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112 results in Mathematical Methods

Page 1 of 6

Tensors
  • Basics and Applications with Scilab Problems
  • Pushpa Bindal, Vandna Luthra
  • Coming soon
  • Expected online publication date:
    October 2025
    Print publication:
    01 November 2026

Probability Theory for Quantitative Scientists
  • Luca Leuzzi, Enzo Marinari, Giorgio Parisi
  • Coming soon
  • Expected online publication date:
    September 2025
    Print publication:
    30 September 2025
  • Based on the long-running Probability Theory course at the Sapienza University of Rome, this book offers a fresh and in-depth approach to probability and statistics, while remaining intuitive and accessible in style. The fundamentals of probability theory are elegantly presented, supported by numerous examples and illustrations, and modern applications are later introduced giving readers an appreciation of current research topics. The text covers distribution functions, statistical inference and data analysis, and more advanced methods including Markov chains and Poisson processes, widely used in dynamical systems and data science research. The concluding section, 'Entropy, Probability and Statistical Mechanics' unites key concepts from the text with the authors' impressive research experience, to provide a clear illustration of these powerful statistical tools in action. Ideal for students and researchers in the quantitative sciences this book provides an authoritative account of probability theory, written by leading researchers in the field.

Solving Problems with Projections
  • From Phase Retrieval to Packing
  • Veit Elser
  • Coming soon
  • Expected online publication date:
    June 2025
    Print publication:
    30 June 2025
  • It is a curious fact that even notoriously difficult computational problems can be expressed in the form of a high-dimensional Venn diagram, where solutions lie in the overlap of a pair of remarkably simple sets, A and B. The simplicity of these sets enables operations called projections that locate the nearest point of A, or B, starting anywhere within the high-dimensional space. This book introduces a novel method for tackling complex problems that exploits projections and the two-set structure, offering an effective alternative to traditional, gradient-based approaches. Beginning with phase retrieval, where A and B address the properties of an image and its Fourier transform, it progresses to more diverse challenges, such as sphere packing, origami design, sudoku and tiling puzzles, data dimension reduction, and neural network training. The text presents a detailed description of this powerful and original approach and is essential reading for physicists and applied mathematicians.

Advanced Linear Algebra
  • A Concise Text with Contemporary Applications
  • 2nd edition
  • Yisong Yang
  • Coming soon
  • Expected online publication date:
    May 2025
    Print publication:
    31 May 2025
  • The second edition of this engaging textbook for advanced undergraduate students and beginning graduates covers all the core subjects in linear algebra. It has a unique emphasis on integrating ideas from analysis, in addition to pure algebra, and features a balance of abstraction, practicality, and contemporary applications. Four chapters examine some of the most important of these applications, including quantum mechanics, machine learning, data science, and quantum information. The material is supplemented by a rich collection of exercises designed for students from diverse backgrounds, including a wealth of newly added ones in this edition. Selected solutions are provided at the back of the book for use in self-study, and full solutions are available online to instructors.

Rotation Sequences and the Theory of Vectors and Coordinates
  • Don Koks
  • Published online:
    17 April 2025
    Print publication:
    24 April 2025
  • This book applies rotation theory to problems involving vectors and coordinates, with an approach that combines easily visualised procedures with smart mathematics. It constructs rotation theory from the ground up, building from basic geometry through to the motion and attitude equations of rockets, and the tensor analysis of relativity. The author replaces complicated pictures of superimposed axes with a simple and intuitive procedure of rotating a model aircraft, to create rotation sequences that are easily turned into mathematics. He combines the best of the 'active' and 'passive' approaches to rotation into a single coherent theory, and discusses many potential traps for newcomers. This volume will be useful to astronomers and engineers sighting planets and satellites, computer scientists creating graphics for movies, and aerospace engineers designing aircraft; also to physicists and mathematicians who study its abstract aspects.

