SYLLABUS FOR MATH 238 - MULTIVARIABLE CALCULUS
SPRING 2004 SEMESTER AT LYCOMING COLLEGE
IMPORTANT: Math 129 (Calculus II) and Math 130 (Matrix Algebra) are prerequisites for this course; without them, your name will be removed from the roster!!!
Instructor
Name: Dr. Gene D. Sprechini
Office: Academic Center D311
Phone Number: (570) 321-4288
Office Hours: Go here to make an appointment to see me, or email me at sprgene@lycoming.edu.
Grading
The final grade depends on the number of points earned out of the 1200 points possible from the following:
Assignment Set #1 & Exam #1: 200 points (50 points are from in-class and out-of-class assignments leading up to Exam #1, and 150 points are from Exam #1.)
Assignment Set #2 & Exam #2: 200 points (50 points are from in-class and out-of-class assignments leading up to Exam #2, and 150 points are from Exam #2.)
Assignment Set #3 & Exam #3: 200 points (50 points are from in-class and out-of-class assignments leading up to Exam #3, and 150 points are from Exam #3.)
Assignment Set #4 & Exam #4: 200 points (50 points are from in-class and out-of-class assignments leading up to Exam #4, and 150 points are from the Final Exam.)
Assignment Set #5 & Final Exam: 400 points (50 points are from in-class and out-of-class assignments leading up to the Final Exam, and 350 points are from the Final Exam.)
The Assignment Set corresponding to each Exam usually consists of about seven or eight in-class and out-of-class assignments. For all assignments not submitted, a grade of zero is recorded, unless special arrangements are made with the instructor.
For all missed exams, a grade of zero is recorded, unless (1) arrangements to make up the exam are made within 24 hours of the originally scheduled time and (2) the instructor is presented with documented evidence of a medical reason for not completing the exam at the scheduled time.
The final course grade percentage is the percentage of points earned from the total possible points, and letter grades corresponding to the final course grade percentage are assigned according to the following:
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A = above 93.33 |
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A– = 90 to 93.33 |
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B+ = 86.67 to 90 |
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B = 83.33 to 86.67 |
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B– = 80 to 83.33 |
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C+ = 76.67 to 80 |
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C = 73.33 to 76.67 |
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C– = 70 to 73.33 |
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D+ = 66.67 to 70 |
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D = 63.33 to 66.67 |
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D- = 60 to 63.33 |
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F = below 60 |
However, any student who misses more than ten in-class and out-of-class assignments will automatically receive a course grade of F; also, the final course grade percentage will be reduced by 4% for each unexcused absence beyond the 3rd unexcused absence. An absence is considered to be excused only when (1) the student submits within one class day of the absence a written explanation of why class was missed and (2) the instructor approves the explanation.
Materials
Each student will need:
Topics
Graphs and Level Surfaces
Partial Derivatives and Continuity
Differentiability, Derivative Matrix, Tangent Planes
Chain Rule
Gradients and Directional Derivatives
Implicit Differentiation
Higher Order Partial Derivatives
Taylor's Theorem
Maxima and Minima
Second Derivative Test
Constrained Extrema and Lagrange Multipliers
Acceleration
Arc Length
Vector Fields
Divergence and Curl
Volume and Cavalieri's Principle
Double Integrals
Triple Integrals
Change of Variables, Cylindrical and Spherical Coordinates
Line Integrals
Parametrized Surfaces
Area of Surface
Surface Integrals
Green's Theorem
Stokes' Theorem
Gauss' Theorem
Path Independence and the Fundamental Theorems of Calculus
Standards and Policies
Each student should bring to each class the three-ring binder containing all assignments completed and the textbook. Very often in class, the instructor may refer to previously completed assignments.
All work submitted must be of professional quality. All paper must be neat, without ragged edges, rips, tears, smudges, stains, etc. All answers must be clear, complete, and concise; handwriting must be legible. If the instructor can't read it, it's wrong. Assignments will be down-graded if these standards are not met.
