MA 242 Course Syllabus

MA 242 – Calculus III

Section 651

10-week Summer Session 2020

4 Credit Hours

Course Description

Third of three semesters in a calculus sequence for science and engineering majors. Vectors, vector algebra, and vector functions. Functions of several variables, partial derivatives, gradients, directional derivatives, maxima and minima. Multiple integration. Line and surface integrals, Green's Theorem, Divergence Theorems, Stokes' Theorem, and applications. Use of computational tools.

Learning Outcomes

After successfully completing this course, students will be able to:

1.     Use the techniques of partial differentiation and multivariable integration to explore the properties of functions of two or more variables

2.     Set up and solve optimization problems in various contexts

3.     Compute line, surface and volume integrals in various coordinate systems

4.     Identify conservative vector fields and integrate them to find their potential functions

5.     Apply the theorems of Green, Stokes and Gauss to various problems in geometry and the sciences

Course Structure

This course is an online course.  There are 56 video lectures covering the relevant sections of the textbook.  Students devise a weekly schedule based on the supplied week-by-week schedule of topics.  There will be four regular tests during the semester plus a comprehensive final exam.  See the “Course Schedule” below for test dates.  In addition, there will be online WebAssign homework for each section of the textbook that we cover.

Instructors

Larry Norris (lkn) - Instructor
Email:
lkn@ncsu.edu
Web Page:
http://lkn.math.ncsu.edu
Phone: 919-515-7932
Office Location: SAS 4216
Office Hours: Daily, via email

Course Meetings

Lecture

Days: daily
Time: scheduled by the student 

 

Course Materials

Textbooks

Calculus for Engineers and Scientists, Vol. III -  Franke, Griggs, and Norris
Edition: 1st
WebAssign Homework

Web Link: https://www.webassign.net/ncsu/login.html
Cost: Approximately $77.95
This textbook and homework are required.

Materials

The textbook, which you will access via WebAssign, is in streaming video format.

Requisites and Restrictions

Prerequisites

MA 241 with grade of C- or better or AP Calculus credit, or Higher Level IB credit.

Co-requisites

None.

Restrictions

   None

General Education Program (GEP) Information

GEP Category

Mathematical Sciences

Transportation

This course is entirely on-line and will not require attendance at the NCSU campus.

Safety & Risk Assumptions

None.

Grading

Grade Components

Component

Weight

Details

WebAssign

Homework

20%

There will be a WebAssign homework set for each section of the textbook

Midterm Tests

50%

There will be four 60 minute midterm tests.  One page of notes allowed for each test.

Final Exam

30%

The comprehensive final exam will be 180 minutes.  One page of notes allowed.

Letter Grades

This Course uses Standard NCSU Letter Grading:

97

A+

100

93

A

< 

97

90

A-

< 

93

87

B+

< 

90

83

B

< 

87

80

B-

< 

83

77

C+

< 

80

73

C

< 

77

70

C-

< 

73

67

D+

< 

70

63

D

< 

67

60

D-

< 

63

0

F

< 

60

Requirements for Credit-Only (S/U) Grading

In order to receive a grade of S, students are required to take all exams and quizzes, complete all assignments, and earn a grade of C- or better. Conversion from letter grading to credit only (S/U) grading is subject to university deadlines. Refer to the Registration and Records calendar for deadlines related to grading. For more details refer to http://policies.ncsu.edu/regulation/reg-02-20-15.

Requirements for Auditors (AU)

Information about and requirements for auditing a course can be found at http://policies.ncsu.edu/regulation/reg-02-20-04.

Policies on Incomplete Grades

If an extended deadline is not authorized by the instructor or department, an unfinished incomplete grade will automatically change to an F after either (a) the end of the next regular semester in which the student is enrolled (not including summer sessions), or (b) the end of 12 months if the student is not enrolled, whichever is shorter. Incompletes that change to F will count as an attempted course on transcripts. The burden of fulfilling an incomplete grade is the responsibility of the student. The university policy on incomplete grades is located at http://policies.ncsu.edu/regulation/reg-02-50-3.

