Integral Calculus: Math 1206,  Fall 2007, CRN # 93692

MWF     10:10AM - 11:00AM      MCB 332

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: 11:00 AM – 12:00 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 8/20/07

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, August 31, 2006. The sooner you pass it the better! 

Here is a good summary for Math1205: Math 1205 Calculus_all

Or visit http://www.math.vt.edu/people/baccouch/1205_93667.html for more information about Math 1205

Lesson 1: Math_1206_lesson1(PDF)      

 

W 8/22/07

 

sec.5.2 (p. 325-332)

Sigma Notation and Limits of Finite Sums

Lesson 2: Math_1206_lesson2(PDF)      

 

 

F 8/24/07

 

sec.5.3 (p. 332-344)

The Definite Integral (day 1)

Lesson 3: Math_1206_lesson3(PDF)      

Complete Homework Week 1: will be collected Monday 8/27 in your lecture class.

 

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

 

-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.

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M 8/27/07

 

sec.5.3 (p. 332-344)

The Definite Integral (day 2)

Lesson 4: Math_1206_lesson4(PDF)      

In Class quiz 1.  Here is the solution quiz 1_sol

Here is the solution for HW1                                                                                                                                                                                                                     

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Chapter 4: Applications of Derivatives

Date

Sections covered

Notes

W 8/29/07

 

sec.4.8 (p. 296-306)

Antiderivatives (day 1)

Lesson 5: Math_1206_lesson5(PDF)      

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F 8/27/07

 

sec.4.8 (p. 296-306)

Antiderivatives (day 2)

Lesson 6: Math_1206_lesson6(PDF)      

 

Complete Homework Week 2: will be collected Monday 9/3 in your lecture class.

 

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

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Chapter 5: Integration

Date

Sections covered

Notes

M 9/3/07

sec.5.4 (p. 345-353)

The Fundamental Theorem of Calculus (day 1)

Lesson 7: Math_1206_lesson7(PDF)      

In Class quiz 2.  Here is the solution quiz 2_sol

Here is the solution for HW2

W 9/5/07

sec.5.4 (p. 345-353)

The Fundamental Theorem of Calculus (day 2)

Lesson 8: Math_1206_lesson8(PDF)

 take home quiz 1.  It is due at the beginning of class Wednesday Sep 12.

F 9/7/07

sec.5.5 (p. 354-360)

Indefinite Integrals and the Substitution Rule

Lesson 9: Math_1206_lesson9(PDF)  

Complete Homework Week 3: will be collected Monday 9/10 in your lecture class.

 

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 9/10/07

sec.5.6 (p. 360-370)

Substitution and Area Between Curves (day 1)

Lesson 10: Math_1206_lesson10(PDF)      

 

W 9/12/07

Review TEST 1

 
REVIEW Test1 
Here is the solution for HW3

The take home quiz is due at the beginning of class Wednesday Sep 12.

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

F 9/14/07

Test 1

Test 1 Information:

It will be given Friday, September 14 in your regular classroom. Test will be closed book, closed note and no calculator. It will cover from lesson 1-lesson 10. 

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

M 9/17/07

sec.5.6 (p. 360-370)

Substitution and Area Between Curves (day 2)

Test1_Fall_2007  here is the solution

Lesson 11: Math_1206_lesson11(PDF) 

 take home quiz.  It is due Wednesday Sep 19.

 Complete Homework Week 4: will be collected Monday 9/17 in your lecture class.

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.

Here is the solution for HW4
 

W 9/19/07

sec.5.7 (p. 370-381)

The Logarithm Defined as an Integral

 

Lesson 12: Math_1206_lesson12(PDF) 

 

 

Chapter 6: Applications of Definite Integrals

Date

Sections covered

Notes

F 9/21/07

sec.6.1 (p. 391-401)

Volumes by Slicing and Rotation about an Axis (day 1)

Lesson 13: Math_1206_lesson13(PDF)      

 

M 9/24/07

sec.6.1 (p. 391-401)

Volumes by Slicing and Rotation about an Axis (day 2)

Lesson 14: Math_1206_lesson14(PDF)      

Complete Homework Week 5: will be collected Monday 9/24 in your lecture class.

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.

 

W 9/26/07

sec.6.2 (p. 401-408)

Volumes by Cylindrical Shells

Lesson 15: Math_1206_lesson15(PDF)      

In Class quiz 4.  Here is the solution quiz 4_sol

Here is the solution for HW5

 

F 9/28/07

sec.6.3 (p. 408-414)

Lengths of Plane Curves

Lesson 16: Math_1206_lesson16(PDF)      

 

M 10/01/07

sec.6.6 (p. 430-436)

Work (day 1)

Lesson 17: Math_1206_lesson17(PDF)      

 

Complete Homework Week 6: will be collected Monday 10/01 in your lecture class.

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.

 

W 10/03/07

sec.6.6 (p. 430-436)

Work (day 2)

Lesson 18: Math_1206_lesson18(PDF)       

 
Here is the solution for HW6

 

F 10/05/07

sec.6.7 (p. 437-443)

Moments and Centers of Mass (day 1)

Lesson 19: Math_1206_lesson19(PDF)       

 

M 10/08/07

No Class

 

W 10/10/07

sec.6.7 (p. 437-443)

Moments and Centers of Mass (day 2)

You will have in Class quiz: will consist of a 2 questions that
is similar to the homework Week 7.

Lesson 20: Math_1206_lesson20(PDF)      

In Class quiz 5.  Here is the solution  quiz 5_sol

 

Complete Homework Week 7: will be collected Wednesday 10/10 in your lecture class. 