It can be very helpful for some students to work together on daily assignments and to study together; this is encouraged when it does not result in one student simply copying another's work with no understanding. Acts of academic dishonesty will result in a grade of F for the course, and a letter to the Dean describing the circumstances. If you are having problems in the course, talk to the instructor, don't involve yourself in academic dishonesty. With each assignment submitted, students are expected to include a short paragraph indicated from whom help was received and to whom help was given (but this does not affect the grade for the assignment).
The major goal of this course is to provide the student with an understanding how concepts from one-variable calculus are extended to develop multivariable calculus and how techniques can be applied and interpreted in a variety of fields, especially sciences, etc. This course is required for a major or minor in mathematics and is recommended for some science majors.
The following is from the FACULTY HANDBOOK in the section titled Student Course Load:
"It is expected that students will spend, in preparation for courses, two hours of study time outside the classroom for every hour of credit in the classroom."
This means that you should spend, on the average, 8 hours per week outside of class working on a four credit course. While this varies from student to student and from course to course, you should expect that this class will require at least 8 hours per week. Be prepared to spend 8 hours or more per week on this course ! Your time will be spent reading the text, reviewing class notes, and doing exercises.
Some of the exercises assigned both in and out of class may refer back to work done in one or more previous exercises; for this reason, it is important that your notebook or folder containing all assignments completed be kept up to date. The schedule of reading assignments and exam dates is shown in the table below; the written assignments due each day will be given in class and updated regularly in the table.
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Due Dates |
Written Assignments |
Reading Assignments |
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01/13 T |
Exercises for 1.1: # 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31 (Note: In #27, #29, and #31, it is possible for a correct answer to look different from what is given.) Exercises for 1.2: # 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23 |
Sections 1.1, 1.2 |
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01/14 W |
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Section 2.1 |
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01/16 F |
Exercises for 2.1: # 2, 4, 6, 8, 22(name the surface instead of sketching it), 24(name the surface instead of sketching it), 26(name the surface instead of sketching it), 28(name the surface instead of sketching it) |
Section 2.2 |
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01/19 M |
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Section 2.3 |
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01/20 T |
Exercises for 1.3: # 1, 3, 5, 7 Exercises for 1.4: # 1, 3, 5, 7, 9, 11, 13, 15, 21, 23, 25, 27, 29, 31 |
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01/21 W |
Exercises for 2.2: # 2, 4, 6, 8, 10, 12, 14, 16, 18, 30, 33; the two exercises distributed in class |
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01/23 F |
Exercises for 2.3: # 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 |
Section 2.4 |
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01/26 M |
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Section 2.5 |
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01/27 T |
Exercises for 2.4: # 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 |
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01/28 W |
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Section 2.6 |
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01/30 F |
Exercises for 2.5: # 2, 4, 6, 8, 14, 16, 18, 20, 22, 24, 26, 30, 32, 34, 36, 38, 40, 44 |
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02/02 M |
Exercises for 2.6: # 2, 4, 6, 8, 10, 12, 14, 16 |
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02/03 T |
Exam #1 – Here are some suggested practice textbook exercises: with answers are available in the back of the text: Chapter 2 Review Exercises on pages 166-170, #5, 7, 9, 11 (name the surface instead of sketching it) #13, 15, 17, 19 #21, 23 #25, 27 #29, 31 #33, 35, 37, 39 #41, 43 #47, 49, 51, 53, 55 #57, 61, 65 All exercises numbered one less than a homework exercise in each section of Chapter 2. More sample review problems can be found here with answers found here. |
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02/04 W |
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Section 3.1 |
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02/06 F |
Exercises for 3.1: # 2, 4, 6, 8, 12, 14, 16 |
Section 3.2 |
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02/09 M |
Exercises for 3.2: # 2, 4, 6, 8, 10, 12(find all terms up to degree three in the Taylor expansion – there will only be three such terms) |
Section 3.3 |
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02/10 T |
Exercises for 3.3: # 2, 4, 6, 8, 10, 12, 14(Set the surface areas 2xy + 2xz + 2yz equal to some constant S, and solve for z. Then maximize the volume = xyz.), 16 |
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02/11 W |
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Section 3.4 |
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02/13 F |