Late Assignments

·      If a student has a University approved excused reason for turning in an assignment late, they will not be penalized if the assignment is turned in within one week of receiving the assignment (or another negotiated time).  Students wishing to take advantage of this must contact their instructor.

·      If the late assignment is unexcused, automatic extensions can be requested in WebAssign for a 24 hour period up to 5 days after an assignment is due with a 40% reduction in points earned during the extension period.

Attendance Policy

For complete attendance and excused absence policies, please see http://policies.ncsu.edu/regulation/reg-02-20-03

Attendance Policy

Students are expected to keep a regular schedule for viewing video lectures and doing WebAssign homework.

Absences Policy

Students with a University approved excused absence will not be penalized. 

Makeup Work Policy

Test Make-Up Policy: All anticipated absences must be excused in advance of the test date. These include university duties or trips (certified by an appropriate faculty or staff member), required court attendance (certified by the Clerk of Court), or religious observances (certified by the Department of Parent and Family Services 515-2441). Emergency absences must be reported as soon as possible once returning to class and must be appropriately documented (illness by an attending physician or family emergencies by Parent and Family Services). If you are sick on a test day and decide not to take the test, go to the health center or other medical facility. Students who miss a test and have a university approved excuse must submit appropriate documentation.

Additional Excuses Policy

None.

Academic Integrity

Academic Integrity

Students are required to comply with the university policy on academic integrity found in the Code of Student Conduct found at http://policies.ncsu.edu/policy/pol-11-35-01

 

Both faculty and students at North Carolina State University have a responsibility to maintain academic integrity. An informational brochure about academic integrity is available from the university and students are encouraged to obtain a copy.

Academic Honesty

See http://policies.ncsu.edu/policy/pol-11-35-01 for a detailed explanation of academic honesty.

 

Cheating is the giving, taking, or presenting of information or material by a student that unethically or fraudulently aids oneself or another person on any work which is to be considered in the determination of a grade or the completion of academic requirements or the enhancement of that student's record or academic career.” (NCSU Code of Student Conduct)

 

Scholarly activity is marked by honesty, fairness and rigor. A scholar does not take credit for the work of others, does not take unfair advantage of others, and does not perform acts that frustrate the scholarly efforts of others. The violation of any of these principles is academic dishonesty. Penalties for a violation: For the first violation, you will receive a zero for your work and be put on academic integrity probation for the remainder of your stay at NCSU. The second violation may result in your suspension from NCSU. Both situations will involve the Office of Student Conduct. See the website for a full explanation:

http://www.ncsu.edu/policies/student_services/student_discipline/POL11.35.1.php

 

Honor Pledge

Your signature on any test or assignment indicates "I have neither given nor received unauthorized aid on this test or assignment."

Electronically-Hosted Course Components

Students may be required to disclose personally identifiable information to other students in the course, via electronic tools like email or web-postings, where relevant to the course. Examples include online discussions of class topics, and posting of student coursework. All students are expected to respect the privacy of each other by not sharing or using such information outside the course.

Electronically-hosted Components: Class videos, notes, and other materials; homework assignments; forum discussions.

 

Accommodations for Disabilities

Reasonable accommodations will be made for students with verifiable disabilities. In order to take advantage of available accommodations, students must register with the Disability Resource Office at Holmes Hall, Suite 304,Campus Box 7509, 919-515-7653 . For more information on NC State’s policy on working with students with disabilities, please see the Academic Accommodations for Students with Disabilities Regulation (REG02.20.01) 

 

Students with disabilities should additionally contact their instructor about accommodations.

