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Physics is equally appropriate for average and gifted students. The entire program is based on introducing a topic to a student and then allowing them to build upon that concept as they learn new ones. Topics are gradually increased in complexity and practiced every day, providing the time required for concepts to become totally familiar. Includes: Student Textbook (Hardcover) 100 Lessons Appendix with selected tables Periodic Table of the Elements Answers to odd-numbered problems Homeschool Packet With Test Forms 25 Test Forms for homeschooling Answer Key to odd-numbered Textbook Problem Sets Answer Key to all homeschool Tests
The book provides an introduction to minimax methods in critical point theory and shows their use in existence questions for nonlinear differential equations. An expanded version of the author's 1984 CBMS lectures, this volume is the first monograph devoted solely to these topics. Among the abstract questions considered are the following: the mountain pass and saddle point theorems, multiple critical points for functionals invariant under a group of symmetries, perturbations from symmetry, and variational methods in bifurcation theory. The book requires some background in functional analysis and differential equations, especially elliptic partial differential equations. It is addressed to mathematicians interested in differential equations and/or nonlinear functional analysis, particularly critical point theory.
Active engagement is the key to learning. You want your students doing something that stimulates them to ask questions and creates a need to know. Teaching Mathematics Through Games presents a variety of classroom-tested exercises and activities that provoke the active learning and curiosity that you hope to promote. These games run the gamut from well-known favorites like SET and Settlers of Catan to original games involving simulating structural inequality in New York or playing Battleship with functions. The book contains activities suitable for a wide variety of college mathematics courses, including general education courses, math for elementary education, probability, calculus, linear algebra, history of math, and proof-based mathematics. Some chapter activities are short term, such as a drop-in lesson for a day, and some are longer, including semester-long projects. All have been tested, refined, and include extensive implementation notes.
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The textbook provides both beginner and experienced CAD users with the math behind the CAD. The geometry tools introduced here help the reader exploit commercial CAD software to its fullest extent. In fact, the book enables the reader to go beyond what CAD software packages offer in their menus. Chapter 1 summarizes the basic Linear and Vector Algebra pertinent to vectors in 3D, with some novelties: the 2D form of the vector product and the manipulation of “larger" matrices and vectors by means of block-partitioning of larger arrays. In chapter 2 the relations among points, lines and curves in the plane are revised accordingly; the difference between curves representing functions and their geometric counterparts is emphasized. Geometric objects in 3D, namely, points, planes, lines and surfaces are the subject of chapter 3; of the latter, only quadrics are studied, to keep the discussion at an elementary level, but the interested reader is guided to the literature on splines. The concept of affine transformations, at the core of CAD software, is introduced in chapter 4, which includes applications of these transformations to the synthesis of curves and surfaces that would be extremely cumbersome to produce otherwise. The book, catering to various disciplines such as engineering, graphic design, animation and architecture, is kept discipline-independent, while including examples of interest to the various disciplines. Furthermore, the book can be an invaluable complement to undergraduate lectures on CAD.