Course Syllabus

Arapahoe Community College

Calculus III with Engineering Applications, Fall 2025

MAT2431 - 5 credits

 

Instructor Information

Instructor’s Name:

Karen Bukowski

Instructor’s email:

karen.bukowski@dcsdk12.org

I typically reply to emails within 24-48 hours, excluding weekends and holidays.

 

Instructor’s Location:

Room 9500 during Period 4

Instructor’s Office Hours:

Room 9500 during Access. 

Course Information

Course Start Date:

Thursday 14 August 2025

Course End Date:

Friday 19 December 2025

Course Meeting Times and Location:

Room 9500 during Period 4.

Last Day to Apply to ACC:

XX August 2025.  Final day for CE students taking courses at a high school to apply to ACC.

Last Day to Drop the Class – Census Date: XX September 2025.

Students must satisfy one of the following prior to the census date or will be dropped as a “no-show”.

  • Attend class OR
  • Complete an academic, graded assignment.

Registering for MyOpenMath does not count as an academic assignment.

If you drop or are dropped from a class before the census date you are not responsible for payment, and you will not lose College Opportunity Fund (COF) credits. Additionally, a dropped course will not be visible on your permanent student record.  If you have financial aid, dropping or being dropped from a class can affect your financial aid.  It is recommended that you consult with your financial aid advisor.

Withdraw Date: XX November 2025

You can withdraw between the drop and withdrawal dates without affecting your grade point average. However, if you withdraw from a course you will be responsible for full payment and you will lose COF credits.  If you have financial aid, you should consult a financial aid advisor before withdrawing from a course. If you decide to withdraw from a course for any reason, it is recommended that you speak to your advisor about your withdrawal options.

Course Description:

This course focuses on the traditional subject matter of multivariable Calculus. Topics include vectors, vector-valued functions, partial derivatives, analytic geometry, multiple integrals, line integrals, and applications. This course is a Statewide Guaranteed Transfer course in the GT-MA1 category.

Course Prerequisites/Co-requisites:

  • MAT 2420, Calculus II with a grade of "C" or better, OR
  • AP CALC BC exam score of a 4 or better.

Textbook:

Great news: your textbook for this class is available for free online!
Calculus, Volume 3 from OpenStaxLinks to an external site., ISBN 1-947172-16-6

You have several options to obtain this book:

You can use whichever formats you want. Web view is recommended -- the responsive design works seamlessly on any device.

Homework:

We will be using MyOpenMath as our homework platform.

To access the platform, go to myopenmath.com. 

The course name is: MAT 2430 2431 Fall 2025 RCHS

The enrollment key is: MAT2431RCHS25

Required Course Materials:

Calculator

  • A graphing calculator is required.
  • A TI-89 graphing calculator is recommended.
  • Graphing calculators may be borrowed for the year through the Learning Commons. E-mail me directly if you need to check out a calculator for the year.
  • A TI-84se or a TI-Inspire are also quite adequate for the course.

 Coursework:  

  1. Homework/Classwork/Review – 10%: Graded homework is completed in MyOpenMath and is a required component of the class. There is a homework section for each lesson. It is to your benefit to complete all homework, check your answers, and get help if you don’t understand a problem. Check the course calendar and Friday Assignment listings for homework due dates.
  1. Quizzes – 20%: There will be twelve quizzes. These quizzes will be on paper and given during class. Forty-five minutes of class time is permitted for each quiz. If you miss a quiz due to absence, you will be given the quiz during the next class meeting period. You may make quiz corrections.  You will be given back ½ of the points that you missed on the quiz.  Quiz corrections are due within one week of quiz returns.

Quiz dates for Fall 2024 will be:

  • Quiz 1: 22 August
  • Quiz 2: 25 August
  • Quiz 3: 05 September
  • Quiz 4: 19 September
  • Quiz 5: 06 October
  • Quiz 6: 06 October
  • Quiz 7: 24 October
  • Quiz 8: 31 October
  • Quiz 9: 03 November
  • Quiz 10: 14 November
  • Quiz 11: 21 November
  • Quiz 12: 08 December
  1. Projects – 10%: There will be two projects to be completed in this class.
  • Project 1: Crocheting Hyperbolic Paraboloids.
  • Project 2: TBD.