 

Non-Discrimination Policy

NC State University provides equality of opportunity in education and employment for all students and employees. Accordingly, NC State affirms its commitment to maintain a work environment for all employees and an academic environment for all students that is free from all forms of discrimination. Discrimination based on race, color, religion, creed, sex, national origin, age, disability, veteran status, or sexual orientation is a violation of state and federal law and/or NC State University policy and will not be tolerated. Harassment of any person (either in the form of quid pro quo or creation of a hostile environment) based on race, color, religion, creed, sex, national origin, age, disability, veteran status, or sexual orientation also is a violation of state and federal law and/or NC State University policy and will not be tolerated. Retaliation against any person who complains about discrimination is also prohibited. NC State's policies and regulations covering discrimination, harassment, and retaliation may be accessed at http://policies.ncsu.edu/policy/pol-04-25-05 or http://www.ncsu.edu/equal_op/. Any person who feels that he or she has been the subject of prohibited discrimination, harassment, or retaliation should contact the Office for Equal Opportunity (OEO) at 919-515-3148.

Course Schedule

NOTE: The course schedule is subject to change.

MA242.651  10-Week Summer Session 2020

Day-by-day Schedule

Monday

Tuesday

Wednesday

Thursday

Friday

 

 

(May 13)

Lecture 1

 Lecture 2

(May 14)

Lecture 3

 Lecture 4 – 1st half

(May 15)

Lecture 4 – 2nd half

Lecture 5

(May 18)

 

Lecture 6

Lecture 7 – 1st half

 

(May 19)

Lecture 7 – 2nd half

Lecture 8

 

(May 20)

Lecture 9

 Lecture 10 – part1

(May 21)

Lecture 10 – 2nd half

Lecture 11

 

(May 22)

Lecture 12

Lecture 13 – 1st half

(May 25)

HOLIDAY

 

(May 26)

Lecture 13 – 2nd half

Lecture 14  

(May 27)

Lecture 15

Lecture 16 – 1st half

(May 28)

Lecture 16 – 2nd half

Lecture 17 - review

 

(May 29)

 

TEST 1

(2-day window is:

5/28,5/29)

 

Lecture 18

 

(June 1)

Lecture 19

Lecture 20 – 1st half

 

(June 2)

Lecture 20 – 2nd half

Lecture 21

 

(June 3)

Lecture 22

Lecture 23 – 1st half

(June 4)

Lecture 23 – 2nd half

Lecture 24

 

(June 5)

Lecture 25

Lecture 26 – 1st half

 

(June 8)

Lecture 26 – 2nd half

Lecture 27

 

(June 9)

Lecture 28

Lecture 29 – 1st half

(June 10)

Lecture 29 – 2nd half

Lecture 30 – 1st half

(June 11)

Lecture 30 – 2nd half

Lecture 31 review 

 

(June 12)

TEST 2

(2-day window is:

6/11,6/12)

 

Lecture 32

(June 15)

Lecture 33
Lecture 34 – 1st half

(June 16)

Lecture 34 – 2nd half

Lecture 35

(June 17)

Lecture 36

Lecture 37 – 1st half

(June 18)

Lecture 37 – 2nd half

Lecture 38

 

(June 19)

Lecture 39

Lecture 40 – 1st half

(June 22)

Lecture 40 – 2nd half

Lecture 41

 

(June 23)

Lecture 42

Lecture 43 – 1st half

(June 24)

Lecture 43 – 2nd half

Lecture 44

(June 25)

Lecture 45

Lecture 46 – 1st half

 

(June 26)

Lecture 46 – 2nd half

 Lectures 47 –1st half

(June 29)

Lecture 47 – part 3

Lectures 48 Review

(June 30)

 

TEST 3

(2-day window is:

6/29,6/30)

 

Lecture 49

 

(July 1)

Lecture 50

Lecture 51 – 1st half

 

 

(July 2)

 

Lecture 51 – 2nd half

              Lecture 52

 

(July 3)

HOLIDAY

 

(July 6)

Lecture 53

Lecture 54 – 1st half

(July 7)

Lecture 54 – 2nd half

Lecture 55

 

(July 8)

Lecture 56

Lecture 57 – 1st half

(July 9)

