{"id":19,"date":"2017-12-19T23:43:22","date_gmt":"2017-12-20T06:43:22","guid":{"rendered":"https:\/\/blogs.ubc.ca\/math110s1\/?page_id=19"},"modified":"2018-04-13T00:08:10","modified_gmt":"2018-04-13T07:08:10","slug":"lecture-notes","status":"publish","type":"page","link":"https:\/\/blogs.ubc.ca\/math110s1\/lecture-notes\/","title":{"rendered":"Lecture Notes"},"content":{"rendered":"

In this page, I post the notes and the material you need to know for each class (before and after the class!) For each lecture, the textbook section corresponding to that lecture is also posted. For example: Limits: Section 1.1 & 1.2<\/em><\/p>\n

Final Exam Review Material<\/strong><\/span><\/p>\n

Review Notes\u00a0<\/a>Ignore questions 4,15,22,29 of the optimization section.
\nSolutions<\/a>\u00a0to selected problems of the review note.
\nSolutions<\/a>\u00a0to optimization questions
\nShort Questions<\/a>: (updated) True\/False, multiple choice
\nSolutions<\/a>\u00a0to short questions<\/p>\n

* Week 13:\u00a0<\/strong>Taylor Polynomial and Anti-derivative<\/p>\n

Additional Topics<\/a>: Two topics you need to know if you are taking the Integral Calculus course. Not part of our exam.
\nLecture 35<\/a>: Anti-derivative
\nLecture 34<\/a>: Higher degree approximation (Taylor Polynomial)<\/p>\n

* Week 12:<\/strong> Approximation<\/p>\n

Lecture 33<\/a>: Quadratic Approximation vs Linear Approximation
\nLecture 32<\/a>: Linear Approximation<\/p>\n

* Week 11:<\/strong> More on Optimization<\/p>\n

worksheet<\/a>: more samples of optimization problems (there are lots of them on WebWork.)
\nLecture 31<\/a>: Optimization with parameters (Q9 of the worksheet)
\nLecture 30<\/a>: Solving Questions 4 and 3 of the worksheet.\u00a0Complete solution <\/a>\u00a0to Q3 of the worksheet.
\nLecture 29<\/a>: Complete the worksheet from last week and question 1 from the other worksheet.<\/p>\n

* Week 10:<\/strong> Optimization (Good to attend the class for this topic.)<\/p>\n

worksheet<\/a>: Steps in solving an optimization problem & a step-by-step example
\nLecture 28<\/a>: Optimization (completing the examples from last class.)
\nLecture 27<\/a>: Optimization: Examples
\nLecture 26<\/a>: Global Extrema: Graphical and computational.<\/p>\n

*\u00a0Week 9: <\/strong>Curve sketching<\/p>\n

Curve Sketching Practice<\/a>, from UCDavis online notes.
\nLecture 25<\/a>: A warm-up curve sketching exercise before the quiz.
\nLecture 24<\/a>: Sketching the curve of another rational function and an exponential function.
\nLecture 23<\/a>: Sketching the curve of a rational function.<\/p>\n

* Week 8:<\/strong> l’Hopital’s Rule<\/p>\n

Lecture 22<\/a>: One l’Hopital example and Curve Sketching.\u00a0Solution<\/a>\u00a0to the curve sketching exercise in the note.
\nLecture 21<\/a>: Other forms of indeterminate limits: inf-inf , 0 * inf.\u00a0Solution<\/a>\u00a0to limit exercises in the note.
\nReview Hand-out<\/a>, Solution<\/a>\u00a0to solved problems in the review session
\nLecture 20<\/a>\u00a0 l’Hopital’s rule to find 0\/0 and inf\/inf limits.<\/p>\n

* W\u00a0Reading Week \ud83d\ude09<\/span><\/strong><\/p>\n

* Week 7: <\/strong>Vertical and Horizontal Asymptotes of the function<\/p>\n

Lecture 19<\/a>: Asymptotic behavior of a function: Horizontal Asymptote
\nLecture 18<\/a>: Asymptotic behavior of a function: Vertical Asymptote<\/p>\n

* Week 6:\u00a0<\/strong>Concavity of the function f and its relation with the second derivative f”: S3.4<\/strong><\/p>\n