Notes, Problems and Solutions in Differential Equations
  • A. K. Nandakumaran, P.S. Datti
  • Published online:
    15 April 2025
    Print publication:
    31 May 2025
  • This book is designed for senior undergraduate and graduate students pursuing courses in mathematics, physics, engineering and biology. The text begins with a study of ordinary differential equations. The concepts of first- and second-order equations are covered initially. It moves further to linear systems, series solutions, regular Sturm–Liouville theory, boundary value problems and qualitative theory. Thereafter, partial differential equations are explored. Topics such as first-order partial differential equations, classification of partial differential equations and Laplace and Poisson equations are also discussed in detail. The book concludes with heat equation, one-dimensional wave equation and wave equation in higher dimensions. It highlights the importance of analysis, linear algebra and geometry in the study of differential equations. It provides sufficient theoretical material at the beginning of each chapter, which will enable students to better understand the concepts and begin solving problems straightaway.

Quantum Mechanics through Problems
  • With Complete Solutions
  • Rocco Schiavilla
  • Published online:
    05 December 2024
    Print publication:
    12 December 2024
  • This book contains more than 300 problems in quantum mechanics with accompanying solutions, covering topics that are commonly taught in first-year graduate physics programs. Special care is given to each problem's formulation, with detailed and extensive solutions provided to support understanding. The problems span a range of difficulties, from basic exercises to more challenging applications and extensions of the standard material. Students are required to think critically and incorporate physics and mathematical techniques learned previously or concurrently to solve the more challenging problems. Each chapter begins by framing the particular topic being examined with a short theory section that sets the context for and motivates the problems that follow. This text is well suited for self-study or as a useful supplement to the existing quantum mechanics textbooks for upper-undergraduate and graduate students, and their instructors.

A Computational Introduction to Quantum Physics
  • Sølve Selstø
  • Published online:
    24 April 2024
    Print publication:
    25 April 2024
  • This concise textbook introduces an innovative computational approach to quantum mechanics. Over the course of this engaging and informal book, students are encouraged to take an active role in learning key concepts by working through practical exercises. The book equips readers with some basic methodology and a toolbox of scientific computing methods, so they can use code to simulate and directly visualize how quantum particles behave. The important foundational elements of the wave function and the Schrödinger equation are first introduced, then the text gradually builds up to advanced topics including relativistic, open, and non-Hermitian quantum physics. This book assumes familiarity with basic mathematics and numerical methods, and can be used to support a two-semester advanced undergraduate course. Source code and solutions for every book exercise involving numerical implementation are provided in Python and MATLAB®, along with supplementary data. Additional problems are provided online for instructor use with locked solutions.

A First Guide to Computational Modelling in Physics
  • Pawel Scharoch, Maciej P. Polak, Radosław Szymon
  • Software developed by Katarzyna Holodnik-Malecka
  • Published online:
    01 February 2024
    Print publication:
    08 February 2024
  • This innovative text helps demystify numerical modelling for early-stage physics and engineering students. It takes a hands-on, project-based approach, with each chapter focusing on an intriguing physics problem taken from classical mechanics, electrodynamics, thermodynamics, astrophysics, and quantum mechanics. To solve these problems, students must apply different numerical methods for themselves, building up their knowledge and practical skills organically. Each project includes a discussion of the fundamentals, the mathematical formulation of the problem, an introduction to the numerical methods and algorithms, and exercises, with solutions available to instructors. The methods presented focus primarily on differential equations, both ordinary and partial, as well as basic mathematical operations. Developed over many years of teaching a computational modelling course, this stand-alone book equips students with an essential numerical modelling toolkit for today's data-driven landscape, and gives them new ways to explore science and engineering.

Computing in Scilab
  • Chetana Jain
  • Published online:
    15 October 2023
    Print publication:
    05 January 2023
  • SciLab is a free open-source computing and graphics tool that allows students to learn physical and mathematical concepts with ease. Computing in SciLab has been designed for undergraduate students of physics and electronics following the CBCS-LOCF syllabus, and with extensive coverage of concepts, it focuses primarily on the applications of SciLab in improving the problem-solving skills of readers. All these tools are classroom-tested and focus on data visualization and numerical computing with SCILAB. The book covers important topics like linear algebra, matrices, plotting tools, curve fitting, differential equations, integral calculus, Fourier analysis, and equation solving.