Lecture 57 – 2nd half

Lecture 58

 

(July 10)

Lecture 59

 

(July 13)

Lecture 60

(July 14)

Lecture 62 Review

(July 15)

TEST 4

(2-day window is:

7/14,7/15)

(July 16)

Lecture 61

Lecture 63 – 1st half

(July 17)

Lecture 63 – 2nd half

Lecture 64

  

(July 20)

Lecture 65

1st half

(July 21)

Lecture 65

2nd half

 

(July 22)

Lecture 66

 

(July 23)

Lecture 67

 

 

 

 

(July 24)

Lecture 68

 

 

(July 27)

 

Final Exams – Day 1

(July 28)

 

Final Exams – Day 2

 

 

 

 

 

 

 

 

Grades due at 11:59 pm on Thursday 7/30

 

 

List of Topics for the VIDEO LECTURES

 

Lecture #

Chapter

#

Section

#

Topic

1

 

---

Introduction to the course

1

1

Begin Chapter 1: “Euclidean Geometry in 3-dimensional Space”.

Review Cartesian Coordinates in the Plane; Begin study of Cartesian coordinates in 3-dimensional space.

2

1

2

Begin study of Vectors in two and three dimensions

3

1

2

More on vectors; Positions vector representation of a vector

4

 

---

Brief discussion of Maple

1

3

Begin study of the dot product of 2 vectors A and B

5

1

3

More on the dot product

1

4

Begin study of the cross product of 2 vectors A and B

6

1

4

More on the cross product

7

1

4

Example: orthogonal decomposition of vector A with respect to vector B

1

5

Equations of Lines and Planes

8

1

5

More on equations of Lines and Planes

9

2

1

Begin Chapter 2: “The Geometry of Curves in Space

Vector-valued functions, limits and continuity

10

2

1

Differentiating vector-valued functions, rules of differentiation, definite integrals of vector-valued functions

11

2

1

Sketching curves in 3-d using Maple

Anti-derivatives of vector-valued function, parameterized curves

2

Parametrized curves in space, Introduction to the idea of curvature, reparametrizing a curve in terms of arc length,

Initial-value problems, Application: Newton’s second law and motion under gravity

12

2

2

Example of motion under gravity

3

Begin section 3: “Fundamental Quantities Associated with a Curve”,

 Smooth curve, principal tangent vector to a curve, unit tangent vector,  velocity, speed and acceleration of a point particle

13

2

3

Arc length of a curve, arc length reparametrization of a curve, Curvature of a curve

14

2

2

Exercise #23, section 2.2,

3

The curvature of a circle of radius R is K = 1/R, curvature of a curve in terms of an arbitrary parameter

15

2

4

The Unit Normal Vector N,The osculating plane,

Theorem:  Acceleration vector is always parallel to the osculating plane.

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The Unit Binormal vector B

16

2

4

The osculating circle of a curve, instantaneous linear and instantaneous centripetal acceleration, simple formulas for the tangential and normal components of acceleration, and for curvature.

17

 

 

Review for Test #1

Test #1 on chapters 1 and 2

18

3

1

Begin Chapter 2: “Differential Multivariable Calculus”

Definition and graphical representation; Level curves of f(x,y); Quadric surfaces;

19

3

1

Review level curves of f(x,y); Level surfaces of f(x,y,z),  examples of level surfaces of functions of 3 variables.

20

3

1

Examples of: Ellipsoids, paraboloids, cones, planes and cylinders;

2

Limits of multivariable functions; theorems on limits

21

3

2

Continuity of multivariable functions; theorems on continuity

3

Begin Directional Derivatives of multivariable functions

22

3

3

x-, y- and z-partial derivatives; higher partial derivatives; new notation for partial derivatives

23

3

3

Geometrical interpretation of x- and y-partial derivatives of f(x,y).

Tangent planes to the graph of f(x,y);  Linearization of a function near a point

24

3

4

Differentiability of multivariable functions; examples;

Theorem: a multivariable function is continuous at P if it is differentiable at P. 

