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Syllabus: M408D (Fall 15)

SEQUENCES, SERIES, AND MULTIVARIABLE CALCULUS

Instructor:Gustavo Cepparo Office: RLM 13.148 Phone: 232-6189e-mail:gcepparo@math.utexas.edu

Lectures:JGB 2.216 M W F 8:00 - 9:00 a.m.

Instructors Office hours:

M W11:05 a.m. - 12:05 p.m.

F 7:00 - 8:00 a.m.

Meeting times by section number:

Section Time Location

52770 T Th 8:30-9:30 SZB 370

52775 T Th 5:00-6:00 ECJ 1.204

Text: Stewart, Calculus, 7th Edition (Early Transcendentals)

Prerequisite and degree relevance:A grade of C or better in M408C or the equivalent.

(Note: The pace of M408C and M408D is brisk. For this reason, transfer students with

one semester of Calculus at another institution are requested to consult with theUndergraduate Adviser for Mathematics to determine whether M408D or an alternative,

M408L, is the appropriate second course.). M408D may not be counted by students with

credit for Mathematics 408L or 308M. M408C and M408D (or the equivalent sequence

M408K, M408L, M408M) are required for mathematics majors, and mathematics majorsare required to make grades of C or better in these courses.

Certain sections of this course are reserved as advanced placement or honors sections;

they are restricted to students who have scored well on the advanced placement AP/BCexam, or are honors students, or who have the approval of the Mathematics Advisor.

Such sections and their restrictions are listed in the Course Schedule for each semester.

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Course description:M408C and M408D is our standard first-year Calculus sequence. It

is directed at engineering students and students in the natural and social sciences. The

emphasis in this course is on problem solving, not on the presentation of theoreticalconsiderations. While the course necessarily includes some discussion of theoretical

notions, its primary objective is not the production of theorem-provers. M408D contains

integration techniques, brief modeling with differential equations, parametric equations, atreatment of infinite series, partial derivatives, and multiple integrals.

Resources for Students

Some of our students have weak study skills. The Learning Skills Center in Jester has a

wide variety of material designed to help students through Calculus: tutors, drills, video-taped lectures, computer programs, counseling, math anxiety workshops, reviews of

Algebra, Trigonometry, and Calculus.

Calc Lab:The Math Department Calculus Lab(see

www.ma.utexas.edu/academics/undergraduate/calculus-lab/ )This is a joint TA sessionfor allcalculus classes taught at UT, and will be staffed at all times by at least two TAs

and 3 undergraduate Learning Assistants. No matter what your question, you can alwaysget help at Calc Lab.

Grading:

Your grade will be based on your performance on homework and exams following thegrading scheme below. This course does not have extra credit. Homework will be due

every week, and there will be three exams. To master the course material, you must stay

caught up with the topics covered in lectures and with the related homework. This course

will move fast and cover a lot of material! In addition, staying caught up will help youidentify questions to ask during class, which will certainly help others as well.

The specific grading scheme and exam information are as follows:

Written-Homework, due every week in discussion session (Thursday): 8%

Quest-Homework, due every week (Saturday) by 11:00 pm: 8%

2 in-class mid-term exams: 27% each

Final exam (Comprehensive): 30%

Grading. A: 90-100; B: 80-89; C: 70-79; D: 60-69; F: below 60

Homework:

Al l sections covered in one week are due the foll owing week on Thursdayat the

TA discussion. For example during week 1 we will go over Sections 5.5 and 7.1, so

during week 2 by Thursday you must complete the homework (below see calendar)

before the TA discussion.

https://www.ma.utexas.edu/academics/undergraduate/calculus-labhttps://www.ma.utexas.edu/academics/undergraduate/calculus-labhttps://www.ma.utexas.edu/academics/undergraduate/calculus-lab

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The grader will not grade any disorganized or difficult-to-read assignments. Your

homework is your best piece of work. I will not accept homework on loose sheets of

paper. No late homework wil l be accepted. I wil l drop two Quest Homework grades.

Format:Must be stapled, and no ripped pages from a notebook will be accepted. Writeyour name at the top of each page. The first page should state the class, section number,

instructors name, and book sections included in the homework assignment. Label eachquestion clearly, specifying the section and exercise number (i.e. 14.1 #32). It should be

organized, clean, and easy to read.

Mid-term Exams:The exams will be held during lecture and there will be no make-ups. The dates

are on the calendar (below).

Final Exam:The date and location of the final will be announced in lecture sometime during

the semester.

