Analysis And Beyond An Introduction Exam
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ANALYSIS and BEYOND an INTRODUCTION EXAM
Author: LIU
language: en
Publisher: World Scientific Publishing Company
Release Date: 2021-01-24
This volume aims to bridge between elementary textbooks on calculus and established books on advanced analysis. It provides elucidation of the reversible process of differentiation and integration through two featured principles: the chain rule and its inverse -- the change of variable -- as well as the Leibniz rule and its inverse -- the integration by parts. The chain rule or differentiation of composite functions is ubiquitous since almost all (a.a.) functions are composite functions of (elementary) functions and with the change of variable method as its reverse process. The Leibniz rule or differentiation of the product of two functions is essential since it makes differentiation nonlinear and with the method of integration by parts as its reverse process.Readers will find numerous worked-out examples and exercises in this volume. Detailed solutions are provided for most of the common exercises so that readers remain enthusiastically motivated in solving and understanding the concepts better.The intention of this volume is to lead the reader into the rich fields of advanced analysis and to obtain a much better view of useful mathematics.
Analysis and Argument in First-Year Writing and Beyond
Author: SILVIA. MITCHELL PESSOA (THOMAS D. GOMEZ-LAICH, DR MARIA PIA.)
language: en
Publisher: University of Michigan Press
Release Date: 2024-10-29
Developing a language for students and teachers to discuss good writing
Beyond the Bubble Test
Author: Linda Darling-Hammond
language: en
Publisher: John Wiley & Sons
Release Date: 2014-05-14
Performance assessment is a hot topic in school systems, and educators continue to analyze its costs, benefits, and feasibility as a replacement for high-stakes testing. Until now, researchers and policymakers have had to dig to find out what we know and what we still have to learn about performance assessment. Beyond the Bubble Test: How Performance Assessments Support 21st Century Learning synthesizes the latest findings in the field, and not a moment too soon. Statistics indicate that the United States is in danger of falling behind if it fails to adapt to our changing world. The memory and recall strategies of traditional testing are no longer adequate to equip our students with the skills they need to excel in the global economy. Instead teachers need to engage students in deeper learning, assessing their ability to use higher-order skills. Skills like synthesizing information, understanding evidence, and critical problem-solving are not achieved when we teach to multiple-choice exams. Examples in Beyond the Bubble Test paint a useful picture of how schools can begin to supplement traditional tests with something that works better. This book provides new perspectives on current performance assessment research, plus an incisive look at what’s possible at the local and state levels. Linda Darling-Hammond, with a team of leading scholars, bring together lessons learned, new directions, and solid recommendations into a single, readily accessible compendium. Beyond the Bubble Test situates the current debate on performance assessment within the context of testing in the United States. This comprehensive resource also looks beyond our U.S. borders to Singapore, Hong Kong, and other places whose reform-mindedness can serve as an example to us.