Project due dates TBD.

  1. Tests – 50%: We will have four in class tests. Your lowest test score will be automatically dropped. If you miss a test due to absence, you will be given the makeup test during the next class meeting period.  Clear your calendar for the testing dates listed below.  In college/university there are no makeup tests.  Look at the dates below and clear your calendar.  Testing dates for Fall 2025 will be:
  • Test 1: 08 September - Chapters 2 & 3
  • Test 2: 08 October - Chapter 4
  • Test 3: 05 November - Chapter 5
  • Test 4: 10 December - Chapter 6

If you choose not to take a test, it will be used as your dropped test. 

  1. Final Exam – 10%:

The ACC Created Department Final Exam will be cumulative and taken during RCHS Finals week. This final is the same for all students taking MAT2431.  Your final will be given on 16 December 2025 during the Period 4 Final time slot.

Grading Scheme:

  • Your grade is a weighted grade with the percentage distribution listed below.

Category

%

HW/CW/Review

10

Quizzes

20

Projects

10

Tests

50

Final Exam

10

 

  • I will use the DCSD 10-point grading scale listed below.

 

Letter Grade

     %

A

90 - 100

B

80 - 89

C

70 - 79

D

60 - 69

F

00 - 59

Make-up/Late Work Policies:

I do not accept late work.  Any missed quizzes and/or tests must be taken during the next class meeting. Homework is due by midnight on the Friday listed on the syllabus and on Canvas

 

Attendance Policy:

Each class session will provide meaningful content and valuable interactions with your classmates.  For this reason, attendance is strongly recommended so that you can have the best possible learning experience. 

 

I do recognize that you may have other commitments and/or life happens resulting in a missed class. In this event, please email me or follow up with a classmate to be sure you know what material was covered and what announcements were made. You are still responsible for turning in any assignments that were due on a missed day and the material covered. Canvas is a great resource for material that has been covered in class.

 

ACC Student Learning Outcomes:

Preparing learners for life success is an important commitment at Arapahoe Community College.  These learning outcomes address the knowledge, skills, and values that are fundamental to the personal and professional growth of our students, employees and community.

1.             Communication

Construct, deliver, and engage in effective, knowledgeable communication for a variety of audiences and purposes.

2.             Information Management

Identify, retrieve and synthesize information in order to think critically, reason creatively and make informed judgments.

3.             Personal Development

Identify and continually develop one’s aptitudes and abilities in pursuit of goals.

4.             Responsibility and Accountability

Employ personal and social accountability, recognize ethical issues, practice ethical behavior, and balance personal freedom with the interest of the community.

5.             Quantitative Reasoning

Retrieve, interpret and evaluate information and numerical concepts to determine trends, make predictions, and develop informed opinions.

6.             Cultural Awareness

Identify, distinguish, or express a diversity of aesthetic, cultural, and historical perspectives.

Course Learning Outcomes:

After successful completion of this course the student should be able to:

Number

Course Learning Outcomes

1

Apply vector algebra to the geometry of space.

2

Analyze 2 and 3 dimensional curves given as vector valued functions using calculus techniques.

 

3

Examine surfaces/multivariable functions and their graphs using calculus techniques.

 

 

4

Construct multiple integrals for regions in the plane and space using rectangular, polar, cylindrical, and spherical coordinates to measure areas, volumes, and other applications.

5

Evaluate double and triple integrals.

 

6

Determine vector field properties.

7

Apply theorems of vector calculus, such as Fundamental Theorem of line integrals, Green’s Theorem, Stokes’ Theorem, and Divergence Theorem.

8

Apply multivariable Calculus techniques to engineering and physics problems.

