Math 262 Section 2326 - Calculus II
Fall 2012
Professor: Dr. Jess Lenarz
Meeting Time & Place: 10:30 am – 11:20 am MTWHF Bridges 261
Office: Maclean 375R
Office Hours: Monday – Friday 9:30 – 10:30; Monday & Wednesday 1:30 – 3:30,
Friday 1:30 – 2:30; other times by appointment
Phone: 477 – 4026
email: jessie.lenarz@mnstate.edu
Website: http:\\web.mnstate.edu\lenarz\Math262\F12\index.htm
Text: Calculus by Swokowski, the Classic Edition. We will cover most of Chapters 6
through 11.
Prerequisite: Math 261
Course Description: Continuation of Calculus of one variable. We will focus on
techniques and applications of integration and on convergence and divergence of
sequences and series.
Math 260:
Math 260, Computer Calculus, is a one-credit companion course to this course. It is
required of all Mathematics majors and of anyone who needs to take Math 323, MultiVariable and Vector Calculus (this includes Physics and Chemistry majors). It is
designed to be taken concurrently with Math 261.
Course Goals:
The student-learning goals of Math 262 include learning one-variable calculus and
some applications to the sciences. It is part of a larger three-semester sequence in
calculus. Math 261, Calculus I, which precedes this course, begins teaching onevariable calculus, and Math 323, Multi-Variable and Vector Calculus, extends the
concepts from Math 261 and Math 262 to functions of two or more variables.
Course Outline – The successful student will be able to:
 Finding areas, volumes, and arc lengths.
 Work and center of mass.
 Formal definitions of logarithms, exponential functions, inverse trigonometric
functions, their derivatives and uses as antiderivatives, and applications of all of
these in the calculus.
 Integration techniques.
 Sequences and series, and determinations of convergence.
 Taylor/Maclaurin series, power series representation of functions, proofs of
convergence.
Lenarz – Math 262
Fall 2012
Page 2
Student Competencies/Learning Outcomes – The successful student will be able to:
 Use a variety of integral calculus techniques to solve real-world problems.
 Prove when an infinite sequence or series converges or diverges.
 Be able to find a series representation of a function and determine its interval of
convergence.
Free Tutoring: The Mathematics Department provides free walk-in tutoring in MacLean
383, Monday – Friday from 8 am to 4:30 pm.
Grading: Final grades will be determined by the following components:
Component
Labs
Quizzes
Exam 1
Exam 2
Exam 3
Exam 4
Final Exam
%
15 %
10 %
15 %
15 %
15 %
15 %
15 %
Date
Various Dates
Weekly
September 18
October 9
October 31
November 29
December 17
Grades will be based on the following scale:
Percentage
93 − 100
90 − 92
87 − 89
83 − 86
80 − 82
77 − 79
Grade
A
AB+
B
BC+
Percentage
73 − 76
70 − 72
67 − 69
63 − 66
60 − 62
0 − 59
Grade
C
CD+
D
DF
Labs: Once or twice a week we will do in-class “labs” to reinforce lecture material and
delve deeper into the subject matter. These will be due the following class period and
graded for both content and presentation. Each lab will be graded out of 20 points. We
will do a total of 23 labs and your lowest 3 scores will be dropped at the end of the term.
Quizzes & Daily Homework: Homework problems for each section will be posted on
the webpage. The answers to all odd-numbered problems are in the back of the book.
I encourage you to work together outside of class and to see the calculus tutor. I will not
be collecting the daily homework. We will have one pop-quiz a week. Each quiz will be
graded out of 10 points and your lowest 3 scores will be dropped at the end of the term.
Exams: There will be 4 in-class exams given during the course as well as a
comprehensive final exam. Each in-class exam will be 50 minutes long. Attendance is
required for exams. If you can not attend for some reason, you must contact me
BEFORE the exam to schedule a makeup exam.
Lenarz – Math 262
Fall 2012
Page 3
Calculators: Calculators will be prohibited for certain quizzes or exams. You may use a
calculator at any other time, but exams will be written in such a way that a calculator
gives no unfair advantage. Please see me if you need help selecting a calculator.
Partial Credit: Partial credit will be awarded. If your final answer is incorrect, but your
thought processes were correct in general, you will receive some credit. In a similar
manner, if no thought processes are indicated and your answer is correct, you will not
receive full credit. YOU MUST ALWAYS SHOW YOUR WORK!
Academic Honesty: All students are expected to follow the policies set forth in the
Academic Honesty section of the catalog. Cheating will NOT be tolerated. If you are
caught cheating, you will receive a zero for that quiz, exam or assignment.
Special Accommodations: Students with disabilities who believe they may need an
accommodation in this class are encouraged to contact Greg Toutges, Director of
Disability Services at 477-4318 (Voice) or 1-800-627-3529 (MRS/TTY), Flora Frick 154
as soon as possible to ensure that accommodations are implemented in a timely
fashion. Information regarding Disability Services is available at
http://web.mnstate.edu/disability/
Attendance: Students are expected to attend and participate in class. If you aren’t in
class, you won’t learn anything! All absences will be considered unexcused unless
instructor approval is given. Make-up classwork or quizzes will be given only for those
with excused absences.
Classroom Behavior: Please respect your fellow classmates. This means not
distracting other students during class with ringing cell phones, talking on the phone,
talking with your neighbor, etc. I do not mind if you eat or drink during class, just clean
up after yourself.
