Integral Calculus: Math 1206, Spring 2008, CRN # 13776

MWF     4:00PM - 5:15PM      MCB 304

Mahboub Baccouch

PhD Candidate in the Mathematics Department at Virginia Tech

Welcome to Math 1206: Math 1206 is a three-credit second semester integral calculus course. Topics of study include integration, applications of integrals, and transcendental functions. The main topic covered is integral calculus.

Resource Links:

Text: University Calculus 1st edition by Hass, Weir & Thomas

Office Hours: 

1- MW: 3:00 PM 4:00 PM, and other time by appointment. You do not need to make an appointment to see me during my regular office hours.

2- Help with practice tests is available in the Math Emporium during math help hours.


Course Materials

Dates and assignments are subject to change, so check this page often.

·             Derivative Formulas
·             Trigonometry Functions
·             Review of Log & Exponential Properties and some Trig
·             General Review
·             Goal

These notes are notes. This means there are typos, errors and incomplete sentences with bad spelling. The topics presented here are roughly the same as the topics covered in class, but not always.

Please feel free to give me a list of typos, corrections and any suggestions that might improve the notes for the next class.

Chapter 5: Integration


Date

Sections covered

Notes

M 01/14/08

First day of class

sec.5.1 (p. 315-324)

Estimating with Finite Sums (Areas and Distances)

Read the syllabus and Course Contract.

Be sure to pass the BST by Friday, January, 25, 2008. The sooner you pass it the better!

Further information about the Basic Skills Test may be found here.

Here is a good summary for Math1205: Math 1205 Calculus_all 

Lesson 1: Math_1206_lesson1(PDF)      

W 01/16/08

 

sec.5.2 (p. 325-332)

Sigma Notation and Limits of Finite Sums

 

Lesson 2: Math_1206_lesson2(PDF)      

 

Complete Homework Week 1: will not be collected

 

p. 322: 1, 3, 5, 7, 9, 11, 15, 17, 19

p. 331: 1, 3, 5, 7, 13, 15, 17, 19, 25, 31, 33

 

-Answers to the odd-numbered problems are given in the back of the book so you can check your progress, but I expect to also see the steps that lead to those answers.

 

M 01/21/08

 

No class will be held on Monday, January 21.

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W 01/23/08

 

sec.5.3 (p. 332-344)

The Definite Integral

Lesson 3: Math_1206_lesson3(PDF)      

 

Complete Homework 1: will not be collected

p. 322: 1, 3, 5, 7, 9, 11, 15, 17, 19

p. 331: 1, 3, 5, 7, 13, 15, 17, 19, 25, 31, 33

p. 341: 3, 5, 7, 15, 17, 19, 51D, 53D, 54D

Here is the solution for HW1                                                                                                                                                                                                                     

 

M 01/28/08

 

sec.5.3 (p. 332-344)

The Definite Integral

sec.4.8 (p. 296-306)

Antiderivatives

 

Lesson 4: Math_1206_lesson4_1(PDF)       and   Math_1206_lesson4_2(PDF)      

W 01/30/08

 

sec.5.4 (p. 345-353)

The Fundamental Theorem of Calculus

take home quiz 1.  It is due on Wednesday Jan 30.

Lesson 5: Math_1206_lesson5(PDF)      

 

Complete Homework 2: p. 341: 9, 29, 31, 43, 47, 59, 60, 65

p. 302: 29, 35, 37, 39, 41, 45, 49, 53, 55, 59, 61, 69, 78, 81

p. 302: 87, 91, 105, 108, 109, 111, 119, 121, 125

 

Here is the solution for HW2

 

M 02/04/08

 

sec.5.5 (p. 354-360)

Indefinite Integrals and the Substitution Rule

sec.5.6 (p. 360-370)

Substitution and Area Between Curves (day 1)

Lesson 6: Math_1206_lesson6_1(PDF)      and   Math_1206_lesson6_2(PDF)       

Complete Homework 3:     Here is the solution for HW3

Take home Quiz1:Solution take home quiz_1_key.  

W 02/06/08

Review TEST 1

We will go over take home quiz 1 and 2. Since I’ll collect the quiz 2 at the beginning of class, please bring with you a copy or your questions. I’d be pleased to answer any questions you may have.

take home quiz 2.  .  It is due at the beginning of class Wednesday Feb 6.

Complete Homework4:    Here is the solution for HW4

 

 Take home Quiz2:Solution take home quiz_2_key.  

