Analytical Mechanics: Solutions to Problems in Classical Physics

Analytical Mechanics: Solutions to Problems in Classical Physics by Ioan Merches and Daniel Radu


English | 2014 | ISBN: 1482239396 | 456 pages | PDF | 2,5 MB

Giving students a thorough grounding in basic problems and their solutions, Analytical Mechanics: Solutions to Problems in Classical Physics presents a short theoretical description of the principles and methods of analytical mechanics, followed by solved problems. The authors thoroughly discuss solutions to the problems by taking a comprehensive approach to explore the methods of investigation. They carefully perform the calculations step by step, graphically displaying some solutions via Mathematica® 4.0.




This collection of solved problems gives students experience in applying theory (Lagrangian and Hamiltonian formalisms for discrete and continuous systems, Hamilton-Jacobi method, variational calculus, theory of stability, and more) to problems in classical physics. The authors develop some theoretical subjects, so that students can follow solutions to the problems without appealing to other reference sources. This has been done for both discrete and continuous physical systems or, in analytical terms, systems with finite and infinite degrees of freedom. The authors also highlight the basics of vector algebra and vector analysis, in Appendix B. They thoroughly develop and discuss notions like gradient, divergence, curl, and tensor, together with their physical applications.




There are many excellent textbooks dedicated to applied analytical mechanics for both students and their instructors, but this one takes an unusual approach, with a thorough analysis of solutions to the problems and an appropriate choice of applications in various branches of physics. It lays out the similarities and differences between various analytical approaches, and their specific efficiency.

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Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics) by Frederick Mosteller

Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics) by Frederick Mosteller


English | May 1, 1987 | ISBN: 0486653552 | 96 Pages | PDF | 2 MB

Can you solve the problem of "The Unfair Subway"?


Marvin gets off work at random times between 3 and 5 p.m. His mother lives uptown, his girlfriend downtown. He takes the first subway that comes in either direction and eats dinner with the one he is delivered to. His mother complains that he never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain.


Marvin's adventures in probability are one of the fifty intriguing puzzles that illustrate both elementary ad advanced aspects of probability, each problem designed to challenge the mathematically inclined. From "The Flippant Juror" and "The Prisoner's Dilemma" to "The Cliffhanger" and "The Clumsy Chemist," they provide an ideal supplement for all who enjoy the stimulating fun of mathematics.


Professor Frederick Mosteller, who teaches statistics at Harvard University, has chosen the problems for originality, general interest, or because they demonstrate valuable techniques. In addition, the problems are graded as to difficulty and many have considerable stature. Indeed, one has "enlivened the research lives of many excellent mathematicians." Detailed solutions are included. There is every probability you'll need at least a few of them.

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Bayesian Networks: With Examples in R

Bayesian Networks: With Examples in R By Marco Scutari


2014 | 241 Pages | ISBN: 1482225581 | PDF | 2 MB

Understand the Foundations of Bayesian Networks—Core Properties and Definitions Explained


Bayesian Networks: With Examples in R introduces Bayesian networks using a hands-on approach. Simple yet meaningful examples in R illustrate each step of the modeling process. The examples start from the simplest notions and gradually increase in complexity. The authors also distinguish the probabilistic models from their estimation with data sets.


The first three chapters explain the whole process of Bayesian network modeling, from structure learning to parameter learning to inference. These chapters cover discrete Bayesian, Gaussian Bayesian, and hybrid networks, including arbitrary random variables.


The book then gives a concise but rigorous treatment of the fundamentals of Bayesian networks and offers an introduction to causal Bayesian networks. It also presents an overview of R and other software packages appropriate for Bayesian networks. The final chapter evaluates two real-world examples: a landmark causal protein signaling network paper and graphical modeling approaches for predicting the composition of different body parts.


Suitable for graduate students and non-statisticians, this text provides an introductory overview of Bayesian networks. It gives readers a clear, practical understanding of the general approach and steps involved.

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