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Math%19A%(Online)% Calculus'for'Science'Engineering'and'Mathematics' University'of'California'Santa'Cruz%

' Instructors%and%Course%Creators% Tony'Tromba,'PhD,'Distinguished'Professor,'Mathematics'Department,'UC'Santa'Cruz' Frank'Bäuerle,'PhD,'Continuing'Lecturer,'Mathematics'Department,'UC'Santa'Cruz' Katrina'Fullman,'Instructional'Designer,'UC'Online'Education,'UCOP% '

Course%Description%(from%the%UCSC%course%catalog)% The'limit'of'a'function,'calculating'limits,'continuity,'tangents,'velocities,'and'other' instantaneous'rates'of'change.'Derivatives,'the'chain'rule,'implicit'differentiation,'higher' derivatives.'Exponential'functions,'inverse'functions,'and'their'derivatives.'The'mean' value'theorem,'monotonic'functions,'concavity,'and'points'of'inflection.'Applied' maximum'and'minimum'problems.''

% Pre@Requisites%and%Entrance%Requirements% Passing'grade'in'Math'3'(Precalculus)'or'Applied'Mathematics'and'Statistics'3,'or' mathematics'placement'examination'(MPE)'score'of'400'or'higher;'or'AP'Calculus'AB' exam'score'of'3'or'higher.'

% Course%Learning%Objectives% 1. Understand'the'concept'of'an'instantaneous'rate'of'change'and'the'derivative'of'a' function' ' 2. Learn'how'to'calculate'derivatives'explicitly'and'implicitly'and'to'master'how' derivatives'affect'the'behavior'of'a'function' ' 3. Master'the'application'of'the'derivative'notion'to'optimization'problems'

% % Learning%Activities% The'course'uses'a'learning'management'system'(LMS)'to'organize'content'and'act'as'a' portal'to'various'other'platforms'including'an'interactive'eTtextbook,'a'homework' platform'with'immediate'feedback,'and'a'discussion'forum.'There'are'ten'weekly' modules'in'the'course,'but'these'can'be'reconfigured'to'accommodate'a'shorter'

Math 19A (Online) University of California Santa Cruz – Course Outline

summer'session'term.'Within'each'module,'there'are'1T3'lessons'and'each'of'these' lessons'outline'four'learning'activities.'To'be'successful'in'this'course,'students'must' actively'engage'in'all'four'activities:' ' 1. Read'the'textbook' 2. Watch'the'video'lectures' 3. Do'the'homework' 4. Interact'with'others' ' 1.%Readings' Each'lesson'indicates'the'required'reading'and'links'to'the'interactive'eTtextbook'based' on'Jon'Rogawski's'textbook,'Calculus,(Early(Transcendentals,(2nd(ed.'As'students'read' each'section'in'the'eTbook,'they'encounter'graded'progressTcheck'questions'as'well'as' supplemental'exercises.'ProgressTcheck'questions'provide'immediate'feedback'and'are' set'up'to'allow'three'attempts.' ' 2.%Videos% Each'lesson'also'links'to'short'video'lectures'that'explain'major'course'concepts'and' techniques'and'provide'examples.'Students'are'encouraged'to'alternate'between' viewing'the'videos'and'reading'the'corresponding'sections'in'the'eTbook.'Students'can' pause'or'rewind'lecture'videos'if'they'don’t'understand'content'covered.'They'can'also' come'back'for'review'at'any'time.' ' In'the'first'module,'students'are'encouraged'to'watch'supplemental'lectures'that' provide'context'and'historical'background'to'the'mathematics'covered'in'the'course.'' While'this'content'is'not'covered'on'assessments,'it'is'an'integral'part'of'the'course,' providing'students'with'a'deeper'understanding'of'the'concepts'covered'in'the'regular' lectures.' ' 3.%Homework' Each'lesson'indicates'the'required'homework'assignment'and'links'to'the'online' homework'system.'This'system'provides'immediate'feedback'on'answers'submitted'and' allows'unlimited'attempts.'In'preparation'for'exams,'students'are'provided'with' optional'ungraded'practice'materials.'

