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Lutzer Carl V.: Professional Calculus,
Multivariable

Professional Calculus, Multivariable

This book offers a comprehensive treatment of the core mathematical topics required for a modern engineering degree. The book begins with an introduction to the basics of mathematical reasoning and builds up the level of complexity as it progresses.

Mathematics for Engineers

The text is divided into three main parts: unconstrained optimization, constrained optimization, and linear programming. The first part addresses unconstrained optimization in single-variable and multivariable functions, introducing key algorithms such as steepest descent, Newton, and quasi-Newton methods.The second part focuses on constrained optimization, starting with linear equality constraints and extending to more general cases, including inequality constraints. It details optimality conditions, sensitivity analysis, and relevant algorithms for solving these problems.The third part covers linear programming, presenting the formulation of LP problems, the simplex algorithm, and sensitivity analysis. Throughout, the text provides numerous applications to data science, such as linear regression, maximum likelihood estimation, expectation-maximization algorithms, support vector machines, and linear neural networks.

Continuous Optimization For Data Science

Can one prove that 1 + 1 = 2? Which US president proved Pythagoras' theorem? How long is the coastline of Britain? These and many other questions are answered in this book on famous equations and their historical development. The equations come from a range of mathematical disciplines, and cover 4,000 years from early counting to fractal geometry.

Equations and Their Origins

Sum Stories

Unlock the mysteries of Calculus with a fresh approach rooted in simplicity and historical insight. This book reintroduces a nearly forgotten idea from René Descartes (1596-1650), showing how the fundamental concepts of Calculus can be understood using just basic algebra. Starting with rational functions -- the core of early Calculus -- this method allows the reader to grasp the rules for derivatives without the intimidating concepts of limits or real numbers, making the subject more accessible than ever.But the journey doesn't stop there. While attempting to apply this algebraic approach to exponential functions, the reader will encounter the limitations of simple methods, revealing the necessity for more advanced mathematical tools. This natural progression leads to the discovery of continuity, the approximation process, and ultimately, the introduction of real numbers and limits. These deeper concepts pave the way for understanding differentiable functions, seamlessly bridging the gap between elementary algebra and the profound ideas that underpin Calculus.Whether you're a student, educator, or math enthusiast, this book offers a unique pathway to mastering Calculus. By connecting historical context with modern mathematical practice, it provides a richer, more motivating learning experience. For those looking to dive even deeper, the author's 2015 book, What is Calculus? From Simple Algebra to Deep Analysis, is the perfect next step.

Calculus: A New Approach For Schools That Starts With Simple Algebra

"From the author of Calculus Simplified, an accessible, personalized approach to Calculus 2Second-semester calculus is rich with insights into the nature of infinity and the very foundations of geometry, but students can become overwhelmed as they struggle to synthesize the range of material covered in class. Oscar Fernandez provides a "Goldilocks approach" to learning the mathematics of integration, infinite sequences and series, and their applications-the right depth of insights, the right level of detail, and the freedom to customize your student experience. Learning calculus should be an empowering voyage, not a daunting task. Calculus 2 Simplified gives you the flexibility to choose your calculus adventure, and the right support to help you master the subject.Provides an accessible, user-friendly introduction to second-semester college calculusThe unique customizable approach enables students to begin first with integration (traditional) or with sequences and series (easier)Chapters are organized into mini lessons that focus first on developing the intuition behind calculus, then on conceptual and computational masteryFeatures more than 170 solved examples that guide your learning and more than 400 exercises, with answers, that help assess your understandingIncludes optional chapter appendixesComes with supporting materials online, including video tutorials and interactive graphs"--

Integration and Infinite Series

Calculus 2 Simplified

Fractional Order Thinking in Exploring the Frontiers of STEM

Theory and Practice

Fractional Order Intelligent Modeling for Lithium-Ion Batteries

This comprehensive compendium addresses a critical need in the AI and machine learning era by bridging foundational information theory (IT) concepts with practical applications in statistical learning. Unlike traditional IT textbooks, this volume emphasizes how IT principles, such as entropy and source coding, underpin modern machine learning techniques like cross-entropy, decision trees, and evidence-lower bounds.This unique book connects IT with probabilistic inference, illustrated through real-world applications, such as decoding LDPC codes for error correction. The inclusion of the Lea probabilistic programming package is particularly valuable for pedagogy, offering students a hands-on tool to solve numerical problems and reinforce theoretical concepts.The useful reference text benefits professionals, researchers, academics and students in the fields of calculus and probability, communications and information sciences.

Introduction To Information Theory And Probabilistic Inference, An

Principles And Methods Of Applied Mathematics

Advanced Engineering Calculus is a content-rich, user-friendly and compact learning and teaching resource. It offers over 440 problems -- many with multiple parts -- as well as detailed figures to aid readers in visualizing and understanding the topics covered.Engaging with a wide range of advanced calculus topics and their applications, this book caters to students enrolled in the sciences and applied sciences. Each chapter begins with an accessible summary of the relevant mathematical notions and their properties. Questions are sorted by topic and accompanied by detailed solutions. To further aid readers, precise and consistent mathematical notation and vocabulary are used throughout. This produces a learning resource capable of clearly communicating complex and advanced calculus ideas and their applications.In short, this book serves as a cross between a handbook, a learning guide, and rich teaching resource on a wide range of advanced calculus topics, something that has been missing in the otherwise crowded field of calculus titles.

Advanced Engineering Calculus: A Collection Of Problems With Solutions

"An authoritative, self-contained introduction to geometrical tensor calculus for scientists and engineersTensors are widely used in physics and engineering to describe physical properties that have multiple dimensions and magnitudes. In recent years, they have become increasingly important for data analytics and machine learning, allowing for the representation and processing of data in neural networks and the modeling of complex relationships in multidimensional spaces. This incisive book provides a geometrical understanding of tensors and their calculus from the point of view of a physicist. With a wealth of examples presented in visually engaging boxes, it takes readers through all aspects of geometrical continuum mechanics and the field and dynamic equations of Einstein, Einstein-Cartan, and metric-affine theories of general relativity. A Geometrical Introduction to Tensor Calculus gives graduate students, advanced undergraduates, and researchers a powerful and mathematically elegant tool for comprehending the behavior and applications of tensors across an array of fields.Offers a physicist's perspective on geometrical tensor calculusIncludes dozens of examples that illustrate the geometrical use of tensors in continuum mechanics and general relativityCan serve as the basis for a course in tensor calculus for physicists and engineersInvaluable as a supplementary guide for anyone studying areas of physics that rely on tensor calculus, such as electrodynamics, geophysics, fluid and continuum mechanics, and general relativity"--

A Geometrical Introduction to Tensor Calculus

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Non-Newtonian Sequence Spaces with Applications presents an alternative to the usual calculus based on multiplication instead of addition.

Non-Newtonian Sequence Spaces with Applications

Professional Calculus, Multivariable

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