Exercises for 3.4: # 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 |
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02/16 M |
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Section 3.5 |
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02/17 T |
Exercises for 3.5(Just set up the equations for each exercises; we will solve the equations in class): # 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22 |
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02/18 W |
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Section 4.1 |
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02/20 F |
Class Handout for Section 4.1 |
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02/23 M |
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02/24 T |
Exam #2 – Here are some suggested practice textbook exercises: with answers are available in the back of the text: Chapter 3 Review Exercises on pages 221-226, #1, 3, 5, 11 #13 #15, 19 #23, 25 #29, 33 All exercises numbered one less than a homework exercise in each section of Chapter 3 |
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02/25 W |
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02/27 F |
Exercises for 4.1: # 2, 4, 6, 8, 10, 12, 14 |
Section 4.2 |
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03/08 M |
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Section 4.3 |
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03/09 T |
Exercises for 4.2: # 2, 4, 6, 8, 10 |
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03/10 W |
Exercises for 4.3: # 2, 4, 6, 8, 10, 12, 14, 16, 18 |
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03/12 F |
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Section 4.4 |
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03/15 M |
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03/16 T |
Exercises for 4.4: # 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 32 |
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03/17 W |
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Section 5.1 |
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03/19 F |
Class Handout for Section 4.4 |
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03/22 M |
Exercises for 5.1: # 2, 4, 6, 8, 10, 12, 14 |
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03/23 T |
Exam #3 – Here are some suggested practice textbook exercises: with answers are available in the back of the text: Chapter 4 Review Exercises on pages 263-267, #1, 3, 5, 7 #8 #9, 13 #15, 17, 19, 21 #27 All exercises numbered one less than a homework exercise in each section of Chapter 4 |
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03/24 W |
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Section 5.2 |
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03/26 F |
Exercises for 5.2: # 2, 4, 6, 8, 10, 12(just find this double integral with only one order of integration), 14, 16, 18 |
Section 5.3 |
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03/29 M |
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Section 5.4 |
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03/30 T |
Exercises for 5.3: # 2, 4, 6, 8, 10(just sketch the region without evaluating the integral), 12, 14, 16, 18, 20, 22, 24(you should have to do no work for this exercise, once you realize that sin(-x) = -sin(x) and cos(-x) = cos(x)) |
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03/31 W |
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Section 5.5 |
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04/02 F |
Exercises for 5.4: # 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24 |
Section 6.1 |
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04/05 M |
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Section 6.2 |
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04/06 T |
Exercises for 5.5: # 2, 4, 6, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30(change the exponent of e to -(x2+y 2+z2)2), 32, 34, 36(change the function being integrated to (4-x2-y2)z2), 38, 40 |
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04/07 W |
Class Handout for Section 5.5 |
Section 6.3 |
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04/12 M |
Exercises for 6.1: # 2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28 |
Section 6.4 |
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04/13 T |
Exam #4 - Here are some suggested practice textbook exercises: with answers are available in the back of the text: Chapter 5 Review Exercises on pages 350-354, #11, 13 #21, 23, 25 #27, 29, 31 #33, 35 #37, 39, 41 In Section 5.5 on page 339, #37, #39 All exercises numbered one less than a homework exercise in Sections 5.1 to 5.5. More sample review problems can be found here. |
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04/14 W |
Exercises for 6.2: # 2, 4, 6, 8, 10 |
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04/16 F |
Exercises for 6.3: # 2, 4, 6, 8, 10, 12, 14, 18, 20, 22 |
Section 7.1 |
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04/19 M |
Exercises for 6.4: # 2(use the “outward” normal parametrization), 4(use the “outward” normal), 6, 8 |
Section 7.2 |
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04/20 T |
Homework Handout Exercises for 7.1 |
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04/21 W |
Homework Handout Exercises for 7.2 |
Section 7.3 |
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04/23 F |
Homework Handout Exercises for 7.3 |
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04/26-04/30 |
Final Exam (in the Final Exam Period) some sample review problems can be found here |
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