Quick Test<\/a>: Graphical interpretation of f’ and f”.\u00a0Solution<\/a>
\nLecture 17<\/a>: Strategies in computations of f’, f”, critical numbers, etc.
\nLecture 16<\/a>: Examples of sign charts for f’ and f”
\nLecture 15<\/a>: Concavity of f and the sign of f”<\/p>\n

* Week 5: <\/strong>Increasing\/Decreasing function and the 1st derivative test: S3.3<\/strong><\/p>\n

Lecture 13&14 + practice problems<\/a>: Examples on finding the local extrma using the 1st derivative test. Intervals of increase and decrease in f.
\nLecture 12<\/a>: Finding intervals of increase\/decrease of a function using its derivative, 1st derivative test to find local extrema.
\nQuick Test 3<\/a>\u00a0(with solution)
\nQuick Test 2\u00a0<\/a>, \u00a0Solution<\/a>
\nQuick Test 1<\/a>\u00a0(with solution)<\/p>\n

Check out the following tutorials from <\/span>Paul’s Online Math Notes<\/em>\u00a0on <\/span>working with inequalities to determine the sign of expressions:<\/em><\/span> Tutorial 1: Polynomials<\/a> Tutorial 2: Rational functions<\/a><\/p>\n

* Week 4:<\/strong> Local extrema, critical numbers, Mean Value Theorem: S3.1 & 3.2<\/strong><\/p>\n

Trapezoidal Tank<\/a>: Follow these steps to solve the WebWork 2.4 problem.
\nLecture 11<\/a>: Mean Value Theorem, Rolle’s Theorem, application and examples<\/span>
\nLecture 10<\/a>: More examples on finding critical numbers.<\/span>
\nWorksheet 4<\/a>: Intro to Mean Value Theorem.\u00a0Solution<\/a>\u00a0to worksheet 4.<\/span>
\nLecture 9<\/a>: Local max\/min and critical numbers (concept, definition, examples)<\/span><\/p>\n

* Week 3: <\/strong>Related Rates Cont’d<\/p>\n

In class Worksheet 3<\/a>.\u00a0Solution<\/a>\u00a0to worksheet 3.
\nIn class Worksheet 2<\/a>.\u00a0Solution<\/a>\u00a0to worksheet 2.<\/p>\n

* Week 2:<\/strong>\u00a0Implicit\u00a0differentiation cont’d\u00a0& Related rates: <\/em>S2.6<\/strong><\/p>\n

Lecture 4&5<\/a>: Introduction to related rates word\u00a0problems and the strategies to solve a typical related rates problem.
\nIn class\u00a0Worksheet 1<\/a>.\u00a0Solution<\/a>\u00a0to worksheet 1.
\nLecture 3<\/a>: Finding the second derivative of an implicit\u00a0curve. Solve the practice problems<\/strong>\u00a0at the end of the notes.\u00a0Solution to practice problems<\/a>\u00a0of this lecture.<\/p>\n

* Week 1:\u00a0<\/strong>Implicit Differentiation:\u00a0<\/em>S2.9<\/strong><\/p>\n

Lecture 2<\/a>: Implicit differentiation, the\u00a0tangent line to an implicit curve.
\nLecture 1<\/a>: Review of the chain rule, introduction to implicit curves.<\/p>\n","protected":false},"excerpt":{"rendered":"

In this page, I post the notes and the material you need to know for each class (before and after the class!) For each lecture, the textbook section corresponding to that lecture is also posted. For example: Limits: Section 1.1 & 1.2 Final Exam Review Material Review Notes\u00a0Ignore questions 4,15,22,29 of the optimization section. Solutions\u00a0to […]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-19","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.ubc.ca\/math110s1\/wp-json\/wp\/v2\/pages\/19","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ubc.ca\/math110s1\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.ubc.ca\/math110s1\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/math110s1\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ubc.ca\/math110s1\/wp-json\/wp\/v2\/comments?post=19"}],"version-history":[{"count":80,"href":"https:\/\/blogs.ubc.ca\/math110s1\/wp-json\/wp\/v2\/pages\/19\/revisions"}],"predecessor-version":[{"id":349,"href":"https:\/\/blogs.ubc.ca\/math110s1\/wp-json\/wp\/v2\/pages\/19\/revisions\/349"}],"wp:attachment":[{"href":"https:\/\/blogs.ubc.ca\/math110s1\/wp-json\/wp\/v2\/media?parent=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}