis course after
Advanced Calculus. It can be taken parallel to or prior to real analysis.
The main purpose is to provide students basic functional analysis
background for studying applied mathematics, including partial
differential equations, image science, inverse problems and computational mathematics.

I will mainly follow the lecture note on Applied Analysis written by
John Hunter and Bruno Nachtergaele.
In the first semester, I will cover Chapter 1-9. In the second semester, I will cover Chapter 10-13 with more applications on Calculus of Variation.
In this course, applications and examples will be emphersized. In addition to the examples provided in the textbook, students are requested to find more examples to understand the insight of important analytic techniques.
The table of contents of this textbook is the follows.

Chapter 1: Metric and Normed Spaces (1-34)
Chapter 2: Continuous Functions (35-60)
Chapter 3: The Contraction Mapping Theorem (61-79)
Chapter 4: Topological Spaces (81-89)
Chapter 5: Banach Spaces (91-123)
Chapter 6: Hilbert Spaces (125-147)
Chapter 7: Fourier Series (149-186)
Chapter 8: Bounded Linear Operators on a Hilbert Space (187-214)
Chapter 9: The Spectrum of Bounded Linear Operators (215-243)
Chapter 10: Linear Differential Operators and Green's Functions (245-286)
Chapter 11: Distributions and the Fourier Transform (287-333)
Chapter 12: Measure Theory and Function Spaces (335-377)
Chapter 13: Differential Calculus and Variational Methods (379-426)
References (427-429)

The e-book is available on the website.