{"product_id":"mathematical-foundations-for-robotics-systems-andr-oid-9798241892782","title":"Mathematical Foundations for Robotics Systems Engineering: Linear Algebra, Multivariable Calculus, and Lie Groups for Motion, Estimation, and Dynamics","description":"\u003cp\u003eBuild robotics models you can trust by mastering the mathematics that governs motion, estimation, and rigid-body geometry.\u003c\/p\u003e\u003cp\u003eThis engineering-focused text develops the essential tools behind modern robotic systems, starting from core linear algebra and multivariable calculus and extending through dynamics, discretization, and uncertainty. The emphasis is always on sensitivity, stability, and validation, so results are not only derived correctly but also checked for conditioning, error growth, and physical consistency.\u003c\/p\u003e\u003cp\u003eInside you will work through the mathematical backbone of robotics, including: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eLinear algebra for real-world solves: rank and null spaces, QR and Cholesky structure, eigendecomposition, SVD, pseudoinverses, regularization, and condition numbers\u003c\/li\u003e\n\u003cli\u003eMultivariable calculus that drives kinematics and estimation: Jacobians, Hessians, chain rules, and implicit differentiation for constrained mechanisms\u003c\/li\u003e\n\u003cli\u003eNonlinear least squares and constrained optimization: Gauss-Newton, Levenberg-Marquardt, Lagrange multipliers, KKT conditions, and quadratic programs\u003c\/li\u003e\n\u003cli\u003eDifferential equation modeling and discretization: state-space ODEs, matrix exponential solutions for LTI systems, sampling effects, truncation error, and stiffness-aware integration ideas\u003c\/li\u003e\n\u003cli\u003eUncertainty and error propagation: first-order sensitivity, covariance propagation through nonlinear maps, and Mahalanobis geometry\u003c\/li\u003e\n\u003cli\u003eRigid-body geometry with Lie groups: SO(3) and SE(3), exponential and logarithm maps, left and right Jacobians, adjoints, and consistent perturbation models\u003c\/li\u003e\n\u003cli\u003eKinematics and dynamics fundamentals: product of exponentials forward kinematics, Jacobians and singularities, spatial vector dynamics, and Lagrangian structure\u003c\/li\u003e\n\u003cli\u003eEstimation foundations: linear Kalman filtering and manifold-aware extensions using tangent-space error models\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003eEvery chapter includes multiple choice questions plus practice questions with full answers, designed to reinforce \"derive, solve, validate\" skills. The result is a rigorous, problem-driven pathway to the mathematical foundations needed for reliable robotics systems engineering.\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Andr Oid\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9798241892782\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Independently Published\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 12\/30\/2025\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 338\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.73lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 11.00h x 8.50w x 0.70d","brand":"Andr Oid","offers":[{"title":"Paperback","offer_id":48437619982591,"sku":"9798241892782","price":39.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0662\/2982\/9887\/files\/img_11ddd0d3-71bc-4e64-9502-e1719cbf58bb.jpg?v=1777162949","url":"https:\/\/www.whiterainbookhouse.com\/products\/mathematical-foundations-for-robotics-systems-andr-oid-9798241892782","provider":"WR Book House","version":"1.0","type":"link"}