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A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author's own theoretical developments. The book — which aims to present new mathematical curricula based on symmetry and invariance principles — is tailored to develop analytic skills and “working knowledge” in both classical and Lie's methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author's extensive teaching experience at Novosibirsk and Moscow universities in Russia, Collège de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.
Build solid mathematical understanding and develop key conceptual connections. The inquiry-based approach integrates the MYP key concepts, helping you shift to a concept-based classroom and cement mathematical comprehension. Fully comprehensive and matched to the Revised MYP to support achievement. Progress your learners into IB Diploma - fully comprehensive and matched to the MYP Next Chapter curriculum Develop conceptual understanding in the best way for your learners - learn by mathematical unit or by key concept Drive active, critical exploration of mathematical principles - build rounded comprehension framed within the key and related concepts Develop meaningful cross-curricular connections that help learners recognize and manipulate mathematical ideas in other disciplines Support higher level thinking skills through an approach grounded in factual, conceptual and debatable questions Build a solid foundation of practical skills with extensive practice equipping learners to apply skills Fully prepare learners for the MYP eAssessment Multiplatform access, compatible with a wide range of devices Your first login will be facilitated by a printed access card that will be sent to you in the mail Includes one print course book and one online course book
Take a deep dive into the five practices for facilitating productive mathematical discussions Enhance your fluency in the five practices—anticipating, monitoring, selecting, sequencing, and connecting—to bring powerful discussions of mathematical concepts to life in your elementary classroom. This book unpacks the five practices for deeper understanding and empowers you to use each practice effectively. • Video excerpts vividly illustrate the five practices in action in real elementary classrooms • Key questions help you set learning goals, identify high-level tasks, and jumpstart discussion • Prompts guide you to be prepared for and overcome common challenges Includes planning templates, sample lesson plans and completed monitoring tools, and mathematical tasks.
Build solid mathematical understanding and develop meaningful conceptual connections. The inquiry-based approach holistically integrates the MYP key concepts, helping you shift to a concept-based approach and cement comprehension of mathematical principles. Fully comprehensive and matched to the Revised MYP, this resource builds student potential at MYP and lays foundations for cross-curricular understanding. Using a unique question cycle to sequentially build skills and comprehension, units introduce factual questions, followed by concept-based questions and conclude with debatable questions. This firm grounding in inquiry-based learning equips learners to actively explore mathematical concepts and relate them to the wider 21st Century world, strengthening comprehension. Progress your learners into IB Diploma - fully comprehensive and matched to the Revised MYP Develop conceptual understanding in the best way for your learners learn by mathematical unit or by key concept Drive active, critical exp
Build solid mathematical understanding and develop key conceptual connections. The inquiry-based approach integrates the MYP key concepts, helping you shift to a concept-based classroom and cement mathematical comprehension. Fully comprehensive and matched to the Revised MYP to support achievement. Progress your learners into IB Diploma - fully comprehensive and matched to the MYP Next Chapter curriculum Develop conceptual understanding in the best way for your learners - learn by mathematical unit or by key concept Drive active, critical exploration of mathematical principles - build rounded comprehension framed within the key and related concepts Develop meaningful cross-curricular connections that help learners recognize and manipulate mathematical ideas in other disciplines Support higher level thinking skills through an approach grounded in factual, conceptual and debatable questions Build a solid foundation of practical skills with extensive practice equipping learners to apply skills Fully prepare learners for the MYP eAssessment Multiplatform access, compatible with a wide range of devices Your first login will be facilitated by a printed access card that will be sent to you in the mail Includes one print course book and one online course book
Many physical processes in fields such as mechanics, thermodynamics, electricity, magnetism or optics are described by means of partial differential equations. The aim of the present book is to demontstrate the basic methods for solving the classical linear problems in mathematical physics of elliptic, parabolic and hyperbolic type. In particular, the methods of conformal mappings, Fourier analysis and Green`s functions are considered, as well as the perturbation method and integral transformation method, among others. Every chapter contains concrete examples with a detailed analysis of their solution.The book is intended as a textbook for students in mathematical physics, but will also serve as a handbook for scientists and engineers.
This classic text is known to and used by thousands of mathematicians and students of mathematics thorughout the world. It gives an introduction to the general theory of infinite processes and of analytic functions together with an account of the principle transcendental functions.
Excerpt from The Edinburgh New Philosophical Journal, 1828 A few Remarks on the class Mollusca in Dr fleming's Work on British Animals; with Descriptions of some new Species. By george johnston, M.D. Fellow of the Royal College of Surgeons of Edinburgh. Communicated by the Author. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
This text places the basic ideas of real analysis and numerical analysis together in an applied setting that is both accessible and motivational to young students. The essentials of real analysis are presented in the context of a fundamental problem of applied mathematics, which is to approximate the solution of a physical model. The framework of existence, uniqueness, and methods to approximate solutions of model equations is sufficiently broad to introduce and motivate all the basic ideas of real analysis. The book includes background and review material, numerous examples, visualizations and alternate explanations of some key ideas, and a variety of exercises ranging from simple computations to analysis and estimates to computations on a computer.
Designed for undergraduate students of set theory, Classic Set Theory presents a modern perspective of the classic work of Georg Cantor and Richard Dedekin and their immediate successors. This includes:The definition of the real numbers in terms of rational numbers and ultimately in terms of natural numbersDefining natural numbers in terms of setsThe potential paradoxes in set theoryThe Zermelo-Fraenkel axioms for set theoryThe axiom of choiceThe arithmetic of ordered setsCantor's two sorts of transfinite number - cardinals and ordinals - and the arithmetic of these.The book is designed for students studying on their own, without access to lecturers and other reading, along the lines of the internationally renowned courses produced by the Open University. There are thus a large number of exercises within the main body of the text designed to help students engage with the subject, many of which have full teaching solutions. In addition, there are a number of exercises without answers so students studying under the guidance of a tutor may be assessed.Classic Set Theory gives students sufficient grounding in a rigorous approach to the revolutionary results of set theory as well as pleasure in being able to tackle significant problems that arise from the theory.