Calculus Special Edition Chapters 9-13
Edition: 7
Copyright: 2017
Pages: 600
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This section of the text offers a deep and structured exploration of multivariable calculus, focusing on vector geometry, vector-valued functions, partial differentiation, multiple integration, and vector analysis—essential tools in advanced mathematics, physics, and engineering.
Chapter 9 introduces vectors in both two and three dimensions, including the dot and cross products, and their applications to lines, planes, and quadric surfaces in space. This forms the geometric foundation for future concepts.
Chapter 10 explores vector-valued functions, covering their calculus, motion modeling (e.g., planetary trajectories), and vector geometry concepts like curvature and acceleration components, bridging physics with mathematics.
Chapter 11 dives into partial differentiation, emphasizing multivariable functions, gradients, tangent planes, chain rules, and optimization using Lagrange multipliers—tools critical for real-world applications in science and engineering.
Chapter 12 focuses on multiple integration in various coordinate systems, including applications in surface area, mass, and probability. Techniques like Jacobians and coordinate transformations are also introduced.
Chapter 13 culminates with vector analysis, presenting vector fields, line and surface integrals, and key theorems: Green’s, Stokes’, and the Divergence Theorem. These unify earlier concepts and are central to fluid dynamics, electromagnetism, and field theory.
Group projects and cumulative reviews enhance collaborative learning and conceptual mastery.
Monty Strauss has been on the mathematics faculty at Texas Tech University for almost forty years. He has a Ph.D. from the Courant Institute of Mathematical Sciences at New York University and has taught all levels of mathematics at Texas Tech, from precollege mathematics to doctoral level. He particularly has enjoyed working with honors students and with mathematics and engineering majors. Among his administrative assignments have been departmental undergraduate programs chair and departmental associate chair.
Karl J. Smith received his B.A. and M.A. degrees in mathematics from UCLA. In 1968, he moved to northern California to teach mathematics at Santa Rosa Junior College, where he taught until his retirement in 1993. Along the way, he served as department chair, and he received a Ph.D. in 1979 in mathematics education at Southeastern University. A past president of the American Mathematical Association of Two-Year Colleges, Professor Smith is active nationally in mathematics education. He was the founding editor of the Western AMATYC News, a chairperson of the Committee on Mathematics Excellence, and an NSF grant reviewer. In 1979 he received an Outstanding Young Men of America Award, in 1980 an Outstanding Educator Award, and in 1989 an Outstanding Teacher Award. Professor Smith is the author of over 60 successful textbooks. Over two million students have learned mathematics from his textbooks.
Magdalena Toda holds a PhD in Mathematics from University of Kansas and a PhD in Applied Mathematics from University Politehnica Bucharest. She is employed as a Professor of Mathematics at Texas Tech University, in Lubbock, TX, where she has served as interim chairperson between 2015-2016, and as department chairperson since 2016.
She has authored and co-authored 35 refereed articles, in the areas of differential geometry and geometric PDEs, and has served as an editor for a research monograph that appeared in 2017. She has extensive experience in teaching Calculus, in both the traditional, face-to-face format (since 1995), and online (since 2011). She is a recipient of 6 teaching awards (2 at University of Kansas and 4 at Texas Tech University - including the President's Award for Excellence in Teaching, 2008).
This section of the text offers a deep and structured exploration of multivariable calculus, focusing on vector geometry, vector-valued functions, partial differentiation, multiple integration, and vector analysis—essential tools in advanced mathematics, physics, and engineering.
Chapter 9 introduces vectors in both two and three dimensions, including the dot and cross products, and their applications to lines, planes, and quadric surfaces in space. This forms the geometric foundation for future concepts.
Chapter 10 explores vector-valued functions, covering their calculus, motion modeling (e.g., planetary trajectories), and vector geometry concepts like curvature and acceleration components, bridging physics with mathematics.
Chapter 11 dives into partial differentiation, emphasizing multivariable functions, gradients, tangent planes, chain rules, and optimization using Lagrange multipliers—tools critical for real-world applications in science and engineering.
Chapter 12 focuses on multiple integration in various coordinate systems, including applications in surface area, mass, and probability. Techniques like Jacobians and coordinate transformations are also introduced.
Chapter 13 culminates with vector analysis, presenting vector fields, line and surface integrals, and key theorems: Green’s, Stokes’, and the Divergence Theorem. These unify earlier concepts and are central to fluid dynamics, electromagnetism, and field theory.
Group projects and cumulative reviews enhance collaborative learning and conceptual mastery.
Monty Strauss has been on the mathematics faculty at Texas Tech University for almost forty years. He has a Ph.D. from the Courant Institute of Mathematical Sciences at New York University and has taught all levels of mathematics at Texas Tech, from precollege mathematics to doctoral level. He particularly has enjoyed working with honors students and with mathematics and engineering majors. Among his administrative assignments have been departmental undergraduate programs chair and departmental associate chair.
Karl J. Smith received his B.A. and M.A. degrees in mathematics from UCLA. In 1968, he moved to northern California to teach mathematics at Santa Rosa Junior College, where he taught until his retirement in 1993. Along the way, he served as department chair, and he received a Ph.D. in 1979 in mathematics education at Southeastern University. A past president of the American Mathematical Association of Two-Year Colleges, Professor Smith is active nationally in mathematics education. He was the founding editor of the Western AMATYC News, a chairperson of the Committee on Mathematics Excellence, and an NSF grant reviewer. In 1979 he received an Outstanding Young Men of America Award, in 1980 an Outstanding Educator Award, and in 1989 an Outstanding Teacher Award. Professor Smith is the author of over 60 successful textbooks. Over two million students have learned mathematics from his textbooks.
Magdalena Toda holds a PhD in Mathematics from University of Kansas and a PhD in Applied Mathematics from University Politehnica Bucharest. She is employed as a Professor of Mathematics at Texas Tech University, in Lubbock, TX, where she has served as interim chairperson between 2015-2016, and as department chairperson since 2016.
She has authored and co-authored 35 refereed articles, in the areas of differential geometry and geometric PDEs, and has served as an editor for a research monograph that appeared in 2017. She has extensive experience in teaching Calculus, in both the traditional, face-to-face format (since 1995), and online (since 2011). She is a recipient of 6 teaching awards (2 at University of Kansas and 4 at Texas Tech University - including the President's Award for Excellence in Teaching, 2008).