Margaret L. Lial, Thomas W. Hungerford, and John P. Holcomb
Algebra and equations -- Graphs, lines, and inequalities -- Functions and graphs -- Exponential and logarithmic functions -- Mathematics of finance -- Systems of linear equations and matrices -- Linear programming -- Sets and probability -- Counting, probability distributions, and further topics in probability -- Introduction to statistics -- Differential calculus -- Applications of the derivative -- Integral calculus -- Multivariate calculus -- Appendix A: Graphing calculus -- Appendix B: Tables. Formulas from geometry ; Areas under the normal curve ; Integrals.
Ives Felix, John F. Oprea, and Daniel Tanre
Rational homotopy is a very powerful tool for differential topology and geometry. This text aims to provide graduates and researchers with the tools necessary for the use of rational homotopy in geometry. Algebraic Models in Geometry has been written for topologists who are drawn to geometrical problems amenable to topological methods and also for geometers who are faced with problems requiring topological approaches and thus need a simple and concrete introduction to rational homotopy. This is essentially a book of applications. Geodesics, curvature, embeddings of manifolds, blow-ups, complex and Kahler manifolds, symplectic geometry, torus actions, configurations and arrangements are all covered. The chapters related to these subjects act as an introduction to the topic, a survey, and a guide to the literature. But no matter what the particular subject is, the central theme of the book persists; namely, there is a beautiful connection between geometry and rational homotopy which both serves to solve geometric problems and spur the development of topological methods.
John F. Oprea
Differential geometry has a wide range of applications, going far beyond strictly mathematical pursuits to include architecture, engineering, and just about every scientific discipline. John Oprea's second edition of Differential Geometry and Its Applications illuminates a wide range of ideas that can be beneficial to students majoring not only in mathematics but also in other fields. Differential Geometry and Its Applications was written to help students adapt to "a type of mathematics that is a unified whole," one that mixes together geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and various notions from the sciences. The textbook touches on many different mathematical concepts, including aspects of linear algebra, the Gauss-Bonnet Theorem, and geodesics. It also encourages students to visualize and experiment with the ideas they are studying through their use of the computer program Maple. This allows students to develop a better understanding of the mathematics involved in differential geometry. The book is full of exercises that challenge students to combine concepts from different areas of mathematics to obtain solutions.