' 3.%Interaction' The'course'includes'an'onTline'discussion'forum'centered'on'questions'relating'to'the' video'lectures,'homework,'reading,'and'course'logistics.'In'addition,'the'teaching'staff' Page 2

Math 19A (Online) University of California Santa Cruz – Course Outline

hold'regular'onTline'and'inTperson'office'hours,'as'well'as'an'all'day'dropTin'section.' Finally'the'course'includes'studentTrun,'locationTbased'study'groups'with'corresponding' online'group'interaction'spaces'in'the'LMS.'Details'on'how'to'participate'are'outlined'on' the'lesson'pages'and'other'dedicated'pages'in'the'LMS.''

% % Course%Modules.'' ' Get%Started%%% • Prepare%for%Online%Learning'(Essential'course'information'on'getting'connected' to'course'tools'and'getting'help'with'logistical,'content'and'technical'issues)' • Syllabus%(Table'view'of'due'dates'and'syllabus'with'course'policies)' • Calculus%Diagnostic%Test'(Optional'test'to'determine'readiness'for'Calculus)' • Office%Hours'(Schedule'and'information'on'participating'in'online'and'inTperson' office'hours)' • Exam%Information'(Dates'and'expectations)' • Academic%Integrity'(Campus'academic'integrity'rules'and'policies)' • •

MSI%Session%Poll'(Tutoring'session'times)' Course%Contract'(Pledge'to'abide'by'academic'integrity'policy)'

'

''

To(access(the(course(materials,(students(must(complete(the(course(contract(by(the(end(of(the(first(week(of( instruction(

' '' ''' '' Module%1%% Learning'Objectives:'' • Understand'the'foundations'for'the'study'of'the'material'that'lies'ahead' Understand'why'mathematics'was'and'continues'to'be'so'crucial'in'the' development'of'our'modern'society'and'why'calculus'is'an'essential'part'of'a' science'curriculum.' • Understand'the'notion'of'limit'and'its'informal'definition' • Demonstrate'an'introductory'understanding'of'the'instantaneous'velocity'of'a' moving'object' Topics:' • Introductory'Lectures:'The'Birth'of'Calculus' • Lesson'2.1:'Limits,'Rates'of'Change,'Tangent'Lines' • Lesson'2.2:'Limits:'A'Numerical'and'Graphical'Approach''' ''' '' ' Module%2% Learning'Objectives:'' •

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Math 19A (Online) University of California Santa Cruz – Course Outline

Understand'basic'properties'of'limits'' Demonstrate'basic'techniques'to'calculate'limits'effectively.'' Gain'a'basic'understanding'of'what'it'means'for'a'function' 'to'be' continuous'at'a'point' ' Topics:' • Lesson'2.3'Basic'Limit'Laws''' '' • Lesson'2.4:'Limits'and'Continuity' • Lesson'2.5:'Evaluating'Limits'Algebraically' % Module%3% Learning'Objectives:'' • Understand'and'apply'the'squeeze'theorem'to'calculate'trigonometric'limits' • • •

• Understand'and'calculate'limits'at'infinity' • Understand'and'apply'the'Intermediate'Value'Theorem' Topics:% • Lesson'2.6:'Trigonometric'Limits' • Lesson'2.7:'Limits'at'Infinity' ''' ''' '' • Lesson'2.8:'The'Intermediate'Value'Theorem' % Module%4% Learning'Objectives:' • Understand'how'to'precisely'define'instantaneous'velocity,'and'more'generally,' instantaneous'rates'of'change.'' • Understand'a'limit'definition'of'the'central'notion'of'the'course:'the'derivative.' • •

Gain'a'basic'understanding'of'the'notion'of'the'derivative'as'a'function.' Apply'the'first'set'of'rules'on'how'to'effectively'calculate'derivatives'

Apply'alternate'notations'for'the'derivative' Understand'the'definition'of'the'number'"e"'and'gain'a'basic'understanding'of' its'significance.' Topics:' • Chapter'3'Introduction' • •

Lesson'3.1:'Definition'of'the'Derivative' Lesson'3.2:'The'Derivative'as'a'Function' MATH19A'Midterm1Review'' ' ''' ''' '' Module%5% Learning'Objectives:' • Understand'the'product'and'quotient'rules.'' • • •

