Introduction

Math 140 - Calculus I

Catalin Zara

UMass Boston

September 8, 2009

Catalin Zara (UMB) Introduction September 8, 2009 1 / 1

Back by popular demand

Catalin Zara (UMB) Introduction September 8, 2009 2 / 1

Back by popular demand For a limited time only

Catalin Zara (UMB) Introduction September 8, 2009 2 / 1

Back by popular demand For a limited time only

In a location near you

Catalin Zara (UMB) Introduction September 8, 2009 2 / 1

Back by popular demand For a limited time only

In a location near you A mid-morning special

Catalin Zara (UMB) Introduction September 8, 2009 2 / 1

Back by popular demand For a limited time only

In a location near you A mid-morning special

UMass BostonDepartment of Mathematics

presents

Catalin Zara (UMB) Introduction September 8, 2009 2 / 1

ACatalin Zaraproduction

Catalin Zara (UMB) Introduction September 8, 2009 3 / 1

ACatalin Zaraproduction

Math 140: Calculus I

Catalin Zara (UMB) Introduction September 8, 2009 3 / 1

ACatalin Zaraproduction

Math 140: Calculus I

Based on a true storyAny resemblance with reality has been thoroughly investigated and

proven to be correct.

Catalin Zara (UMB) Introduction September 8, 2009 3 / 1

ACatalin Zaraproduction

Math 140: Calculus I

Based on a true storyAny resemblance with reality has been thoroughly investigated and

proven to be correct.

Rated: 130-B or C-26

Catalin Zara (UMB) Introduction September 8, 2009 3 / 1

ACatalin Zaraproduction

Math 140: Calculus I

Based on a true storyAny resemblance with reality has been thoroughly investigated and

proven to be correct.

Rated: 130-B or C-26as in: Math 130 with B or better or

Catalin Zara (UMB) Introduction September 8, 2009 3 / 1

ACatalin Zaraproduction

Math 140: Calculus I

Based on a true storyAny resemblance with reality has been thoroughly investigated and

proven to be correct.

Rated: 130-B or C-26as in: Math 130 with B or better orPlacement Test C with 26 or higher

Catalin Zara (UMB) Introduction September 8, 2009 3 / 1

Directed by

Catalin Zaracatalin.zara@umb.eduScience, 3rd Floor, 3-091617-287-6463www.math.umb.edu/∼czara

Screenplay

Based on(Single Variable) Calculus6th Editionby James Stewart

Technical SupportUMass Online - BlackboardURochester - WeBWorKWolfram - Mathematica

Catalin Zara (UMB) Introduction September 8, 2009 4 / 1

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina A

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra Tasha

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,Sanabel

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin Michael

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,Blanka

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina E

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,Carol

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a Abdul

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a AbdulHorton,William

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a AbdulHorton,WilliamInashima,Kunikazu

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a AbdulHorton,WilliamInashima,KunikazuKem,Marina

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a AbdulHorton,WilliamInashima,KunikazuKem,MarinaLaguerre,Philip Nathanael

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a AbdulHorton,WilliamInashima,KunikazuKem,MarinaLaguerre,Philip NathanaelLau,Ka Yeung

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a AbdulHorton,WilliamInashima,KunikazuKem,MarinaLaguerre,Philip NathanaelLau,Ka YeungLe,Trang Vu

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a AbdulHorton,WilliamInashima,KunikazuKem,MarinaLaguerre,Philip NathanaelLau,Ka YeungLe,Trang VuMercedes,Christopher Blass

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a AbdulHorton,WilliamInashima,KunikazuKem,MarinaLaguerre,Philip NathanaelLau,Ka YeungLe,Trang VuMercedes,Christopher BlassMurphy,Michael Joseph

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a AbdulHorton,WilliamInashima,KunikazuKem,MarinaLaguerre,Philip NathanaelLau,Ka YeungLe,Trang VuMercedes,Christopher BlassMurphy,Michael JosephNelson,James Douglas

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a AbdulHorton,WilliamInashima,KunikazuKem,MarinaLaguerre,Philip NathanaelLau,Ka YeungLe,Trang VuMercedes,Christopher BlassMurphy,Michael JosephNelson,James DouglasPoudyal,Rasendra

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Abelard,Christina AAlcindor,Alexandra TashaAlmomani,SanabelAmaral,Kevin MichaelArmiri,BlankaD’Amico,Kristina EDarwich,CarolEl-Shaar,Ala’a AbdulHorton,WilliamInashima,KunikazuKem,MarinaLaguerre,Philip NathanaelLau,Ka YeungLe,Trang VuMercedes,Christopher BlassMurphy,Michael JosephNelson,James DouglasPoudyal,RasendraRyan,Richard J

