[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-seo-143619-105":3,"detail-sidebar-cat-0-en-105":81,"doc-detail-143619-en":131},{"code":4,"msg":5,"data":6},0,"ok",{"site_id":7,"language":8,"slug":9,"title":10,"keywords":11,"description":12,"schema_data":13,"social_meta":74,"head_meta":76,"extra_data":78,"updated_unix":80},105,"en","precalculus-core-review-for-calculus","Precalculus - Core Review for Calculus","","Precalculus is designed as a concise review course for first-year natural science and engineering students who have only a moderate grasp of high school mathematics. It builds foundational understanding required for calculus by covering functions, trigonometric functions, vectors, complex numbers and matrices, and then leading into differentiation and integration for polynomial, trigonometric, and basic rational/irrational functions. The book emphasizes core methods, basic applications, and the Fundamental Theorem of Calculus, preparing students for deeper university calculus study.",{"@graph":14,"@context":73},[15,34,56],{"@type":16,"itemListElement":17},"BreadcrumbList",[18,23,27,31],{"item":19,"name":20,"@type":21,"position":22},"https://docshare.wps.com","Home","ListItem",1,{"item":24,"name":25,"@type":21,"position":26},"https://docshare.wps.com/document/","Document",2,{"item":28,"name":29,"@type":21,"position":30},"https://docshare.wps.com/document/exam/","Exam",3,{"item":32,"name":10,"@type":21,"position":33},"https://docshare.wps.com/document/precalculus-core-review-for-calculus/143619/",4,{"url":32,"name":10,"@type":35,"image":36,"author":41,"headline":10,"publisher":44,"fileFormat":47,"inLanguage":8,"description":12,"dateModified":48,"datePublished":49,"encodingFormat":47,"isAccessibleForFree":50,"interactionStatistic":51},"DigitalDocument",{"url":37,"@type":38,"width":39,"height":40},"https://docshare.wps.com/thumbnails/precalculus-core-review-for-calculus/143619.png","ImageObject",300,407,{"name":42,"@type":43},"Ezra","Person",{"url":19,"name":45,"@type":46},"DocShare","Organization","application/pdf","2026-10-20","2026-08-25",true,{"@type":52,"interactionType":53,"userInteractionCount":55},"InteractionCounter",{"@type":54},"ViewAction",23,{"@type":57,"mainEntity":58},"FAQPage",[59,65,69],{"name":60,"@type":61,"acceptedAnswer":62},"What problem does Precalculus aim to solve for students entering university?","Question",{"text":63,"@type":64},"It targets students who have incomplete knowledge of high school mathematics, helping them avoid difficulties when following university calculus courses.","Answer",{"name":66,"@type":61,"acceptedAnswer":67},"Which topics are covered before differentiation and integration?",{"text":68,"@type":64},"The book reviews functions, trigonometric functions, vectors, and complex numbers and matrices, forming the base needed for calculus.",{"name":70,"@type":61,"acceptedAnswer":71},"What key relationship between differentiation and integration is emphasized?",{"text":72,"@type":64},"The Fundamental Theorem of Calculus is examined as the basic relation connecting these two concepts.","https://schema.org",{"og:url":32,"og:type":75,"og:title":10,"og:site_name":45,"og:description":12},"article",{"robots":77,"canonical":32},"index,follow",{"doc_id":79,"site_id":7},143619,1787696034,{"code":4,"msg":82,"data":83},"success",[84,88,92,95,100,105,110,115,120,123,127],{"id":22,"doc_module":4,"doc_module_name":25,"category_name":85,"show_sort_weight":86,"slug":87},"Story & Novel",90,"story-novel",{"id":26,"doc_module":4,"doc_module_name":25,"category_name":89,"show_sort_weight":90,"slug":91},"Literature",80,"literature",{"id":33,"doc_module":4,"doc_module_name":25,"category_name":29,"show_sort_weight":93,"slug":94},70,"exam",{"id":96,"doc_module":4,"doc_module_name":25,"category_name":97,"show_sort_weight":98,"slug":99},5,"Comic",60,"comic",{"id":101,"doc_module":4,"doc_module_name":25,"category_name":102,"show_sort_weight":103,"slug":104},6,"Technology",50,"technology",{"id":106,"doc_module":4,"doc_module_name":25,"category_name":107,"show_sort_weight":108,"slug":109},7,"Healthcare",40,"healthcare",{"id":111,"doc_module":4,"doc_module_name":25,"category_name":112,"show_sort_weight":113,"slug":114},8,"Research & Report",30,"research-report",{"id":116,"doc_module":4,"doc_module_name":25,"category_name":117,"show_sort_weight":118,"slug":119},9,"Religion & Spirituality",20,"religion-spirituality",{"id":118,"doc_module":4,"doc_module_name":25,"category_name":121,"show_sort_weight":118,"slug":122},"World Cup","world-cup",{"id":124,"doc_module":4,"doc_module_name":25,"category_name":125,"show_sort_weight":124,"slug":126},10,"Lifestyle","lifestyle",{"id":128,"doc_module":4,"doc_module_name":25,"category_name":129,"show_sort_weight":96,"slug":130},19,"General","general",{"code":4,"msg":82,"data":132},{"doc_id":79,"user_id":133,"nickname":42,"user_avatar":134,"doc_module":4,"category_id":33,"category_name":29,"doc_title":10,"doc_description":12,"doc_content":135,"file_id":136,"file_url":137,"file_type":138,"file_size":139,"view_count":55,"is_deleted":4,"is_public":22,"is_downloadable":22,"audit_status":22,"page_count":140,"language":141,"language_code":8,"site_id":7,"html_lang":8,"table_of_contents":142,"faqs":143,"seo_title":144,"seo_description":12,"update_tm":80,"read_time":145},1099514068035,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","Copyright