25

3

4

Theorem: A multivariable function is differentiable at P if its partial derivatives are continuous at P. 

Examples:  Use the theorem to prove that a function is differentiable at a point.

5

The directional derivative and the Gradient of a function.

Examples.

26

3

5

What does the gradient of the function f tell us about f?

Tangent planes to level surfaces of a function f(x,y,z).

27

3

5

The chain rules for multivariable functions;  Parametrizing functions that are graphs of functions; Implicit differentiation

28

3

6

Optimization of function of two variables:  finding local extreme values of f(x,y);  Examples

29

3

6

The second derivative test;  examples

30

3

6

Global extreme values of f(x,y) on closed and bounded sets

31

 

 

Review of chapter 3 for test #2

Test #2 on chapter 3

32

4

1

Begin Chapter 4: “Double and Triple Integrals in Cartesian Coordinates”.  Start with double integrals over rectangles.

33

4

1

Fubini’s Theorem for rectangles.  Examples.

34

4

1

Type I regions.  Fubini’s theorem for Type I regions. Examples.

35

4

1

Type II regions.  Fubini’s theorem for Type II regions. Examples.

36

4

1

Reversing the order of integration; Numerous examples

37

4

2

Applications of double integrals: area; average values; volume between two surfaces; moments and center of mass of plane laminas,

38

4

2

More on applications of double integrals

39

4

3

Triple integrals in Cartesian Coordinates

40

4

3

More on triple integrals:  z-simple, x-simple, and y-simple regions; 

41

4

3

More examples of triple integrals

42

4

3

Applications of triple integrals: Volume; average value; mass and charge density; energy density; moments of inertia

43

5

1

Begin Chapter 5: Double and Triple Integrals in Curvilinear Coordinates.  Begin with double integrals in polar coordinates

44

5

1

Examples of double integrals in polar coordinates

45

5

2

Triple integrals in cylindrical coordinates

46

5

3

Triple integrals in spherical coordinates

47

5

3

More on triple integrals in spherical coordinates; Examples

48

 

 

Review of chapters 4 and 5 for test #3

Test #3 on chapters 4 & 5

49

6

1

Begin Chapter 4: “Line and Surface Integrals”.  Start with vector fields in space.  Numerous examples.

50

6

2

Line integrals of functions. 

51

6

2

Solutions to selected exercises in Section 6.2.1 on Line integrals of functions

52

6

3

Line integrals of vector fields.  Work and other examples

53

6

3

The Fundamental Theorem for Line Integrals; Line integrals of vector fields that are independent of path.

54

6

3

Characterizing conservative vector fields.  Finding potential functions for conservative vector fields

55

6

3

More on finding potential functions; Conservation of total energy forNewtonian motion under a conservative force.

4

Parametric surfaces in space

56

6

4

Parametrizing surfaces that are graphs of functions of two variables

57

6

5

Surface integrals; surface area of a parametrized surface;  example:  surface area of a sphere

58

6

5

Surface integrals of functions; examples

59

6

5

Surface integrals of vector fields; examples

60

6

5

More examples of flux integrals

62

 

 

Review of chapter 6 for test #4

Test #4 on chapter 6

61

7

1

Begin Chapter 7: “Vector Analysis”.  Start with integral curves of vector fields in space. 

2

Differentiating vector fields:  The divergence and curl.

63

7

2

The concept of “flux density” and its relationship to divergence

64

7

2

Divergence and curl in terms of the “del” operator.  Geometrical interpretation of the divergence and curl of a vector field. A vector field is conservative if and only if its curl is zero.

65

7

2

More on the geometrical interpretation of curl and divergence

3

Green’s theorems for both circulation and flux.  Examples

66

7

4

Stokes’ Theorem.  Examples

67

7

5

The Divergence Theorem of Gauss – begin with review of Green’s theorem for flux.

68

7

6,7

Semester Review

Comprehensive Final Exam