 

Topical Outline:

  1. I) Apply vector algebra to the geometry of space
  2. a) Vector addition and subtraction, geometrically and algebraically
  3. b) Properties of Vectors in 2 and 3 dimensional space
  4. c) Dot product, cross product, and projection
  5. d) Applications of the dot and cross products
  6. e) Distances in 3-space

 

  1. II) Analyze 2 and 3 dimensional curves given as vector valued functions using calculus techniques
  2. a) Graph curves given in vector valued form
  3. b) Construct a vector valued function for a given curve
  4. c) Evaluate limits
  5. d) Determine continuity and smoothness
  6. e) Differentiate and integrate vector valued functions
  7. f) Parametric and symmetric forms of a line
  8. g) Find the unit tangent and unit normal vectors of a curve
  9. h) Examine applications of vector valued functions
  10. i) Find arc length and curvature
  11. j) Projectile motion

 

III) Examine surfaces/multivariable functions and their graphs using calculus techniques

  1. a) Graph cylinders and quadric surfaces
  2. b) Graphs of lines and planes in 3 dimensional space
  3. c) Graph cylindrical and spherical coordinates and surfaces

d)Construct level curves and level surfaces  

  1. e) Graph a surface given in parametric form
  2. f) Limits and continuity of surfaces
  3. g) Find the domain of surfaces/multivariable functions
  4. h) Evaluate limits using the definition and theorems
  5. i) Find partial derivatives and directional derivatives
  6. j) Use the chain rule
  7. k) Use implicit differentiation
  8. l) Differentials
  9. m) Find the gradient
  10. n) Find the tangent plane and normal line
  11. o) Optimization of surfaces using calculus
  12. p) Show differentiability of a multivariable function

 

  1. IV) Construct multiple integrals for regions in the plane and space using rectangular, polar, cylindrical, and spherical coordinates to measure areas, volumes, and other applications.
  2. a) Transform equations of surfaces between rectangular, cylindrical and spherical forms
  3. b) Transform double integrals between rectangular and polar
  4. c) Transform triple integrals between rectangular, cylindrical and spherical

 

  1. V) Evaluate double and triple integrals
  2. a) Evaluate iterated integrals
  3. b) Change the order of integration in a double or triple integral

 

  1. VI) Determine vector field properties
  2. a) Conservative vector fields
  3. b) Find curl
  4. c) Find divergence

 

VII) Apply theorems of vector calculus, such as Fundamental Theorem of Line Integrals, Green’s Theorem, Stokes’ Theorem, and Divergence Theorem.

  1. a) Evaluate a line integral
  2. b) Evaluate a line integral in a vector field
  3. c) Use the Fundamental Theorem of line integrals
  4. d) Use independence of path
  5. e) Use Green’s Theorem
  6. f) Use Stokes’ Theorem
  7. g) Use Divergence Theorem
  8. h) Evaluate a surface integral
  9. i) Evaluate a surface integral in a vector field
  10. j) Find work done in a vector field using theorems related to line integrals
  11. k) Find flux in a vector field using theorems related to surface integrals

 

VIII) Apply Multivariable Calculus Techniques to Engineering and Physics problems

  1. a) Use the Jacobian
  2. b) Lagrange Multipliers
  3. c) Find center of mass using iterated integrals
  4. d) Work (as a projection of a vector)
  5. e) Torque
  6. f) Static force system
  7. g) Moments of Inertia

Textbook Topical Outline

Chapter 2: Vectors and Vector-Valued Functions

2.1 Vectors in the Plane

2.2 Vectors in Three Dimensions

2.3 The Dot Products

2.4 The Cross Product

2.5 Equations of Lines and Planes in Space

2.6 Quadric Surfaces

2.7 Cylindrical and Spherical Surfaces

Chapter 3: Vector-Valued Functions

3.1 Vector-Valued Functions and Space Curves

3.2 Calculus of Vector Valued Functions

3.3 Arc Length and Curvature

3.4 Motion in Space

Chapter 4: Functions of Several Variables

4.1 Functions of Several Variables

4.2 Limits and Continuity

4.3 Partial Derivatives

4.4 Tangent Planes and Linear Approximation

4.5 The Chain Rule

4.6 Directional Derivatives and the Gradient

4.7 Maximum/Minimum Problems

4.8 Lagrange Multipliers

Chapter 5: Multiple Integration

5.1 Double Integrals over Rectangular Regions

5.2 Double Integrals over General Regions

5.3 Double Integrals in Polar Coordinates

5.4 Triple Integrals

5.5 Triple Integrals in Cylindrical and Spherical Coordinates

5.6 Calculating Centers of Mass and Moments of Inertia

5.7 Change of Variables in Multiple Integrals

Chapter 6: Vector Calculus

6.1 Vector Fields

6.2 Line Integrals

6.3 Conservative Vector Fields

6.4 Green’s Theorem

6.5 Divergence and Curl

6.6 Surface Integrals

6.7 Stokes’ Theorem

6.8 Divergence Theorem

GT Pathways Requirements

The Colorado Commission on Higher Education has approved MAT 2430/2431 for inclusion in the Guaranteed Transfer (GT) Pathways program in the GT-MA1 category.  For transferring students, successful completion with a minimum C‒ grade guarantees transfer and application of credit in this GT Pathways category. More information on the GT Pathways program.