Python for Chemists
  • Christian Hill
  • Published online:
    12 October 2023
    Print publication:
    26 October 2023
  • This accessible and self-contained guide provides a comprehensive introduction to the popular programming language Python, with a focus on applications in chemistry and chemical physics. Ideally suited to students and researchers of chemistry learning to employ Python for problem-solving in their research, this fast-paced primer first builds a solid foundation in the programming language before progressing to advanced concepts and applications in chemistry. The required syntax and data structures are established, and then applied to solve problems computationally. Popular numerical packages are described in detail, including NumPy, SciPy, Matplotlib, SymPy, and pandas. End of chapter problems are included throughout, with worked solutions available within the book. Additional resources, datasets, and Jupyter Notebooks are provided on a companion website, allowing readers to reinforce their understanding and gain confidence applying their knowledge through a hands-on approach.

Computational Grains
  • Micromechanical Genome for Heterogeneous Materials
  • Leiting Dong, Satya N. Atluri
  • Published online:
    05 October 2023
    Print publication:
    19 October 2023
  • This is the first book that systemically introduces the theory and implementation of Computational Grains for micromechanical modeling of heterogeneous materials. This book covers the specifically designed mathematics embedded in Computational Grains, and the entire process of microstructure construction, tessellation, CG simulation and homogenization. The Computational Grains discussed in this book consider elastic, non-elastic, and multi-physics solids. Materials damage development are also preliminarily discussed, with CGs considering matrix-inclusion debonding as well as embedded microcracks. Presenting the theory step-by-step and with detailed examples and MATLAB codes, the material is accessible and practical for readers. This will be ideal for graduate students and researchers in mechanical and aerospace engineering and applied mechanics.

Numerical Methods in Physics with Python
  • 2nd edition
  • Alex Gezerlis
  • Published online:
    30 August 2023
    Print publication:
    20 July 2023
  • Bringing together idiomatic Python programming, foundational numerical methods, and physics applications, this is an ideal standalone textbook for courses on computational physics. All the frequently used numerical methods in physics are explained, including foundational techniques and hidden gems on topics such as linear algebra, differential equations, root-finding, interpolation, and integration. The second edition of this introductory book features several new codes and 140 new problems (many on physics applications), as well as new sections on the singular-value decomposition, derivative-free optimization, Bayesian linear regression, neural networks, and partial differential equations. The last section in each chapter is an in-depth project, tackling physics problems that cannot be solved without the use of a computer. Written primarily for students studying computational physics, this textbook brings the non-specialist quickly up to speed with Python before looking in detail at the numerical methods often used in the subject.

Data Modeling for the Sciences
  • Applications, Basics, Computations
  • Steve Pressé, Ioannis Sgouralis
  • Published online:
    17 August 2023
    Print publication:
    31 August 2023
  • With the increasing prevalence of big data and sparse data, and rapidly growing data-centric approaches to scientific research, students must develop effective data analysis skills at an early stage of their academic careers. This detailed guide to data modeling in the sciences is ideal for students and researchers keen to develop their understanding of probabilistic data modeling beyond the basics of p-values and fitting residuals. The textbook begins with basic probabilistic concepts, models of dynamical systems and likelihoods are then presented to build the foundation for Bayesian inference, Monte Carlo samplers and filtering. Modeling paradigms are then seamlessly developed, including mixture models, regression models, hidden Markov models, state-space models and Kalman filtering, continuous time processes and uniformization. The text is self-contained and includes practical examples and numerous exercises. This would be an excellent resource for courses on data analysis within the natural sciences, or as a reference text for self-study.

Computational Design of Engineering Materials
  • Fundamentals and Case Studies
  • Yong Du, Rainer Schmid-Fetzer, Jincheng Wang, Shuhong Liu, Jianchuan Wang, Zhanpeng Jin
  • Published online:
    29 June 2023
    Print publication:
    29 June 2023
  • Introducing state-of-the art computational methods, this book combines detailed explanations with real-world case studies to give a full grounding in the design of engineering materials. This book presents a wide spectrum of key computational methods, such as CALPHAD-method, first-principles calculations, phase-field simulation and finite element analysis, covering the atomic-meso-macro scale range. The reader will see these methods applied to case studies for steel, light alloys, superalloys, cemented carbides, hard coating and energy materials, demonstrating in detail how real-world materials are designed. Online ancillary material includes input files for computational design software, providing the reader with hands-on design experience. Step-by-step instructions will allow you to perform and repeat the simulations discussed in the book. Aimed at both graduate and undergraduate students as well as non-specialist researchers in materials science and engineering, including ceramics, metallurgy, and chemistry, this is an ideal introductory and reference book.