M 02/11/08

Test 1

Test 1 Information:

It will be given Monday, February 11 in your regular classroom. Test will be closed book, closed note and no calculator. It will cover from lesson 1-lesson 6.

REVIEW SHEET Test1 

The following are not necessarily representative of what will be on the test, but they do provide practice in many of the topics you will be tested on.

Test1_Review  here is the solution

Test1_Spring_2002  here is the solution

Practice 1 for Test 1  with solution

Test1_Spring_2004  with solution

Practice 2 for Test 1  with solution

Test1_Fall_2004  with solution

Practice 3 for Test 1  with solution

Test1_Simple

W 02/13/08

sec.5.6 (p. 360-370)

Substitution and Area Between Curves (day 2)

 sec.5.7 (p. 370-381)

The Logarithm Defined as an Integral

 

 

Test1_Spring_2008  here is the solution

Lesson 7: Math_1206_lesson7_1(PDF)   and Math_1206_lesson7_2(PDF) 

Complete Homework Week 5

 

 

 

 

Chapter 6: Applications of Definite Integrals


Date

Sections covered

Notes

M 02/18/08

sec.6.1 (p. 391-401)

Volumes by Slicing and Rotation about an Axis

Lesson 8: Math_1206_lesson8(PDF)      

 

W 02/20/08

sec.6.2 (p. 401-408)

Volumes by Cylindrical Shells

Lesson 9: Math_1206_lesson9(PDF)      

Here is the solution for HW5

 

M 02/25/08

sec.6.3 (p. 408-414)

Lengths of Plane Curves

sec.6.6 (p. 430-436)

Work (day 1)

Lesson 10: Math_1206_lesson10_1(PDF)  and  Math_1206_lesson10_2(PDF)      

Complete Homework Week 6

Here is the solution for HW6

 

W 02/27/08

sec.6.6 (p. 430-436)

Work (day 2)

take home quiz 3.  It is due at the beginning of class Wednesday Feb 27.
Take home Quiz3: Solution take home quiz_3_key.  

Lesson 11: Math_1206_lesson11(PDF)      

 

M 03/10/08

sec.6.7 (p. 437-443)

Moments and Centers of Mass

Lesson 12:  Math_1206_lesson12(PDF)       
 
Complete Homework Week 7:
Here is the solution for HW7
 

W 03/12/08

Review TEST 2

take home quiz 4.  It is due at the beginning of class Wednesday March 12.
Take home Quiz4: Solution take home quiz_4_key.  

Complete Homework Week 8:

Here is the solution for HW8
 

M 03/17/08

Test 2

Test 2 Information:

It will be given Monday, March 17 in your regular classroom. Test will be closed book, closed note and no calculator. It will cover from lesson 7- 12

 

The following are not necessarily representative of what will be on the test, but they do provide practice in many of the topics you will be tested on. 
Practice 1 for Test 2  with solution 
Practice 2 for Test 2  here is the solution
Practice 3 for Test 2  with solution 
Practice 4 for Test 2  with solution 
Practice 5 for Test 2  with solution 
Practice 6 for Test 2  with solution 
Practice 7 for Test 2  with solution 
Practice 8 for Test 2  with solution 
Guide for Test 2  with solution 
Review_sheet for Test 2  
 

W 03/19/08

sec.7.1 (p. 448-455)

Integration by Parts

Test2_Spring_2008  here is the solution

Lesson 13: Math_1206_lesson13(PDF)      

 

M 03/24/08

sec.7.2 (p. 455-460)

Trigonometric Integrals

Lesson 14: Math_1206_lesson14(PDF)      

 

Complete Homework Week 9

Here is the solution for HW9

 

W 03/26/08

sec.7.3 (p. 461-464)

Trigonometric Substitutions

Lesson 15: Math_1206_lesson15(PDF)      

Complete Homework Week 10:

Here is the solution for HW10

 

M 03/31/08

sec.7.4 (p. 464-471)

Integration of Rational Functions by Partial Fractions (day 1)

Lesson 16: Math_1206_lesson16(PDF)      

 

W 04/02/08

sec.7.4 (p. 464-471)

Integration of Rational Functions by Partial Fractions (day 2)

 

take home quiz 5.  It is due at the beginning of class Wednesday April 2.
Take home Quiz5: Solution take home quiz_5_key.  
 

Lesson 17: Math_1206_lesson17(PDF)      

Complete Homework Week 11

Here is the solution for HW11

 

M04/07/08

sec.7.5 (p. 471-476)

Integral Tables and Computer Algebra Systems

 

Practice problems: Strategy for Integration Math_1206_practic(PDF)      

Lesson 18: Math_1206_lesson18(PDF)      

 

take home quiz 6.  It is due at the beginning of class Monday April 14.
Take home Quiz6: Solution take home quiz_6_key.  
 