•

Understand'derivatives'of'derivatives'called'higher'derivatives.'' Page 4

Math 19A (Online) University of California Santa Cruz – Course Outline

• Calculate'the'derivatives'of'the'trigonometric'functions.'' Topics:' • Lesson'3.3:'Product'and'Quotient'Rules' • Lesson'3.5:'Higher'Derivatives' • Lesson'3.6:'Trigonometric'Functions' ' ''' ''' '' Module%6% Learning'Objectives' • Gain'a'basic'understanding'of'the'chain'rule'for'calculating'the'derivative'of'a' composition'of'differentiable'functions.'' • Apply'the'chain'rule'to'determine'the'derivatives'of'inverse'functions'of' differentiable'functions'as'well'as'the'derivatives'of'general'exponential'and' logarithmic'functions.'' • Understand'and'apply'a'comprehensive'way'to'calculate'the'derivative'of'all' elementary'functions'(such'as'combinations'and'compositions'of'polynomial,' rational,'trigonometric,'inverse'trigonometric,'logarithmic'and'exponential' functions).' Topics:' • Lesson'3.7:'The'Chain'Rule' • Lesson'3.8:'Derivatives'of'Inverse'Functions' • Lesson'3.9:'Derivatives'of'General'Exponential'and'Logarithmic'Functions' % %%% %%% %% Module%7% Learning'Objectives' • Understand'how'to'the'chain'rule'is'used'to'calculate'the'derivatives'of'implicitly' defined'functions.'' • Apply'the'chain'rule'to'the'computation'of'"Related'Rates,”'our'first'real' application'of'the'derivative.' Topics:' • Lesson'3.10:'Implicit'Differentiation' • Lesson'3.11:'Related'Rates' • MATH19A'Midterm'2'Review' % Module%8% Learning'Objectives' • Gain'a'basic'understanding'of'the'notion'of'maximum'and'minimum'of'a' function.'' • Gain'a'basic'understanding'of'"Mean'Value'Theorem”'

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Math 19A (Online) University of California Santa Cruz – Course Outline

• Understand'how'the'derivative'helps'us'understand'the'shape'of'graphs' Topics:' • Chapter'4'Introduction' • •

Lesson'4.2:'Extreme'Values' Lesson'4.3:'The'Mean'Value'Theorem'and'Monotonicity'

•

Lesson'4.4:'The'Shape'of'a'Graph'

'''

'''

''

' Module%9' Learning'Objectives:' • Gain'a'further'understanding'of'how'the'derivative'helps'us'understand'the' shape'of'graphs' • Gain'an'understanding'of'L’Hôpital’s'Rule'and'use'it'to'compute'limits' Topics:' • Lesson'4.5:'L’Hôpital’s'Rule' • Lesson'4.6:'Graph'Sketching'and'Asymptotes' ' Module%10% Learning'Objectives' ''' '' • Apply'the'derivative'to'basic'optimization'problems' • Understand'how'to'model'a'physical'phenomenon'by'a'function'y=f(x)'and'apply' our'methods'to'optimize'f(x)'independent'of'what'f(x)'actually'represents' • (Optional)'Gain'an'overview'of'"Newton's'method,”'a'technique'that'uses'the' derivative'to'address'the'problem'of'solving'equations'numerically,'a'topic'which' is'very'important'in'engineering'applications' Topics:' • Lesson'4.7:'Applied'Optimization' • Lesson'4.8:'Newton's'Method' ' Final%Exam%Review% • Exam'Information' • Math'19A'Practice'Finals' •

Math'19A'Practice'Problems'for'Final'

' Course%Resources% • Course'Overview' • Course'Introduction' • • •

Instructor'Introductions' All'Lecture'Videos' Homework'(CalcPortal)' Page 6

Math 19A (Online) University of California Santa Cruz – Course Outline

' Support%Options% • CollegeTBased'Study'Groups' • Tutoring'Options' • MSI'(Modified'Supplemental'Instruction)'in'Santa'Cruz' • Disability'Accommodations' • Study'Tips' •

Office'Hours'

% % '''

