Tim Hsu, San Jose State University, CA.

• OvertureComplex functions of a real variable: Real and complex numbersComplex-valued calculusSeries of functionsFourier series and Hilbert spaces: The idea of a function spaceFourier seriesHilbert spacesConvergence of Fourier seriesOperators and differential equations: PDEs and diagonalizationOperators on Hilbert spacesEigenbases and differential equationsThe Fourier transform and beyond: The Fourier transformApplications of the Fourier transformWhat's next?Rearrangements of seriesLinear algebraBump functionsSuggestions for problemsBibliographyIndex of selected notationIndex

“-;This is an interesting take on the second course in analysis: rather than the Lebesgue integral, we study Fourier analysis and applications. The book is well done and makes a strong case for this approach. The Introduction (which is the Introduction for the Instructor) is one of the best I.ve read, and you should definitely study if you are considering adopting the book. It explains very clearly the goals of the book, the limitations of this approach, and some other unusual features of the book.” - Allen Stenger, MAA Reviews

Tim Hsu, San Jose State University, CA.

• OvertureComplex functions of a real variable: Real and complex numbersComplex-valued calculusSeries of functionsFourier series and Hilbert spaces: The idea of a function spaceFourier seriesHilbert spacesConvergence of Fourier seriesOperators and differential equations: PDEs and diagonalizationOperators on Hilbert spacesEigenbases and differential equationsThe Fourier transform and beyond: The Fourier transformApplications of the Fourier transformWhat's next?Rearrangements of seriesLinear algebraBump functionsSuggestions for problemsBibliographyIndex of selected notationIndex

“-;This is an interesting take on the second course in analysis: rather than the Lebesgue integral, we study Fourier analysis and applications. The book is well done and makes a strong case for this approach. The Introduction (which is the Introduction for the Instructor) is one of the best I.ve read, and you should definitely study if you are considering adopting the book. It explains very clearly the goals of the book, the limitations of this approach, and some other unusual features of the book.” - Allen Stenger, MAA Reviews

Tim Hsu, San Jose State University, CA.

• OvertureComplex functions of a real variable: Real and complex numbersComplex-valued calculusSeries of functionsFourier series and Hilbert spaces: The idea of a function spaceFourier seriesHilbert spacesConvergence of Fourier seriesOperators and differential equations: PDEs and diagonalizationOperators on Hilbert spacesEigenbases and differential equationsThe Fourier transform and beyond: The Fourier transformApplications of the Fourier transformWhat's next?Rearrangements of seriesLinear algebraBump functionsSuggestions for problemsBibliographyIndex of selected notationIndex

“-;This is an interesting take on the second course in analysis: rather than the Lebesgue integral, we study Fourier analysis and applications. The book is well done and makes a strong case for this approach. The Introduction (which is the Introduction for the Instructor) is one of the best I.ve read, and you should definitely study if you are considering adopting the book. It explains very clearly the goals of the book, the limitations of this approach, and some other unusual features of the book.” - Allen Stenger, MAA Reviews