Principles of Applied Mathematics: Transformation and Approximation (Advanced Book Program)

Rating:
Summary: Am I stupid or this book is too advance???
Review: This book doesn't clearify anything for you. No examples, No further explanation. It only keeps introduce various theories to you. It can compact theories that other books take 2-3 pages to explain it into 5 lines! I think you can imagine. Obviously, this book is not suitable to be your first book (not the second also). Buy it if you are sure that you are smart enough to understand it!

Rating:
Summary: Excellently organized book.
Review: This book presents various mathematical principles in an organization I have not seen before. It starts with the idea of a transformation, then goes on to relate eigenvalues and eigenvectors to general spectral theory, explain how the need for closed function spaces naturally leads to Lebesgue integration (I know about Lebesgue integration before but I didn't know why it was needed), and show how the definition of certain inverse operators leads to distribution theory. This is a very natural way of organizing these principles. While other books, such as Strang's Intro to Applied Mathematics and Rudin's Real & Complex Analysis, provide you with one mathematical "toy" after another (Fourier series, Lebesgue integration, etc.), Keener's book tells you why you need the toy before giving it to you.

Rating:
Summary: Excellently organized book.
Review: This book presents various mathematical principles in an organization I have not seen before. It starts with the idea of a transformation, then goes on to relate eigenvalues and eigenvectors to general spectral theory, explain how the need for closed function spaces naturally leads to Lebesgue integration (I know about Lebesgue integration before but I didn't know why it was needed), and show how the definition of certain inverse operators leads to distribution theory. This is a very natural way of organizing these principles. While other books, such as Strang's Intro to Applied Mathematics and Rudin's Real & Complex Analysis, provide you with one mathematical "toy" after another (Fourier series, Lebesgue integration, etc.), Keener's book tells you why you need the toy before giving it to you.