 

Content Criteria for GT-MA1 Courses

Students should be able to:

  • Demonstrate good problem-solving habits, including:
    • Estimating solutions and recognizing unreasonable results.
    • Considering a variety of approaches to a given problem, and selecting one that is appropriate.
    • Interpreting solutions correctly.
  • Generate and interpret symbolic, graphical, numerical, and verbal (written or oral)

            representations of mathematical ideas.

  • Communicate mathematical ideas in written and/or oral form using appropriate mathematical

           language, notation, and style.

  • Apply mathematical concepts, procedures, and techniques appropriate to the course.
  • Recognize and apply patterns or mathematical structure.
  • Utilize and integrate appropriate technology.

 

Competencies and Student Learning Outcomes Associated with GT-MA1 Courses - GT Pathways Competency: Quantitative Literacy

Competency in quantitative literacy represents a student’s ability to use quantifiable information and mathematical analysis to make connections and draw conclusions. Students with strong quantitative literacy skills understand and can create sophisticated arguments supported by quantitative evidence and can clearly communicate those arguments in a variety of formats (using words, tables, graphs, mathematical equations, etc.).

1. Student Learning Outcome (SLO 1): Interpret Information

·               Explain information presented in mathematical forms (e.g., equations, graphs, diagrams,

           tables, words).

  1. Student Learning Outcome (SLO 2): Represent Information
  • Convert information into and between various mathematical forms (e.g., equations, graphs,

           diagrams, tables, words).

 

  1. Student Learning Outcome (SLO 3): Perform Calculations
  • Solve problems or equations at the appropriate course level.
  • Use appropriate mathematical notation.
  • Solve a variety of different problem types that involve a multi-step solution and address the

           validity of the results.

  1. Student Learning Outcome (SLO 4): Apply and Analyze Information
  • Make use of graphical objects (such as graphs of equations in two or three variables,

           histograms, scatterplots of bivariate data, geometrical figures, etc.) to supplement a solution to

           a typical problem at the appropriate level.

  • Formulate, organize, and articulate solutions to theoretical and application problems at the

           appropriate course level.

  • Make judgments based on mathematical analysis appropriate to the course level.
  1. Student Learning Outcome (SLO 5): Communicate using Mathematical Forms
  • Express mathematical analysis symbolically, graphically, and in written language that

           clarifies/justifies/summarizes reasoning (may also include oral communication).

 

Accommodations Statement

ACC provides accommodations to students with diagnosed or suspected disabilities that affect them in academic settings.  The Americans with Disabilities Act (ADA) defines a disability as a “physical or mental impairment that substantially limits one or more major life activity.” This may include learning, mobility, and/or cognitive disabilities; mental health conditions; temporary disabilities; and other physical and/or mental conditions. To protect student privacy, disability information is kept separate from academic records.

Students with accommodations are responsible for requesting their accommodation letter each semester and for knowing current accommodation policies and procedures.  Accommodations start when your instructor receives your accommodation letter and not before. It may take several days to create your accommodation letter, and some accommodations (testing, etc.) need to be requested at least 7 days in advance.  So please request accommodations early. Students and instructors are encouraged to have a conversation about accommodations and how they apply in each class. Please contact Disability Access Services (DAS, www.arapahoe.edu/das/) for more information. To request accommodations, please contact DAS at disability.access@arapahoe.edu or 303.797.5860.  Students can also schedule an intake appointment online through Navigate.