Mathematical Methods for Physics
  • An Introduction to Group Theory, Topology and Geometry
  • Esko Keski-Vakkuri, Claus Montonen, Marco Panero
  • Published online:
    08 December 2022
    Print publication:
    22 December 2022
  • This detailed yet accessible text provides an essential introduction to the advanced mathematical methods at the core of theoretical physics. The book steadily develops the key concepts required for an understanding of symmetry principles and topological structures, such as group theory, differentiable manifolds, Riemannian geometry, and Lie algebras. Based on a course for senior undergraduate students of physics, it is written in a clear, pedagogical style and would also be valuable to students in other areas of science and engineering. The material has been subject to more than twenty years of feedback from students, ensuring that explanations and examples are lucid and considered, and numerous worked examples and exercises reinforce key concepts and further strengthen readers' understanding. This text unites a wide variety of important topics that are often scattered across different books, and provides a solid platform for more specialized study or research.

Continuous Groups for Physicists
  • Narasimhaiengar Mukunda, Subhash Chaturvedi
  • Published online:
    24 November 2022
    Print publication:
    05 January 2023
  • Continuous Groups for Physicists is written for graduate students as well as researchers working in the field of theoretical physics. The text has been designed uniquely and it balances coverage of advanced and non-standard topics with an equal focus on the basic concepts for a thorough understanding. The book describes the general theory of Lie groups and Lie algebras, the passage between them, and their unitary/ Hermitian representations in the quantum mechanical setting. The four infinite classical families of compact simple Lie groups and their representations are covered in detail. Readers will benefit from the discussions on topics like spinor representations of real orthogonal groups, the Schwinger representation of a group, induced representations, systems of coherent states, real symplectic groups important in quantum mechanics, Wigner's theorem on symmetry operations in quantum mechanics, ray representations of Lie groups, and groups associated with non-relativistic and relativistic space-time.

An Introduction to Python Programming for Scientists and Engineers
  • Johnny Wei-Bing Lin, Hannah Aizenman, Erin Manette Cartas Espinel, Kim Gunnerson, Joanne Liu
  • Published online:
    20 August 2022
    Print publication:
    07 July 2022
  • Python is one of the most popular programming languages, widely used for data analysis and modelling, and is fast becoming the leading choice for scientists and engineers. Unlike other textbooks introducing Python, typically organised by language syntax, this book uses many examples from across Biology, Chemistry, Physics, Earth science, and Engineering to teach and motivate students in science and engineering. The text is organised by the tasks and workflows students undertake day-to-day, helping them see the connections between programming tools and their disciplines. The pace of study is carefully developed for complete beginners, and a spiral pedagogy is used so concepts are introduced across multiple chapters, allowing readers to engage with topics more than once. “Try This!” exercises and online Jupyter notebooks encourage students to test their new knowledge, and further develop their programming skills. Online solutions are available for instructors, alongside discipline-specific homework problems across the sciences and engineering.

Mathematical Methods and Physical Insights
  • An Integrated Approach
  • Alec J. Schramm
  • Published online:
    15 July 2022
    Print publication:
    16 June 2022
  • Mathematics instruction is often more effective when presented in a physical context. Schramm uses this insight to help develop students' physical intuition as he guides them through the mathematical methods required to study upper-level physics. Based on the undergraduate Math Methods course he has taught for many years at Occidental College, the text encourages a symbiosis through which the physics illuminates the math, which in turn informs the physics. Appropriate for both classroom and self-study use, the text begins with a review of useful techniques to ensure students are comfortable with prerequisite material. It then moves on to cover vector fields, analytic functions, linear algebra, function spaces, and differential equations. Written in an informal and engaging style, it also includes short supplementary digressions ('By the Ways') as optional boxes showcasing directions in which the math or physics may be explored further. Extensive problems are included throughout, many taking advantage of Mathematica, to test and deepen comprehension.

Fourier Analysis
  • T. W. Körner
  • Foreword by Terence Tao
  • Published online:
    19 May 2022
    Print publication:
    09 June 2022
  • Fourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. This diversity of interest is often overlooked, but in this much-loved book, Tom Körner provides a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering. The prerequisites are few (a reader with knowledge of second- or third-year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. This edition of Körner's 1989 text includes a foreword written by Professor Terence Tao introducing it to a new generation of fans.

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