cKKLL PUBLISHED BY PUBLISHER First printing, June 2016  \nP r e f a c e  \nStudents of the colleges of the natural sciences and engineering are required to take calculus courses during their first year before they begin their majors. The contents of calculus courses are composed on the assumption that freshmen possess a moderate understanding of high school mathematics. A small number of students, however, seem to have an incomplete knowledge of high school mathematics. These students may encounter serious difficulties in following calculus courses. As a result, they could experience a stressful introduction to university. To help these students, universities offer an extra review course of high school mathematics. This book, titled “Precalculus”, is designed for this review course, and is written so concisely that three hours of lecture per week in one semester can cover the materials completely.  \nThe first chapter is titled “Function”. In this chapter the basic concept of the function, from which many other mathematical concepts are defined, is explained. Without understanding functions, we cannot fully grasp the intricacies of mathematics well. The second chapter is devoted for Trigonometric Functions. They are periodic functions which are widely used in studying periodic phenomena in nature. In this section various formulas for trigonometric functions are given and some basic applications are also discussed. Vectors are introduced in the third chapter. Vectors are used to describe the magnitude and direction of an object simultaneously. They are frequently used in studying physical quantities such as forces, velocities and accelerations. Complex numbers and matrices are introduced in the forth chapter. Complex numbers are the largest number system containing real numbers and matrices are rectangular arrays of real or complex numbers. In this chapter algebraic operations such as addition, subtraction and multiplication for complex numbers and matrices are defined and their basic properties are explained.  \nChapter 5 and 6 form the core of this book, in which differentiation and integration are introduced for polynomial functions, trigonometric functions and simple types of rational and irrational functions. In these two chapters basic methods of calculating the differentiation and integration for various functions are explained and some applications are discussed. The basic relation between these two concepts, called the Fundamental Theorem of Calculus, is also examined. All material in this book will be discussed further in the university calculus courses at a deeper level.  \nThis book is in fact an updated version of the book written by J. Kim, K. Kim and Y. Lee in Korean, which was published in Cheong Moon Gak Publishing Company under the title of Elementary Mathematics in 2012. In this revised and translated edition, the authors added a chapter for complex numbers and matrices, and improved some parts in contents and exercises.  \nFinally, the authors would like to thank Scott Schafer and Cheongil Namgung for checking the manuscript carefully. It is the authors’ intention that students utilize this book to build strong self-confidence in mathematics and eventually this book becomes great help to study their majors.  \nC o n t e n t s  \nCHAPTER 1 Function  \n1.1 Definition of a Function 11  \nPolynomial Functions, Rational Functions and Irrational Functions 13  \nGraphs of Functions 14  \n1.2 Basic Properties of Functions 19  \n1.3 Exponential Functions and Logarithmic Functions 27  \nExponential Functions 27  \nGraphs of Exponential Functions 28  \nLogarithmic Functions 31  \nCHAPTER 2 Trigonometric Functions  \n2.1 Angles and Trigonometric Ratios 41  \n2.2 Trigonometric Functions 45  \nGraph of Sine Function 50  \nGraph of Cosine Function 51  \nGraph of Tangent Function 52  \n2.3 Properties of Trigonometric Functions 60  \n2.4 Triangles and Trigonometric Functions 71  \nCHAPTER 3 Vectors  \n3.1 The Concept of Vectors and Basic Op","cbCaiqsGnhNEF61T","https://ap.wps.com/l/cbCaiqsGnhNEF61T","pdf",5016483,216,"English","# Preface\n# Contents\n## Chapter 1 Function\n## Chapter 2 Trigonometric Functions\n## Chapter 3 Vectors\n## Chapter 4 Complex Numbers and Matrices\n## Chapter 5 Differentiation\n## Chapter 6 Integration","[{\"question\":\"What problem does Precalculus aim to solve for students entering university?\",\"answer\":\"It targets students who have incomplete knowledge of high school mathematics, helping them avoid difficulties when following university calculus courses.\"},{\"question\":\"Which topics are covered before differentiation and integration?\",\"answer\":\"The book reviews functions, trigonometric functions, vectors, and complex numbers and matrices, forming the base needed for calculus.\"},{\"question\":\"What key relationship between differentiation and integration is emphasized?\",\"answer\":\"The Fundamental Theorem of Calculus is examined as the basic relation connecting these two concepts.\"}]","Precalculus - Core Review for Calculus | PDF",544]