'''

''

Instructional%Strategy% ' Instructional'Element' Canvas'

CalcPortal'

Intended'Learning'Experience' • Primary'course'portal'that'students'use'to'view'videos'and'find' general'information'and'announcements'on'the'course.'Faculty' update'course'information'as'necessary.' • Canvas'is'used'by'students'for'every'study'session'–'students' access'the'ebook,'discussion'forum,'and'homework'portal' through'Canvas' • Engagement'can'be'evaluated'through'course'analytics'that' provide'data'on'how'frequently'students'login,'number'of'pages' visited,'etc.' Pedagogy:'Canvas'is'a'central'hub'through'which'students'can' access'all'course'information'and'communicate'with'teaching'staff' and'peers.'It'provides'organization'and'structure'to'the'course.' • Homework'platform'that'students'use'to'complete'all' homework'assignments,'quizzes,'and'exams'if'offered'online.' • Faculty'engage'regularly'with'CalcPortal'to'create'exam' questions,'grade'exams,'and'calculate'overall'grade.'The'grade' book'will'be'maintained'in'this'platform,'but'final'grades'for'all' students'will'be'ported'over'to'Canvas'for'export'to'appropriate' Student'Information'Systems' • Engagement'can'be'evaluated'through'course'analytics'that' provide'data'on'how'frequently'students'login,'time'spent'on' homework'questions,'completion'of'assignments,'etc.' Pedagogy:'CalcPortal'allows'students'to'test'their'understanding'of' course'content'frequently.'It'provides'immediate'feedback'on' homework'questions'and'hence'reinforces'knowledge'and'flags' Page 7

Math 19A (Online) University of California Santa Cruz – Course Outline

Instructional'Element' Launchpad'

Piazza'

Brightcove/Video' Lectures'

Office'Hours/Adobe' Connect'

Intended'Learning'Experience' areas'that'need'further'study'or'exploration.' • ETtextbook'platform'that'provides'interactive'reading' assignments'for'each'lesson.' • Course'designers'customized'the'eTbook'by'editing'passages' and/or'deleting'extraneous'material,'embedding'additional' interactive'features,'creating'progress'check'questions,'etc.' • Engagement/performance'can'be'assessed'through'analytics' that'provide'data'on'how'frequently'students'login,'scores'on' progress'check'questions,'pages'visited,'etc.' Pedagogy:'customization'provides'students'with'a'text'that'is'tied' closely'to'other'course'elements.'Interactive'elements'engage' students'and'lead'to'greater'comprehension'of'reading.'Portability' allows'students'to'view'textbook'from'mobile'devices' • Discussion'forum'that'allows'students'to'interact'with' classmates'and'faculty' • Teaching'staff'will'facilitate'and'provide'regular'presence'by' answering'questions'and'endorsing'helpful'student'posts.' Teaching'staff'will'also'create'tags'and'folders'to'organize'posts,' and'provide'seed'questions'to'stimulate'discussion.' • Engagement'can'be'assessed'through'analytics'that'provide'data' on'how'frequently'a'student'logins'and'how'frequently'they' post.' Pedagogy:'discussion'boards'lead'to'less'isolation'in'online'courses,' provide'students'with'opportunities'to'collaborate'and'form' community,'and'allow'for'much'quicker'response'times'to'student' questions.'By'responding'to'classmates’'questions,'students'have'an' opportunity'to'demonstrate'knowledge'and'explain'complicated' concepts'in'their'own'words,'thus'leading'to'greater'understanding' and'comprehension.'' • Online'video'hosting'platform.' Engagement'will'be'assessed'through'analytics'showing'number' and'duration'of'video'views.' Pedagogy:'online'lectures'and'other'course'videos'create'sense'of' instructor'presence,'allow'for'the'presentation'of'complex'material,' allow'students'to'access'course'material'whenever'they'wish,'and' allow'students'to'review'(rewind)'lectures.' • Offered'both'online'and'inTperson'several'times'a'week'by' Faculty'and'TAs.'OneTonTone'appointments'available.'' • Online'Office'Hours'conducted'using'Adobe'Connect,'a'webT •

