MATH 103--CALCULUS I

MATH 104H--CALCULUS 2 Honors

GLENDALE COLLEGE

M-F 8:15-9:16 REGULAR INSTRUCTION

SUPPLEMENTAL INSTRUCTION: TBA

Room: SG 326

SI ROOM :TBA

Spring 2010

TEXT: SINGLE VARIABLE CALCULUS, EDITION 6e

BY JAMES STEWART

STUDENT'S SOLUTION MANUAL *************

DR. SID KOLPAS

PREREQUISITES: MATH 103 WITH A C OR BETTER, OR THE EQUIVALENT. I WILL CHECK TO SEE THAT YOU'VE MET THE PREREQUISITES!

1. PATH TO SUCCESS:

A. ATTEND ALL LECTURES AND TAKE GOOD NOTES.

1. YOU MUST PURCHASE MY LECTURE NOTES IN THE

STUDENT STORE; THEY SHOULD COST APPROX.________.

THEY'LL MAKE THE LECTURES GO MORE SMOOTHLY.

B. READ THE CORRESPONDING MATERIAL IN THE BOOK.

C. DO ALL ASSIGNED HOMEWORK.

*IF YOU HAVE DIFFICULTY, HIRE A QUALIFIED TUTOR,

CALL A FRIEND IN CLASS, OR GO TO THE TUTOR CENTER

ON CAMPUS. "ASK 3 BEFORE YOU ASK ME."

*HOMEWORK IS DUE THE NEXT SESSION AFTER THE

LECTURE IS FINISHED UNLESS YOU ARE ILL.

D. ASK QUESTIONS ABOUT THE HOMEWORK AT THE BEGINNING OF

THE NEXT SESSION; HOWEVER, THERE WILL NOT BE ENOUGH

TIME TO ANSWER EVERY QUESTION. STUDY WITH A FRIEND.

USE THE STUDENT SOLUTION MANUAL.

*PLEASE DON'T BE SHY. THE LIFE YOU SAVE MAY BE

YOUR OWN!

E. STUDY THE NIGHT BEFORE THE EXAM.

2. HOMEWORK:

A. A MINIMUM OF 2 TO 3 HOURS PER SESSION.

B. FOR THE MOST PART, ODD NUMBERED EXERCISES WILL BE

ASSIGNED SO YOU CAN CHECK YOUR ANSWERS BEFORE

COMING INTO CLASS(SEE ATTACHED ASSIGNMENT SHEET).

*IF YOU MISS A PROBLEM, GIVE IT A 2nd OR 3rd TRY

BEFORE GIVING UP AND ASKING ME THE NEXT SESSION.

I DON'T HAVE MUCH TIME TO GO OVER HOMEWORK.

USE THE STUDENT SOLUTION MANUAL TO HELP YOU.

C. NO LATE ASSIGNMENTS WITHOUT A LEGITIMATE EXCUSE.

*I'LL RETURN THE HOMEWORK THE NEXT DAY.

*MAKE UP WORK IS DUE BY THE DAY OF THE EXAM.

D. IF YOU MADE AN HONEST ATTEMPT ON EACH PROBLEM

YOU WILL GET CREDIT FOR THE ASSIGNMENT; OTHERWISE

YOU WILL RECEIVE NO CREDIT.

E. THE PERCENT OF ASSIGNMENTS FOR WHICH YOU RECEIVED

CREDIT, AVERAGED WITH YOUR PROJECT GRADE, WILL COUNT

AS ONE EXAM GRADE, OR APPROX.. 10% OF YOUR FINAL

GRADE.

3. EXAMS:

A. THERE WILL BE APPROX.. 7 EXAMS. YOU MUST USE BLUE

BOOKS TO TAKE THE EXAMS.

B. THE FINAL EXAM WILL BE COMPREHENSIVE (WEIGHT OF 3

EXAMS). IT IS WORTH APPROX.. 30% OF YOUR GRADE!

YOUR FINAL EXAM IS ____________________________.

C. EXAMS WILL USUALLY BE GIVEN AT THE END OF EACH

CHAPTER.