Catalin Zara (UMB) Introduction September 8, 2009 5 / 1

Car

Speed Time Distance

Rate of change

v = ∆D

∆t

Limit∆t → 0

AccumulationD =

∑v · ∆t

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

Speed Time Distance

Rate of change

v = ∆D

∆t

Limit∆t → 0

AccumulationD =

∑v · ∆t

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

Speed Time Distance

Rate of change

v = ∆D

∆t

Limit∆t → 0

AccumulationD =

∑v · ∆t

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

Speed Time Distance

Rate of change

v = ∆D

∆t

Limit∆t → 0

AccumulationD =

∑v · ∆t

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed Time Distance

Rate of change

v = ∆D

∆t

Limit∆t → 0

AccumulationD =

∑v · ∆t

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed Time Distance

Rate of change

v = ∆D

∆t

Limit∆t → 0

AccumulationD =

∑v · ∆t

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Distance = Accumulation of distance traveled over short periods

D =∑

∆D =∑

v · ∆t

Catalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed Time Distance

Rate of change

v = ∆D

∆t

Limit∆t → 0

AccumulationD =

∑v · ∆t

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed

��

Time

wwoooooooooooo

Distance

Rate of change

v = ∆D

∆t

Limit∆t → 0

AccumulationD =

∑v · ∆t

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed

��

Time

wwoooooooooooo

&&MMMMMMMMMMMDistance

��

Rate of change

v = ∆D

∆t

Limit∆t → 0

AccumulationD =

∑v · ∆t

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Distance = Accumulation of distance traveled over short periods

D =∑

∆D =∑

v · ∆t

Catalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed

��

Time

wwoooooooooooo

&&MMMMMMMMMMM

��

Distance

��

Rate of change

v = ∆D

∆t

Limit∆t → 0

AccumulationD =

∑v · ∆t

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed

��

Time

wwoooooooooooo

&&MMMMMMMMMMM

��

Distance

��

Rate of change

v = ∆D

∆t

��

Limit∆t → 0

yyrrrrrrrrrrr

AccumulationD =

∑v · ∆t

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed

��

Time

wwoooooooooooo

&&MMMMMMMMMMM

��

Distance

��

Rate of change

v = ∆D

∆t

��

Limit∆t → 0

yyrrrrrrrrrrr

%%JJJJJJJJJJ

AccumulationD =

∑v · ∆t

��

Derivative

v(t) = dD

dt= D

′(t)FTC

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed

��

Time

wwoooooooooooo

&&MMMMMMMMMMM

��

Distance

��

Rate of change

v = ∆D

∆t

��

Limit∆t → 0

yyrrrrrrrrrrr

%%JJJJJJJJJJ

AccumulationD =

∑v · ∆t

��

Derivative

v(t) = dD

dt= D

′(t)FTCoo //

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed

��

Time

wwoooooooooooo

&&MMMMMMMMMMM

��

Distance

��

Rate of change

v = ∆D

∆t

��

Limit∆t → 0

yyrrrrrrrrrrr

%%JJJJJJJJJJ

AccumulationD =

∑v · ∆t

��

Derivative

v(t) = dD

dt= D

′(t)FTCoo //

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed

��

Time

wwoooooooooooo

&&MMMMMMMMMMM

��

Distance

��

Rate of change

v = ∆D

∆t

��

Limit∆t → 0

yyrrrrrrrrrrr

%%JJJJJJJJJJ

AccumulationD =

∑v · ∆t

��

Derivative

v(t) = dD

dt= D

′(t)FTCoo //

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed

��

Time

wwoooooooooooo

&&MMMMMMMMMMM

��

Distance

��

Rate of change

v = ∆D

∆t

��

Limit∆t → 0

yyrrrrrrrrrrr

%%JJJJJJJJJJ

AccumulationD =

∑v · ∆t

��

Derivative

v(t) = dD

dt= D

′(t)FTCoo //

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Car

vvmmmmmmmmmmmmmmmm

((QQQQQQQQQQQQQQ

Speed

��

Time

wwoooooooooooo

&&MMMMMMMMMMM

��

Distance

��

Rate of change

v = ∆D

∆t

��

Limit∆t → 0

yyrrrrrrrrrrr

%%JJJJJJJJJJ

AccumulationD =

∑v · ∆t

��

Derivative

v(t) = dD

dt= D

′(t)FTCoo //

Integral

D =∫

t2

t1v(t) dt

Speed = Rate of change of distance with respect to time

v =∆D

∆tCatalin Zara (UMB) Introduction September 8, 2009 6 / 1

Goals

Catalin Zara (UMB) Introduction September 8, 2009 7 / 1

Goals

Understand the fundamental concepts of calculus

Catalin Zara (UMB) Introduction September 8, 2009 7 / 1

Goals

Understand the fundamental concepts of calculus

Demonstrate ability to use calculus to solve problems

Catalin Zara (UMB) Introduction September 8, 2009 7 / 1

Goals

Understand the fundamental concepts of calculus

Demonstrate ability to use calculus to solve problems

◮ Construct mathematical model◮ Recognize concepts and techniques◮ Apply formulas and results◮ Interpret and communicate the results

Catalin Zara (UMB) Introduction September 8, 2009 7 / 1

Goals

Understand the fundamental concepts of calculus

Demonstrate ability to use calculus to solve problems

◮ Construct mathematical model◮ Recognize concepts and techniques◮ Apply formulas and results◮ Interpret and communicate the results