W04/09/08

sec.7.6 (p. 477-486)

Numerical integration

Lesson 19: Math_1206_lesson19(PDF)      

 
Complete Homework Week 12:
Here is the solution for HW12
 
 

M04/14/08

Review TEST 3

REVIEW SHEET Test3 
Complete Homework Week 13:
Here is the solution for HW13
 

take home exam 7.  It is due Friday April  18 (4 pm).  An answer sheet to fill out for this exam, is here

Take home Quiz7: Solution take home quiz_7_key.  

 

 

W04/16/08

No class will be held on Wednesday, April 16.

 

M04/21/08

Test 3

Test 3 Information:

It will be given Monday, April 21 in your regular classroom. Test will be closed book, closed note and no calculator. It will cover from lesson 13-lesson 19.

 

Test3_Spring_2008  here is the solution

 

 

The following are not necessarily representative of what will be on the test, but they do provide practice in many of the topics you will be tested on.

Practice 1 for Test 3  here is the solution

Practice 2 for Test 3  with solution

Practice 3 for Test 3  with solution

Practice 4 for Test 3  with solution

Practice 5 for Test 3  with solution

Practice 6 for Test 3  with solution

Practice 7 for Test 3  with solution

Practice 8 for Test 3  with solution   

 

Chapter 4: Applications of Derivatives


Date

Sections covered

Notes

W 23/04/08

 

sec.4.6 (p. 283-291)

Indeterminate Forms and L’Hopital’s Rule

Lesson 20: Math_1206_lesson20(PDF)      

                                                                                                                                                                                             back to top

Chapter 7: Techniques of Integration


Date

Sections covered

Notes

M 28/04/08

 

sec.7.7 (p. 487-497)

Improper Integrals

Lesson 21: Math_1206_lesson21(PDF)   

 

Complete Homework Week 14:

Complete Homework Week 15:

take home exam 8.  It is due Wednesday April  30. This take home is optional. This will substitute your lowest quiz grade

Take home Quiz8: Solution take home quiz_8_key.  
 

 

 

W 30/04/08

Review Final

 

F 02/05/07

The common final exam will be given on Friday, May 2, 4:25pm-6:25 pm (Room McB 226). If there is a conflict with the final in another class that does not have a common-time final, you will be expected to change the other one.

The final exam session is two hours and consists of 2 parts:

 

¨                   The multiple choice part during the first hour, calculators are not allowed.  No one should be allowed to start the second half of the exam until the start of the second hour. At the end of the hour, I will collect the exams and the answer sheets.  You have to put your name on both parts so I can make sure you have filled in the correct form on your answer sheet and results will be sent to you a day or two later.

¨                    The second half of the final will be like the three tests have been: free response and common to all sections, calculators are not allowed.  On this part if you finish early you can leave.

 

REVIEW SHEET Final 

Formulas to Know

 

Partial Fractions: Practice  with solution

LHopitals Rule: Practice  with solution

Improper Integrals : Practice  with solution

Practice 1 for Final  with solution

Practice 2 for Final  with solution

Practice 3 for Final  with solution

Practice 4 for Final  with solution

Practice 5 for Final  with solution

 

Some common final exams in .pdf format can be found here.

http://www.math.vt.edu/courses/commonex/common.php

 

Please stop by if you want to look at your final or any further discussion.
 
Sorry if you didn't enjoy this class. It was a wonderful to have you in my class.
 
Have a good break if I don't see you again. Once again thanks and good luck for your future.
 

 

Instructions for finding the definite integral of a function on a TI-82 calculator. (Also works for TI-83 and 84).

 


Honor Statement for Math 1206:

The constitution of the Undergraduate Honor System explains your rights and responsibilities. All work that you submit for a grade while at Virginia Tech is bound by this constitution, regardless of whether or not it is pledged. The Honor Pledge is, “I have neither given nor received unauthorized assistance on this assignment.” The forms of authorized assistance are completely stated below; any other types of assistance are unauthorized.

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Registration:

You must be registered for this course in order to receive a grade for it. I have no control over the registration process, but can answer questions.

Accommodations:

I really do want to make it possible for you to succeed. You are encouraged to bring to my attention any reasonable need or accommodation (including disability accommodations and religious holidays) that will help you.

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Questions or comments? Mahboub Baccouch

Revision Date: Spring , 2008