Numerical Methods for Ordinary Differential Equations: Initial Value Problems - Griffiths, Higham

[Completed]

This is an exceptional resource for those who want to start learning about the numerical methods used to solve IVPs. Authors adopt a step-by-step approach, explaining new ideas and providing numerous examples and simulations to illustrate the concepts. Mathematical complexities are kept to a minimum making it easy to grasp the fundamental concepts. I particularly enjoyed reading the chapters on geometric integration of Hamiltonian systems for long-term simulations; specialized methods designed to preserve system invariants (I might puruse this topic in the future). Overall, this book is a great starting point to learn about the subject. I truely enjoyed it!

PoW

Stochastic Models, Estimation, and Control: Part 1 - Peter S. Maybeck

[Completed]

This is truly a masterpiece. The author's practical experience implementing Kalman filters shines through in every page. The approach is remarkable—beginning with an accessible introduction to stochastic processes before guiding readers into the realm of filtering. The chapter on performance analysis stands out as an invaluable resource for filter design and tuning, elegantly introducing how sensory data can be combined within the filtering context. It offers profound insights into the fundamental nature of filtering problems. I can't imagine a better treatment of Kalman filtering than what this accomplished author has provided. I'm definitely continuing on to Part II of his book.

PoW

Computer methods for ordinary differential equations and differential-algebraic equations - Ascher, Petzold

[Partially Read]

This book is quite unique. It covers a wide range of interesting ideas, but there are a lot of places in the book where the authors introduce concepts without providing immediate explanations, challenging the reader to persevere and think critically. This book demands active engagement and a willingness to refer to external resources to grasp the more complex ideas. Compared to the previous title (1), it provides a more in-depth analysis of the subject matter using more sophisticated mathematics. I have a love-hate relationship with this book (mostly hate). I love that it introduces complex ideas for solving ODEs, but I hate that it leaves all the heavy lifting needed to understand them to me!