Build and improve portable skills

Catalin Zara (UMB) Introduction September 8, 2009 7 / 1

Goals

Understand the fundamental concepts of calculus

Demonstrate ability to use calculus to solve problems

◮ Construct mathematical model◮ Recognize concepts and techniques◮ Apply formulas and results◮ Interpret and communicate the results

Build and improve portable skills

◮ Analyze data◮ Reason deductively◮ Think abstractly◮ Think analytically◮ Think critically◮ Solve problems

Catalin Zara (UMB) Introduction September 8, 2009 7 / 1

Goals

Understand the fundamental concepts of calculus

Demonstrate ability to use calculus to solve problems

◮ Construct mathematical model◮ Recognize concepts and techniques◮ Apply formulas and results◮ Interpret and communicate the results

Build and improve portable skills

◮ Analyze data◮ Reason deductively◮ Think abstractly◮ Think analytically◮ Think critically◮ Solve problems

Appreciate the beauty and power of mathematics

Catalin Zara (UMB) Introduction September 8, 2009 7 / 1

Goals

Understand the fundamental concepts of calculus

Demonstrate ability to use calculus to solve problems

◮ Construct mathematical model◮ Recognize concepts and techniques◮ Apply formulas and results◮ Interpret and communicate the results

Build and improve portable skills

◮ Analyze data◮ Reason deductively◮ Think abstractly◮ Think analytically◮ Think critically◮ Solve problems

Appreciate the beauty and power of mathematics

Have fun!

Catalin Zara (UMB) Introduction September 8, 2009 7 / 1

Expectations

Catalin Zara (UMB) Introduction September 8, 2009 8 / 1

Expectations

Motivated students

Catalin Zara (UMB) Introduction September 8, 2009 8 / 1

Expectations

Motivated students

Strong background

Catalin Zara (UMB) Introduction September 8, 2009 8 / 1

Expectations

Motivated students

Strong background

Committed to learning

Catalin Zara (UMB) Introduction September 8, 2009 8 / 1

Expectations

Motivated students

Strong background

Committed to learning

Actively involved

Catalin Zara (UMB) Introduction September 8, 2009 8 / 1

Expectations

Motivated students

Strong background

Committed to learning

Actively involved

Able to work in groups

Catalin Zara (UMB) Introduction September 8, 2009 8 / 1

Expectations

Motivated students

Strong background

Committed to learning

Actively involved

Able to work in groups

Secure enough to ask for help

Catalin Zara (UMB) Introduction September 8, 2009 8 / 1

Expectations

Motivated students

Strong background

Committed to learning

Actively involved

Able to work in groups

Secure enough to ask for help

Your expectations?

Catalin Zara (UMB) Introduction September 8, 2009 8 / 1

Expectations

Motivated students

Strong background

Committed to learning

Actively involved

Able to work in groups

Secure enough to ask for help

Your expectations?Complete the Survey on Blackboard!

Catalin Zara (UMB) Introduction September 8, 2009 8 / 1

Your Rights

Catalin Zara (UMB) Introduction September 8, 2009 9 / 1

Your Rights

You have the right to ask questions.

Catalin Zara (UMB) Introduction September 8, 2009 9 / 1

Your Rights

You have the right to ask questions.

Nothing you ask will be used against you in deciding the grade.

Catalin Zara (UMB) Introduction September 8, 2009 9 / 1

Your Rights

You have the right to ask questions.

Nothing you ask will be used against you in deciding the grade.

You have the right to have a tutor.

Catalin Zara (UMB) Introduction September 8, 2009 9 / 1

Your Rights

You have the right to ask questions.

Nothing you ask will be used against you in deciding the grade.

You have the right to have a tutor.

If you cannot afford a private tutor, one will be appointed to youfree of charge if you wish.

Catalin Zara (UMB) Introduction September 8, 2009 9 / 1

Resources

Catalin Zara (UMB) Introduction September 8, 2009 10 / 1

Resources

Message boards on Blackboard

Catalin Zara (UMB) Introduction September 8, 2009 10 / 1

Resources

Message boards on Blackboard

◮ Post questions AND answers◮ Anonymous or signed

Catalin Zara (UMB) Introduction September 8, 2009 10 / 1

Resources

Message boards on Blackboard

◮ Post questions AND answers◮ Anonymous or signed

Tutors, Mathematics Resource Center◮ FREE one-on-one tutoring!!

Catalin Zara (UMB) Introduction September 8, 2009 10 / 1

Resources

Message boards on Blackboard

◮ Post questions AND answers◮ Anonymous or signed

Tutors, Mathematics Resource Center◮ FREE one-on-one tutoring!!

Supplemental Instruction Sessions◮ To be scheduled

Catalin Zara (UMB) Introduction September 8, 2009 10 / 1

Resources

Message boards on Blackboard

◮ Post questions AND answers◮ Anonymous or signed

Tutors, Mathematics Resource Center◮ FREE one-on-one tutoring!!

Supplemental Instruction Sessions◮ To be scheduled

Office hours◮ Thu 11:50am - 12:20pm, 2:00pm - 2:50pm◮ Tu 2:00pm - 2:50pm

Catalin Zara (UMB) Introduction September 8, 2009 10 / 1