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Perry at the University of Kentucky, dated December 7, 2018. Provides exam review meeting details for Thursday, December 13, 6:00–8:00 PM, including final exam room assignments. Organizes learning goals across four units: vectors and space curves, differential calculus, double/triple integrals, and calculus of vector fields. Includes topic-by-topic problem prompts covering dot/cross/triple products, line/plane equations, quadric surfaces, directional derivatives, gradient, Hessian-based second-derivative tests, optimization, and Lagrange multipliers.",{"@graph":63,"@context":118},[64,80,101],{"@type":65,"itemListElement":66},"BreadcrumbList",[67,71,74,77],{"item":68,"name":69,"@type":70,"position":9},"https://docshare.wps.com","Home","ListItem",{"item":72,"name":10,"@type":70,"position":73},"https://docshare.wps.com/template/",2,{"item":75,"name":11,"@type":70,"position":76},"https://docshare.wps.com/template/presentations/",3,{"item":78,"name":59,"@type":70,"position":79},"https://docshare.wps.com/template/calculus-iii-final-exam-study-guide-learning-goals-review-problems-goodbyes/573138/",4,{"url":78,"name":59,"@type":81,"image":82,"author":87,"headline":59,"publisher":90,"fileFormat":93,"inLanguage":57,"description":61,"dateModified":94,"datePublished":95,"encodingFormat":93,"isAccessibleForFree":96,"interactionStatistic":97},"DigitalDocument",{"url":83,"@type":84,"width":85,"height":86},"https://docshare.wps.com/thumbnails/calculus-iii-final-exam-study-guide-learning-goals-review-problems-goodbyes/573138.png","ImageObject",442,249,{"name":88,"@type":89},"nayy☆","Person",{"url":68,"name":91,"@type":92},"DocShare","Organization","application/pdf","2026-10-19","2026-10-13",true,{"@type":98,"interactionType":99,"userInteractionCount":79},"InteractionCounter",{"@type":100},"ViewAction",{"@type":102,"mainEntity":103},"FAQPage",[104,110,114],{"name":105,"@type":106,"acceptedAnswer":107},"When and where is the final exam review session scheduled?","Question",{"text":108,"@type":109},"The sheet schedules review for Thursday, December 13, 6:00–8:00 PM, and notes that students should know the room to go to for the final. Room assignments are listed afterward.","Answer",{"name":111,"@type":106,"acceptedAnswer":112},"What topics are covered in Unit I: Moving Around in Space?",{"text":113,"@type":109},"Unit I includes dot product, cross product, triple product, equations of a line and a plane, quadric surfaces, parametric curves and tangent vectors, and projectile problems.",{"name":115,"@type":106,"acceptedAnswer":116},"Which Unit II concepts are used for optimization with constraints?",{"text":117,"@type":109},"Unit II covers gradient and directional derivative ideas, the Hessian matrix for the second-derivative test, and Lagrange multipliers for optimizing functions with one constraint (with two or three variables).","https://schema.org",{"og:url":78,"og:type":120,"og:title":59,"og:site_name":91,"og:description":61},"article",{"robots":122,"canonical":78},"index,follow",{"doc_id":124,"site_id":56},573138,1792244233,{"code":4,"msg":5,"data":127},{"doc_id":124,"user_id":128,"nickname":88,"user_avatar":129,"doc_module":9,"category_id":8,"category_name":11,"doc_title":59,"doc_description":61,"doc_content":130,"file_id":131,"file_url":132,"file_type":133,"file_size":134,"view_count":79,"is_deleted":4,"is_public":9,"is_downloadable":9,"audit_status":9,"page_count":30,"language":135,"language_code":57,"site_id":56,"html_lang":57,"table_of_contents":136,"faqs":137,"seo_title":138,"seo_description":61,"update_tm":139,"read_time":140},962090893153,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Learning Goals Cheat Sheet Review Problems Goodbyes  \nCalculus III Meets the Final  \nPeter A. Perry University of Kentucky  \nDecember 7, 2018  \nLearning Goals Cheat Sheet Review Problems Goodbyes  \nHomework  \n􀀏 Review for Final Exam on Thursday, December 13, 6:00-8:00 PM  \n􀀏 Be sure you know which room to go to for the 􀀌nal!  \nLearning Goals Cheat Sheet Review Problems Goodbyes  \nFinal Exam Room Assignments  \n\n| Sections 001-008\u003Cbr>Sections 009-013\u003Cbr>Sections 014-016 | BE 111\u003Cbr>BS 107\u003Cbr>KAS 213 |\n| --- | --- |\n\nLearning Goals Cheat Sheet Review Problems Goodbyes  \nThe Big Picture  \nUnit I Vectors and Space Curves Unit II Di􀀋erential Calculus  \nUnit III Double and Triple Integrals Unit IV Calculus of Vector Fields  \nLearning Goals Cheat Sheet Review Problems Goodbyes  \nGoals of the Day  \n􀀏 Craft A Cheat Sheet  \n􀀏 Practice Problems  \n􀀏 Eat Cookies  \nLearning Goals Cheat Sheet Review Problems Goodbyes  \nUnit I: Moving Around in Space (1 of 2)  \n1. Dot product (scalar)  \na 􀀁 b = ja j j bj cos q = 0 if a ? b Geometric: Projection of one vector onto another  \n2. Cross product (vector)  \n􀀌  \n􀀌  \na 􀀂 b = 􀀌  \n􀀌  \n􀀌  \ni  \na1  \nb1  \nj  \na2  \nb2  \nk  \na3  \nb3  \n􀀌􀀌  \n􀀌 = 0 if a k b 􀀌  \n􀀌  \nGeometric: area of parallelogram spanned by a and b  \n3. Triple product (scalar)  \n􀀌􀀌  \na 􀀁 (b 􀀂 c) = 􀀌􀀌􀀌  \na1  \nb1  \nc1  \na2  \nb2  \nc2  \na3  \nb3  \nc3  \n􀀌􀀌  \n􀀌 = 0 if a , b , c coplanar 􀀌  \n􀀌  \nGeometric: Volume of parallelpiped spanned by a , b, and c  \nLearning Goals Cheat Sheet Review Problems Goodbyes  \nUnit I: Moving Around in Space (2 of 2)  \n4. Equation of line r = r0 + tv  \n5. Equation of plane ax + by + cz = d , n = ha , b , ci  \n6. Quadric surfaces; cylinder, ellipsoid, paraboloid, saddle  \n7. Parametric curve r (t) = x(t)i + y(t)j + z(t)k  \n8. Tangent vector r0 (t)  \n9. Projectile problems  \nLearning Goals Cheat Sheet Review Problems Goodbyes  \nUnit II: Di􀀋erential Calculus (1 of 3)  \n1. Chain rule for partial  \n2. Gradient  \npoints in direction of  \n3. Directional derivative  \n4. Critical points rf(a ,  \nderivatives  \n¶f   ¶frf = i + j ¶x ¶y  \ngreatest change (increase) Du f(x , y ) = rf(x , y ) 􀀁 ub) = 0  \nLearning Goals Cheat Sheet Review Problems Goodbyes  \nUnit II: Di􀀋erential Calculus (2 of 3)  \n5. Second derivative test: Hessian matrix  \n0 ¶2 f (a b)  ¶2 f  (a b)1 B ¶x2 , ¶x¶y , C  \nH (f )(a , b) = B ¶2 f ¶2 f C ,  \n@ ¶y ¶x (a , b)  ¶y2 (a , b) A  \nDeterminant  \nD (a , b) = det H(a , b)  \nSecond derivative test D > 0 (max or min), D \u003C 0 (saddle)  \nIf D > 0 and fxx(a , b) > 0, local min  \nIf D > 0 and fxx(a , b) \u003C 0, local max  \n6. Optimization of f (x , y ) over domain D: Find local extrema in D and ¶D  \nLearning Goals Cheat Sheet Review Problems Goodbyes  \nUnit II: Di􀀋erential Calculus (3 of 3)  \n7. Lagrange Multipliers (Two variables, one constraint) Minimize f (x , y ) subject to g(x , y ) = 0: solve  \nrf(x , y ) = lrg(x , y ) g (x , y ) = 0  \n8. Lagrange mutlipliers (three variables, one constraint) Minimize f (x , y , z) subject to g(x , y , z) = 0: solve  \nrf(x , y , z) = lrg(x , y , z) g (x , y , z) = 0","cbCaifvz6lhXxbEl","https://ap.wps.com/l/cbCaifvz6lhXxbEl","pdf",1506562,"English","# Learning Goals Cheat Sheet\n## Review Problems and Goodbyes\n## Homework and Final Exam Details\n## Final Exam Room Assignments\n## The Big Picture\n## Goals of the Day\n## Unit I: Moving Around in Space\n## Unit II: Differential Calculus","[{\"question\":\"When and where is the final exam review session scheduled?\",\"answer\":\"The sheet schedules review for Thursday, December 13, 6:00–8:00 PM, and notes that students should know the room to go to for the final. Room assignments are listed afterward.\"},{\"question\":\"What topics are covered in Unit I: Moving Around in Space?\",\"answer\":\"Unit I includes dot product, cross product, triple product, equations of a line and a plane, quadric surfaces, parametric curves and tangent vectors, and projectile problems.\"},{\"question\":\"Which Unit II concepts are used for optimization with constraints?\",\"answer\":\"Unit II covers gradient and directional derivative ideas, the Hessian matrix for the second-derivative test, and Lagrange multipliers for optimizing functions with one constraint (with two or three variables).\"}]","Calculus III - Final Exam Study Guide - Learning Goals, Review Problems, Goodbyes | PDF",1791933166,6]