CALENDAR

I n class Homework

WEEK 1

Wed., Aug. 265.5 Substitution Rule

Section 5.5Problems 12, 22, 30, 46, 48, 58, 67, 72,78, 81, 86

Fri., Aug. 28

7.1 Integration By Parts

Section 7.1

Problems 5, 8, 10, 14, 15, 18, 22, 26, 42,

52, 68

WEEK 2

Mon., Aug. 31

7.2 Trigonometric Integrals

Section 7.2

Problems 2, 4, 7, 8, 12, 16, 19, 26, 29, 31,

48, 39, 49

Wed., Sep. 2 Section 7.3

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7.3 Trigonometric Substitution Problems 2, 5, 8, 9, 12, 14, 19, 21, 24, 27

Fri., Sep. 4

7.4 Integration of Rational Functions by

Partial Fractions

Section 7.4

Problems 2, 4, 6, 7, 12, 18, 23, 28

WEEK 3

Wed., Sept. 9

7.5 Strategy for Integration

Section 7.5

Problems 2, 3, 13, 15, 22, 25, 31

Fri., Sept. 117.8 Improper Integrals

Section 7.8Problems 5, 10, 12, 15, 18, 20, 35, 49, 57

WEEK 4Mon., Sept. 14

9.1 Modeling with Differential Equations

Section 9.1

Problems 2, 3, 4, 5, 9, 13, 14, 15

Wed., Sept. 16

9.2 Direction Fields and Euler Method

Section 9.2

Problems 3, 4, 5, 6, 10, 11, 14, 21, 27

Fri., Sept. 189.3 Separable Equations

Section 9.3Problems 6, 11, 14, 16, 37, 39, 43, 48

WEEK 5

Mon., Sept. 219.4 Models for Population Growth

Section 9.4Problems 1, 5, 6, 11, 13, 17, 19

Wed., Sept. 23

9.5 Linear Equation

Section 9.5

Problems 1, 2, 3, 4, 6, 7, 8, 10, 16, 17

Fri., Sept. 259.5 Linear Equations (continue)

Section 9.5 (continue)Problems 23, 24, 28, 31, 34

WEEK 6

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Mon., Sep. 28

11.1 Sequences

Section 11.1

Problems 15, 18, 51, 47, 72, 77

Wed., Sep. 30

11.2 Series

Section 11.2

Problems 14, 20, 27, 32, 48, 59

Fri., Oct. 2

TEST 1

Chapters 7 and 9

WEEK 7

Mon., Oct. 5

TEST 1

Chapters 7 and 9

Wed., Oct. 7

11.3 The Integral Test and Estimates ofSums

Section 11.3

Problems 8, 11, 20 (hint: Complete thesquare), 29, 34, 38

Fri., Oct. 9

11.4 Comparison Test

Section 11.4

Problems 2, 7, 13, 16, 20, 26

WEEK 8

Mon., Oct.1211.5 Alternating Series

Section 11.5Problems 2, 5, 14, 23, 26, 32

Wed., Oct.14

11.6 Absolute Convergence and the Ratio

and Root Tests

Section 11.6

Problems 1, 18, 28, 20, 35, 43

Fri., Oct. 1611.7 Strategy for Testing Series

Section 11.7Problems 1, 5, 12, 17, 24, 30

WEEK 9

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Mon., Oct. 19

11.8 Power Series

Section 11.8

Problems 11, 14, 20, 25, 28, 30

Wed., Oct. 2111.9 Representations of Functions as Power

Series

Section 11.9Problems 2, 4, 7, 13, 21, 26

Note: Graph 19 on Mathematica.

Fri., Oct. 23

11.10 Taylor and Maclaurin Series

Section 11.10

Problems 7, 10, 17, 25, 32, 48, 55, 64

WEEK 10

Mon., Oct. 26

11.11 Applications of Taylor Polynomials

Section 11.11

Problems 3, 13, 15, 16, 27

Note: Graph 3 and 13c on Mathematica

Wed., Oct. 2811.11 Applications of Taylor Polynomials(continue)

Fri., Oct. 30

10.1 Curves Defined by Parametric

Equations

Section 10.1

Problems 3, 5, 11, 24, 25,

35 (Mathematica)