D. HOMEWORK COUNTS AS 1 EXAM.

E. THE GRADING SCALE FOR FINAL GRADES WILL BE

90-80-70-60 AS THE ABSOLUTE MINIMUM

REQUIREMENTS FOR A-B-C-D. HOWEVER, I RESERVE

THE RIGHT TO CURVE GRADES OR ADJUST THE GRADING

STANDARDS ON EXAMS IN THE STUDENT'S FAVOR.

F. THE EXAMS WILL BE SIMILAR TO THE ASSIGNED HOMEWORK

PROBLEMS AND SI PROBLEMS. THERE ARE NO CHAPTER

TESTS IN THE BOOK.

THE REVIEW EXERCISES AT THE END OF EACH

CHAPTER CAN BE USED AS ADDITIONAL PREPARATION FOR

EXAMS. I WILL ALSO PROVIDE OLD EXAMS FOR PRACTICE.

G. THERE ARE NO MAKE UP EXAMS IN THIS CLASS.

H. I WILL DROP YOUR LOWEST EXAM SCORE WHEN COMPUTING

FINAL GRADES. HOWEVER, I WILL NOT DROP THE

HOMEWORK GRADE, OR THE FINAL EXAM GRADE.

I. IF YOU ARE CAUGHT CHEATING ON AN EXAM, YOU'LL

RECEIVE A 0. I'LL REFER A SECOND INSTANCE OF

CHEATING TO THE COLLEGE ADMINISTRATION.

J. I GRADE EACH PROBLEM ON LIKE AN ESSAY, AND I DO

GIVE PARTIAL CREDIT. GENERALLY, ON A 10 POINT

QUESTION, THE ANSWER IS WORTH 1 POINT AND THE WORK

LEADING TO THE ANSWER IS WORTH 9 POINTS.

K. I WILL TRY VERY HARD TO RETURN EXAMS THE NEXT DAY,

WITH A MODEL SOLUTION KEY AND GRADING STANDARDS.

4. THE COURSE:

MATH 104 IS A CONTINUATION OF MATH 103. IT PRESUMES

ADEQUATE MASTERY OF MATH 103. TRIGONOMETRY PLAYS A

LARGER ROLE IN THIS CLASS, AS DO POLAR AND PARAMETRIC

FUNCTIONS, EXPONENTIAL, LOGARITHMIC, AND HYPERBOLIC

FUNCTIONS (A NEW TOPIC). THE MAJOR TOPICS ARE THE

DIFFERENTIAL AND INTEGRAL CALCULUS OF TRIG, INVERSE

TRIG, EXPONENTIAL, AND LOGARITHMIC FUNCTIONS,

TECHNIQUES OF INTEGRATION, APPLICATIONS OF INTEGRATION,

DIFFERENTIAL EQUATIONS, PARAMETRIC AND POLAR CALCULUS,

AND THE THEORY OF INFINITE SEQUENCES AND SERIES. POPULAR

OPINION IS THAT MATH 104 IS BASICALLY AN EASY CLASS

COMPARED TO ITS PREREQUISITES. WHAT MAKES IT A

DIFFICULT CLASS IS THE FACT THAT IF YOU HAVE ANY

WEAKNESSES IN MATH 103,TRIG, POLAR, PARAMETRIC, OR LOG

FUNCTIONS, THEY CONTINUALLY COME BACK TO HAUNT YOU.

ALSO, ANYONE WHO HAS TAKEN CALCULUS KNOWS THAT THE

COURSE CONTAINS SO MUCH MATERIAL THAT IT IS IMPOSSIBLE

FOR AN INSTRUCTOR TO SPEND AN ADEQUATE AMOUNT OF

CLASSROOM TIME ON EVERY TOPIC. FOR THIS REASON, A

CALCULUS TEXTBOOK BEARS A MAJOR PORTION OF THE BURDEN IN

THE TEACHING PROCESS; IN OTHER WORDS, READ THE BOOK VERY

CAREFULLY.

