introduction - math 140 - calculus...
TRANSCRIPT
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 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
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 [email protected], 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
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
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
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
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
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