WEEK 11

Mon., Nov. 2

10.2 Calculus with Parametric Equations

Section 10.2

Problems 7, 11, 16, 41, 45 (graph first,

Mathematica), 69

Wed., Nov. 4

10.3 Polar Coordinates

Section 10.3

Problems 2, 7, 11, 22, 25, 36, 54

Fri., Nov. 6

Test 2

Chapter 11

WEEK 12

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Mon., Nov. 9

Test 2

Chapter 11

Wed., Nov. 11

10.4 Areas and Lengths in Polar

Coordinates

Section 10.4

Problems 2, 7, 17, 27, 39 (graph first,

Mathematica), 45Fri., Nov. 13

14.1 Functions of Several Variables

Section 14.1

Problems 2, 4, 8, 12, 14, 39,

43 Mathematica, 55 Mathematica, 59-64

Matching

WEEK 13

Mon., Nov. 1614.2 Limits and Continuity

Section 14.2Problems 7, 11, 14, 16 Squeeze, 17,

24 Mathematica, 29, 40

Wed., Nov. 1814.3 Partial Derivatives Section 14.3Problems 2, 4, 5-8 Matching, 9,

14 Mathematica, 20, 29, 47, 73, 84

Fri., Nov. 2014.5 The Chain Rule

14.4 Tangent Planes and Linear Approx.

Section 14.5Problems 4, 8, 13, 16, 21, 27, 36

Section 14.4

Problems 4, 14, 19, 22, 31

WEEK 14

Mon., Nov. 2315.1 Double Integrals over Rectangles and

15.2 Iterated Integrals

Section 15.1Problems 2, 4, 8, 12

Section 15.2

Problems 2, 18, 23

Wed., Nov. 25

15.3 Double Integrals over GeneralRegions

Section 15.3

Problems 6, 10, 18, 22, 31, 50, 54

WEEK 15

Mon., Nov. 3015.4 Double Integrals in Polar Coordinates Section 15.4Problems 1-4, 6, 15, 19, 29

Wed., Dec. 2

15.10 Change of Variable in Multiple

Integrals

Section 15.10

Problems 1, 2, 3

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Fri., Dec. 4

15.10 Change of Variable in MultipleIntegrals (continue). Review for Final

Finalexam: During final-week (room to

be announced)

"The University of Austin provides upon request

appropriate academic accommodations for qualified

students with disabilities. For more information,

contact the Office of the Dean of Students at 471-

6259, 471-6441 TTY."

Emergency Evacuation Policy

Every member of the university community shall be familiar with theEmergency Evacuation Policy and understand his or her role in these

emergency situations.

In the event of a fire or other emergency, it may be necessary to

evacuate a building rapidly. Upon the activation of a fire alarm or

the announcement of an emergency in a university building, all

occupants of the building are required to evacuate and assemble

outside. Once evacuated, no one may re-enter the building without

instruction to do so from the Austin Fire Department, University of

Texas at Austin Police Department, or Fire Prevention Services office.

University faculty members are responsible for pointing out their

classrooms' building emergency evacuation routes and emergency

procedures to students at the beginning of each semester.

Furthermore, faculty, staff, and students should familiarize

themselves with all the exit doors of each room and building they

occupy at the university, and should remember that the nearest exit

routes may not be the same as the way they typically enter buildings.

Students requiring assistance in evacuation shall inform their

instructors in writing during the first week of class. Faculty

members must then provide this information to the Fire Prevention

Services office by fax (512-232-2759), with "Attn. Mr. Roosevelt

Easley" written in the subject line.

Faculty members should be prepared to give appropriate instructions

in the event of an evacuation. Students should follow theinstructions of faculty members and class instructors during

emergency evacuations.

We can most effectively prepare for and cope with emergencies by

working together. Thus, everyone has a duty to ensure other

occupants of university buildings are aware of emergencies, and to

aid anyone requiring assistance in evacuation. People should only

provide this aid to the best of their abilities, however, and no one

is expected to endanger themselves in order to assist with the

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evacuation of others.

Information regarding emergency evacuation routes and emergency

procedures can be found

at www.utexas.edu/emergency.

Classroom Instruction and Recommended Syllabus Information

To implement this policy and reinforce building evacuation

procedures, each faculty member shall provide the following

information and instructions to students:

Occupants of buildings on The University of Texas at Austin campus

are required to evacuate buildings when a fire alarm is activated.Alarm activation or announcement requires exiting and assembling

outside.

Familiarize yourself with all exit doors of each classroom and

building you may occupy. Remember that the nearest exit door may not

be the one you used when entering the building.

Students requiring assistance in evacuation shall inform their

instructor in writing during the first week of class.

In the event of an evacuation, follow the instruction of faculty or

class instructors.

Do not re-enter a building unless given instructions by the

following: Austin Fire Department, The University of Texas at Austin

Police Department, or Fire Prevention Services office.

Behavior Concerns Advice Line

BCAL: 232-5050

http://www.utexas.edu/emergencyhttp://www.utexas.edu/emergencyhttp://www.utexas.edu/emergency