A. A SPECIAL FEATURE OF THIS COURSE WILL BE THE USE

OF CALCULUS SOFTWARE IN OUR CLASSROOM AND

GRAPHICS CALCULATORS TO VISUALIZE CONCEPTS. IN

FACT, YOU MIGHT WANT TO PURCHASE A GRAPHICS

CALCULATOR (CASIO, TI, OR HP).

B. WE WILL OCCASIONALLY DO COMPUTER LABS.

C. THERE ARE SI SESSIONS

D. COMMENTS ON CHAPTERS:

CHAPTER 7: INVERSE FUNCTIONS: EXPONENTIAL, LOG, AND

TRIG. WE WILL LEARN THE CALCULUS OF THESE

FUNCTIONS, AND HYPERBOLIC FUNCTIONS (A NEW TOPIC).

WE WILL ALSO DISCUSS INDETERMINATE FORMS, AND LEARN

L’HOSPITAL’S RULE, WHICH WILL BE USED THE REST OF

THE SEMESTER.

CHAPTER 8: TECHNIQUES OF INTEGRATION: INTEGRATION

BY PARTS, TRI SUBSTITUION, PARTIAL FRACTIONS,

STRATEGIES, USING INTEGRAL TABLES;APPROXIMATE

INTEGRATION INCUDING THE TRAPEZOIDAL RULE AND

SIMPSON’S RULE; IMPROPER INTEGRALS.

CHAPTER 9: FURTHER APPLICATIONS OF INTEGRATION:

ARC LENGTH, AREA OF A SURFACE OF REVOLUTION, PHYSICS

APPLICATIONS, A SHORT CHAPTER.

CHAPTER 10: DIFFERENTIAL EQUATIONS: MODELING,

DIRECTION FIELDS AND EULER’S METHOD; SEPARABLE

EQUATIONS, EXPONENTIAL GROWTH AND DECAY; LOGISTIC

FUNCTIONS.

CHAPTER 11: PARAMETRIC AND POLAR CALCULUS: FUN

STUFF. CURVES DEFINED BY PARAMETRIC EQUATIONS,

CALCULUS WITH PARAMETRIC CURVES, POOLAR COORDINATES;

AREA AND ARC LENGTHS IN POLAR COORDINATES; CONIC

SECTIONS; CONIC SECTIONS USING POLAR COORDINATES.

CHAPTER 12: MY FAVORITE CHAPTER. A WHOLE COURSE BY

ITSELF. THIS WILL BE BROKEN INTO 2 TESTS.

SEQUENCES AND SERIES; THE INTEGRAL TEST AND

ESTIMATES OF SUMS; THE COMPARISON TESTS; ALTERNATING

SERIES; ABSOLUTE CONVERGENCE AND THE RATIO AND ROOT

TESTS; STRATEGIES FOR TESTING SERIES. THE FIRST

TEST ENDS HERE. POWER SERIES; REPRESENTATIONS OF

FUNCTIONS AS POWER SERIES; TAYLOR AND MACLAURIN

SERIES; THE BINOMIAL SERIES; APPLICATIONS OF TAYLOR

POLYNOMIALS. WHEW!

5. WHY TAKE THE COURSE?:

A. IT IS NEEDED TO GRADUATE.

B. IT IS NEEDED FOR ANOTHER SKILL SUCH AS MEDICINE,

ENGINEERING, COMPUTER SCIENCE, AUTO MECHANICS, ETC.

C. IT IS A PREREQUISITE FOR STILL A HIGHER MATH CLASS.

D. IT IS SOMETHING YOU "ALWAYS WANTED TO LEARN".

6. MY LAST MATH 104 RESULTS :

A. STARTED:

B. CLASS GRADES:

A....

B....

C....

D....

F....

W....5

_ % PASSED THE CLASS

TYPICALLY, 60% PASS MATH 104 AT GCC.

7. ATTENDANCE:

A. I TAKE ROLL EACH SESSION.

B. ON AND AFTER THE 10TH LECTURE ABSENCE, YOU ARE IN

JEOPARDY OF BEING DROPPED FROM THE CLASS. PEOPLE

WHO WERE HABITUALLY ABSENT WERE THE ONES WHO DROPPED

OR WHO EVENTUALLY FAILED.

