This whole book aims to bring ideas and algorithms together. I am convinced that they must be taught and learned in the same course. The algorithm clarifies the idea. The old method, separation of responsibilities , no longer works: Not perfect Mathematics courses teach analytical techniques Engineering courses work on real problems Even within computational science there is a separation we don't need: Not efficient Mathematics courses analyze numerical algorithms Engineering and computer science implement the software I believe it is time to teach and learn the reality of computational science and engineering. I hope this book helps to move that beautiful subj ect forward. Thank you for reading it .