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Math 19A (Online) University of California Santa Cruz – Course Outline

Instructional'Element'

DropTin'Sections''

Tutoring'

CollegeTBased'Study' Groups'

Intended'Learning'Experience' based'conferencing'software'that'allows'for'VOIP,'textTbased' chat,'whiteboard'that'allows'both'faculty'and'students'to'write' equations,'screen'sharing,'and'video'and'powerpoint' presentation.' Pedagogy:'Office'Hours'give'both'remote'and'local'students'an' opportunity'to'connect'with'teaching'staff'and'peers'and'get' individualized'instruction'on'content'with'which'they'are'struggling.'' • Offered'once'a'week'–'extended'meeting'period'where'students' can'drop'in'to'work'faceTtoTface'with'other'students'and'TAs.' TAs'may'provide'miniTlectures'on'concepts'covered'in'weekly' modules.'Extra'meetings'scheduled'during'exam'periods.' Pedagogy:'provides'an'additional'opportunity'for'faceTtoTface' interaction'and'small'group'instruction.' • FaceTtoTFace'Tutoring'available'at'UCSC'through'MSI'(Modified' Supplemental'Instruction,'a'campus'program),'Math' Department,'and'ACE'(a'divisional'program'for'students'of' underrepresented'groups).' Pedagogy:'provides'students'with'additional'support'if'they'are' struggling'with'comprehension'of'the'material.'Can'be'used'by'both' lower'and'higher'performing'students.' • Informal'studentTled'study'group'set'up'for'each'residential' college'and/or'remote'campus.' • One'to'three'student'volunteer'facilitators'appointed.' • Groups'are'encouraged'to'meet'in'person'or'online'at'least'once' a'week.' • Assigned'Canvas'Group'space'to'exchange'notes,'create'wiki,' make'announcements,'meet'online.' • Groups'are'encouraged'to'do'homework'together,'watch' lectures,'work'on'supplemental'problem'worksheets,'etc.' Pedagogy:'provides'a'studentTcentered'learning'activity'with' opportunities'for'both'faceTtoTface'and'online'interaction.'Provides' an'opportunity'for'students'to'share'knowledge'and'form' community.'

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Math 19A (Online) University of California Santa Cruz – Course Outline

Assessment%Activities%

%

'

Component'

Description'

Percentage'

Homework'

Online'Homework'problems'for'each'lesson'accessed'through' CalcPortal''

15%''

• •

Quizzes''

Low'stakes'questions'with'unlimited'attempts'and' immediate'feedback'in'CP.'' Students'can'check'their'understanding'of'the'content'in' each'lesson'and'are'incentivized'to'complete'homework' through'points'earned'toward'final'grade.''

Periodic'online'quizzes'in'CalcPortal'' The'online'quizzes'are'distinguished'from'onTline' homework'by'being'limited'in'time'and'by'the'absence'of' hints'and'feedback.'' • Students'have'only'one'attempt'on'each'question.'' • There'will'be'partial'credit'(where'appropriate).'TAs'and' instructors'will'check'answers'and'may'assign'partial'credit' after'the'computer'score'has'been'calculated.'' • A'final'score'on'a'quiz'or'other'onTline'test'may'be'higher' than'what'students'receive'immediately'after'submitting' the'test'to'CalcPortal.' Reading'progress'check'questions'in'Launchpad'(eTtextbook' platform)'

10%'

•

Reading'

• • 2'Proctored' Midterms''

• Final'

Low'stakes'progress'check'questions'with'3'attempts'on' each'question.'Located'in'each'lesson.' Encourages'students'to'complete'the'readings'and'gives' them'an'opportunity'to'check'their'understanding.''

Online'and'inTperson'options'(online'exams'proctored'by' Proctor'U)' •

30%'

Formative'assessments'that'give'students’'an'opportunity' to'evaluate'progress'and'make'improvements'where' necessary.'' Provides'students'with'examples'of'how'questions'are' formatted'on'final.'

Comprehensive'final'exam.'Online'and'inTperson'options' (online'exams'proctored'by'Proctor'U)' •

5%'

40%'

Summative'assessment'used'to'evaluate'student'learning.' 100.00%'

Total:%

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