C. IF YOU DECIDE TO DROP THE CLASS, IT IS YOUR

RESPONSIBILITY TO DO SO, ESPECIALLY BEFORE THE FINAL

DROP DATE.***********************(GET THE MESSAGE?)

DROP DEADLINE: _______ (NO RECORD). AFTER ________

AND UP TO ________ YOU RECEIVE A "W" IF YOU DROP.

8. BEHAVIOR:

A. YOU'RE IN COLLEGE, AND IT WAS YOUR CHOICE TO BE

HERE.

B. YOU ARE EXPECTED TO BEHAVE LIKE AN ADULT, AND TO

TREAT OTHERS WITH RESPECT.

C. CLASS STARTS PROMPTLY ON THE HOUR. IF YOU ARRIVE

LATE, WALK IN UNOBTRUSIVELY. SINCE I TAKE ROLL

AT THE BEGINNING OF CLASS, LET ME KNOW YOU'VE

ARRIVED LATE AT THE END OF CLASS.

D. THE COLLEGE REQUESTS THAT THERE BE NO FOOD IN

CLASS, SINCE IT IS A COMPUTER LAB.

9. INSTRUCTOR AVAILABILITY:

A. MY OFFICE HOURS ARE: ________________

B. I AM IN THE MATH SCIENCE CENTER ON _______________

C. MY OFFICE IS SG 321.

D. MY EXTENSION ON CAMPUS IS 5378 (818-240-1000)

9. SEMESTER ASSIGNMENTS: EOO MEANS EVERY OTHER ODD.

EOE MEANS EVERY OTHER EVEN.

WE CAN SPEND NO MORE TIME THAN AN AVERAGE OF

1 1/2 DAYS PER SECTION. THUS, IF SOME OF THE FOLLOWING

ASSIGNMENTS PROVE TO BE TOO LENGTHY, WE CAN SPEND SOME

EXTRA TIME ON THEM.

THIS IS SUBJECT TO REVISION.

EACH EXTRA CREDIT (EC) IS WORTH ¼ POINT

7.1 1-41 odd

Discussion 1, 5, 7, 11, 13, 19, 21, 25, 27, 31, 33, 35, 37, 39, 41

7.2 1-19 odd; 23-57 odd; 61-67 odd; 73-83 odd; 89; 93A; 93B EC

Discussion 9, 11, 13, 15, 17, 25, 27, 31, 35, 43, 47, 49, 51, 53, 57, 65, 73, 75, 77, 81, 89

7.3 1-19 odd; 23-37 odd; 43-63 odd, 67 Discussion 3, 5, 7, 9, 17, 19, 23, 27, 33, 35, 37, 43, 47, 49, 53, 55, 61, 67

7.4 1-59 odd; 63; 69-79 odd; 83; 87; 89 EC

Discussion 1, 3, 7, 13, 17, 21, 25, 27, 35, 41, 45, 53, 63, 69, 71, 73, 75, 87

7.5 1,3,9,11,13,15,17 EC

Discussion 1,3,9,11,13,15

7.6 1-71 Odd skip 15,21,49,41,53,55. 47 EC, 51 EC

Discussion 5, 9, 13, 19, 23, 31, 33, 45, 49, 61, 63, 65

7.7 1-65 skip 19,25,27,29,49,51,55,57 Discussion 3,7,9,15,33,37,39,41,45,53,59,61,65

7.8 1-71 odd; 96 skip 1,3,35,65,67,69

Discussion: 5, 7, 9, 11, 15, 17, 19, 21, 27, 31, 43,

47, 55, 59, 96

TEST 1

8.1 1-59 ODD ON 57,59,61 SET UP ONLY. 63 IS EC

Discussion 1,3,5,9,11,17,19,23,25,27,29,33,47,57,59,61 set up only

8.2 1-65 ODD skip 7,9,33,35,37,39,51,53,59

Discussion 1,3,5,11,13,15,19,21,23,29,31,41,45,47,61,65

8.3 1-25 odd & 33