Here is the solution for HW7

 

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.

 

F 10/12/07

Review TEST 2

take home quiz 2.  It is due at the beginning of class Friday October12.

Here is the solution to take home quiz 2

 

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

 

Complete Homework Week 8: will be collected Friday 10/12 in your lecture class.

Here is the solution for HW8

 

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 10/15/07

Test 2

Test 2 Information:

It will be given Monday, October 15 in your regular classroom. Test will be closed book, closed note and no calculator. It will cover from lesson 11-lesson 20.

 

Test2_Fall_2007  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 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 

 

 

Chapter 7: Techniques of Integration

Date

Sections covered

Notes

W 10/17/07

sec.7.1 (p. 448-455)

Integration by Parts (day 1)

Lesson 21: Math_1206_lesson21(PDF)      

 

F 10/19/07

sec.7.1 (p. 448-455)

Integration by Parts (day 2)

You will have in-Class quiz: 2 questions similar to the examples covered last Wednesday

Lesson 22: Math_1206_lesson22(PDF)      

In Class quiz 6.  Here is the solution  quiz 6_sol

 

Complete Homework Week 9: will be collected Monday 10/22 in your lecture class.

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.

Here is the solution for HW9

 

M 10/22/07

sec.7.2 (p. 455-460)

Trigonometric Integrals (day 1)

Lesson 23: Math_1206_lesson23(PDF)      

 

W 10/24/07

sec.7.2 (p. 455-460)

Trigonometric Integrals (day 2)

Lesson 24: Math_1206_lesson24(PDF)      

F 10/26/07

sec.7.3 (p. 461-464)

Trigonometric Substitutions (day 1)

Lesson 25: Math_1206_lesson25(PDF)      

You will have in-Class quiz: Evaluating Integral involving sine and cosine:, and Evaluating Integral involving tangent and secant:

In Class quiz 7.  Here is the solution  quiz 7_sol

 

M 10/29/07

sec.7.3 (p. 461-464)

Trigonometric Substitutions (day 2)

Lesson 26: Math_1206_lesson26(PDF)      

Complete Homework Week 10: will be collected Monday 10/29 in your lecture class.

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.

Here is the solution for HW10
 

W 10/31/07

sec.7.4 (p. 464-471)

Integration of Rational Functions by Partial Fractions (day 1)

 

Complete quiz 8.  : will be collected Wednesday 10/29 in your lecture class.

Here is the solution  quiz 8_sol

Lesson 27: Math_1206_lesson27(PDF)       

 

F 11/2/07

sec.7.4 (p. 464-471)

Integration of Rational Functions by Partial Fractions (day 2)

 

Lesson 28: Math_1206_lesson28(PDF)      

 

M 11/5/07

Strategy for Integration

 

Lesson 29: Math_1206_lesson29(PDF)      

 

Complete Homework Week 11: will be collected Monday 11/5 in your lecture class.

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.

Here is the solution for HW11

 

 

W 11/7/07

sec.7.5 (p. 471-476)

Integral Tables and Computer Algebra Systems

 

Lesson 30: Math_1206_lesson30(PDF)      

Complete quiz 9.  : will be collected Wednesday 11/7 in your lecture class.

Here is the solution  quiz 9_sol

 

F 11/9/07

sec.7.6 (p. 477-486)

Numerical integration (day 1)

 

Lesson 31: Math_1206_lesson31(PDF)      

 

M 11/12/07

sec.7.6 (p. 477-486)

Numerical integration (day 2)

 

Lesson 32: Math_1206_lesson32(PDF)      

Complete Homework Week 12: will be collected Monday 11/12 in your lecture class.

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.

Here is the solution for HW12

 

W 11/14/07

Review TEST 3

take home exam 3.  It is due at the beginning of class Wednesday November 14.  An answer sheet to fill out for this exam, is here

Here is the solution to take home quiz 3

 

Complete Homework Week 13: will be collected Wednesday 11/14 in your lecture class.

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.

Here is the solution for HW13

 

F 11/16/07

Test 3

Test 3 Information:

It will be given Friday, November 16 in your regular classroom. Test will be closed book, closed note and no calculator. It will cover from lesson 21-lesson 32.

 

Test3_Fall_2007  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. 

REVIEW SHEET Test3

 

Practice 1 for Test 1  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

M 11/26/07

 

sec.4.6 (p. 283-291)

Indeterminate Forms and L’Hopital’s Rule (day 1)

Lesson 33: Math_1206_lesson33(PDF)      

                                                                                                                                                                                             back to top

W 11/28/07

 

sec.4.8 (p. 296-306)

Indeterminate Forms and L’Hopital’s Rule (day 2)

Lesson 34: Math_1206_lesson34(PDF)   

Complete quiz 10.  : will be collected Friday 11/30 in your lecture class.

   Here is the solution  quiz 10_sol

 

                                                                                                                                                                                             back to top

Chapter 7: Techniques of Integration

Date

Sections covered

Notes

F 11/30/07

 

sec.7.7 (p. 487-497)

Improper Integrals

Lesson 35: Math_1206_lesson35(PDF)   

 

M 12/3/07

sec.7.7 (p. 487-497)

Review Final

 

Complete Homework Week 14: will be collected Monday 12/3 in your lecture class.

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.

 

 

W 12/5/07

Review Final

Complete Homework Week 15: will be collected Wednesday 12/5 in your lecture class.

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 12/10/07

The common final exam will be given on Monday, December 10, 7:00-9:00 pm (Rooms will be posted on the Announcements page). 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

 

Partial Fractions: Practice  with solution

L’Hopital’s 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: Fall , 2007