Changes: Components of this syllabus are subject to change. If changes need to be
made in the syllabus, students will be involved in the decision process.
Lenarz – Math 262
Fall 2012
Page 4
Tentative Schedule
Date
Aug. 27
Aug. 28
Aug. 29
Aug. 30
Aug. 31
Sept. 3
Sept. 4
Sept. 5
Sept. 6
Sept. 7
Sept. 10
Sept. 11
Sept. 12
Sept. 13
Sept. 14
Sept. 17
Sept. 18
Sept. 19
Sept. 20
Sept. 21
Sept. 24
Sept. 25
Sept. 26
Sept. 27
Sept. 28
Oct. 1
Oct. 2
Oct. 3
Oct. 4
Oct. 5
Oct. 8
Oct. 9
Oct. 10
Oct. 11
Oct. 12
Oct. 15
Oct. 16
Oct. 17
Oct. 18
Oct. 19
Section
Syllabus and Calculus I Review; Lab # 1
6.1 – Area
6.1 – Area; Lab # 2
6.2 – Solids of Revolution
6.2 & 6.3 – Solids of Revolution & Volumes by Cylindrical Shells
Labor Day – No Class
6.3 – Volumes by Cylindrical Shells; Lab # 3
6.4 – Volumes by Cross Sections
6.4 – Volumes by Cross Sections; Lab # 4
6.5 – Arc Length and Surfaces of Revolution
6.5 – Arc Length and Surfaces of Revolution; Lab # 5
6.6 – Work
6.6 & 6.7 – Work & Centers of Mass
6.7 – Moments and Centers of Mass
Catch – up; Lab # 6
Review
Exam 1 – Chapter 6
7.1 & 7.2 – Inverse Functions & The Natural Log Function
7.2 & 7.3 – The Natural Log Function & The Natural Exponential Function
7.3 – The Natural Exponential Function; Lab # 7
7.4 – Integration
7.4 & 7.5 – Integration & General Exponential and Log Functions; Lab # 8
7.5 & 7.6 – General Exponential and Log Functions & Laws of Growth/Decay
7.6 – Laws of Growth/Decay
8.1 – Inverse Trig Functions
8.1 & 8.2 – Inverse Trig Functions & Derivatives and Integrals; Lab # 9
8.2 – Derivatives and Integrals
9.1 – Integration by Parts; Lab # 10
9.1 & 9.2 – Integration by Parts & Trig Integrals
9.2 – Trig Integrals
Review
Exam 2 (Chapters 7 & 8)
9.3 – Trig Substitution
9.3 – Trig Substitution; Lab # 11
9.4 – Integrals of Rational Functions
Fall Breather – No Class
Fall Breather – No Class
9.5 – Integrals Involving Quadratic Expressions
9.6 – Miscellaneous Substitutions; Lab # 12
10.1 – Indeterminate Forms
Lenarz – Math 262
Date
Oct. 22
Oct. 23
Oct. 24
Oct. 25
Oct. 26
Oct. 29
Oct. 30
Oct. 31
Nov. 1
Nov. 2
Nov. 5
Nov. 6
Nov. 7
Nov. 8
Nov. 9
Nov. 12
Nov. 13
Nov. 14
Nov. 15
Nov. 16
Nov. 19
Nov. 20
Nov. 21
Nov. 22
Nov. 23
Nov. 26
Nov. 27
Nov. 28
Nov. 29
Nov. 30
Dec. 3
Dec. 4
Dec. 5
Dec. 6
Dec. 7
Dec. 10
Dec. 11
Dec. 12
Dec. 17
Fall 2012
Page 5
Section
10.1 & 10.2 – Indeterminate Forms & Other Indeterminate Forms
10.2 – Other Indeterminate Forms; Lab # 13
Quiz – Integration Techniques
10.3 – Integrals with Infinite Limits
10.3 & 10.4 – Integrals with Infinite Limits & Integrals with Discontinuities
10.4 – Integrals with Discontinuities; Lab # 14
Review
Exam 3 (Chapter 9 & 10)
11.1 – Sequences
11.1 – Sequences
11.1 – Sequences; Lab # 15
11.2 – Convergent or Divergent Series
11.2 – Convergent or Divergent Series
11.2 – Convergent or Divergent Series; Lab # 16
11.3 – Positive Term Series
11.3 – Positive Term Series; Lab # 17
Quiz – Sequences and Series
11.4 – The Ratio and Root Tests
11.4 – The Ratio and Root Tests; Lab # 18
11.5 – Alternating Series and Absolute Convergence
11.5 – Alternating Series and Absolute Convergence; Lab # 19
11.6 – Power Series
Fall Break – No Class
Fall Break – No Class
Fall Break – No Class
Lab # 20
11.6 – Power Series
Review
Exam 4 (Chapter 11)
11.7 – Power Series Representations of Functions
11.7 – Power Series Representations of Functions; Lab # 21
11.8 – Maclaurin and Taylor Series
11.8 – Maclaurin and Taylor Series; Lab # 22
11.9 – Applications of Taylor Series
11.9 – Applications of Taylor Series; Lab # 23
Review; Capstone Lab
Review; Capstone Lab
Study Day – No Class
Final Exam 12:00 pm