Statement of Academic Integrity

ACC is committed to academic honesty and scholarly integrity. The College can best function and accomplish its mission in an atmosphere of the highest ethical standards.  All members of the College community are expected and encouraged to contribute to such an environment by observing all accepted principles of academic honesty.  Academic dishonesty includes but is not limited to plagiarism, cheating, fabrication, grade tampering, misuse of computers and other electronic technology, and facilitating academic dishonesty. Those found in violation may be subject to academic consequences up to and including failure for the course and potential disciplinary sanctions under the Disciplinary Procedure (SP4-30). Students can find more information about the ACC Student Code of Conduct: Rights and Responsibilities Procedure (AP4-30a) or by contacting the Dean of Students Office at 303.797.5730, room M2720, or acc.dos@arapahoe.edu.

Plagiarism includes, but is not limited to:

  • "Taking and using the thoughts, writings, or ideas of another person or persons, and

            presenting any or all of them as one's own."  (Oxford English Dictionary) 

  • Submitting examinations, web-based materials, or other material as one's own work when

           such work has been prepared by another person or copied from another person (including   

           electronic media sources).

  • Handing in the same paper or work in more than one class.

 

Classroom Community and Mutual Respect

This classroom is a safe space for learning and is an academic environment; you should expect to have your ideas, work, and arguments respectfully challenged. Our population is a variety of students with a great diversity of beliefs, and the class must be respectful of all members. It is encouraged for all students to collaborate on homework, but students are still required to turn in their own work. When participating in any online or written actions, it is expected that all students will use respectful, appropriate, and academic language. When providing feedback to peers, students are expected to do so in a constructive and respectful manner.

 

 

Schedule of Class Assignments:

We may cover more or less material each day but this will give you a guideline.  I reserve the right to change the calendar as needed.

 

MAT2431: CALCULUS III

FALL 2025 PERIOD 4 – BLACK DAY

 

 

MAT2431

CALCULUS III SECTION

MyOpenMath

Homework Assignment

FRIDAY DUE DATES

DAY

DATE

COURSE CONTENT COVERED

HW ASSIGNMENT DUE DATES

01*

14 Aug*

Introduction

 

02*

15 Aug*

2.1: Vectors in the Plane

2.2: Vectors in Three Dimensions

NONE

03

18 Aug

2.3: The Dot Product

2.4: the Cross Product

 

04

20 Aug

2.5: Equations of Lines and Planes in Space

 

05

22 Aug*

Quiz #1: Covering 2.1 – 2.3

2.1 & 2.2

06

25 Aug

Quiz #2: Covering 2.4 – 2.5

3.1: Vector-Valued Functions and Space Curves

 

07

27 Aug

3.2: Calculus of Vector -Valued Functions

 

08

29 Aug*

3.3: Arc Length and Curvature

2.3 & 2.4 & 2.5

09

03 Sept

3.4: Motion in Space

 

10

05 Sept

Quiz #3: 3.1 – 3.4

Review 1

3.1 & 3.2 & 3.3

11

08 Sept

Test 1

 

12

10 Sept

2.6: Quadric Surfaces

4.1: Functions of Several Variables

 

13

12 Sept*

4.2: Limits and Continuity

3.4 & Review 1

14

15 Sept

4.3: Partial Derivatives

 

15

17 Sept

4.4: Tangent Planes and Linear Approximations

 

16

19 Sept*

Quiz #4: Covering 4.1 – 4.3

2.6 & 4.1

17

24 Sept

4.5: The Chain Rule

 

18

26 Sept*

4.6: Directional Derivatives and the Gradient

4.3 & 4.4

19

29 Sept

4.7: Maxima/Minima Problems

 

20

01 Oct

4.8: Lagrange Multipliers

 

21

03 Oct*

Review 2

4.5 & 4.6

22

06 Oct

Quiz #5: Covering 4.4 – 4.5

Quiz #6: Covering 4.6 – 4.8

 

23

08 Oct

Test 2

 

24

10 Oct*

5.1: Double Integrals over Rectangular Regions

5.2: Double Integrals over General Regions

4.7 & 4.8 & Review 2

 

 

 

FALL BREAK

17 Oct: 5.1 & 5.2

25

20 Oct

5.3: Double Integrals in Polar Coordinates

5.4: Triple Integrals

 

26

22 Oct

2.7: Cylindrical and Spherical Coordinates

5.5: Triple Integrals in Cylindrical and

        Spherical Coordinates

 

27

24 Oct*

Quiz #7: Covering 5.1 – 5.3

 

NONE

28

27 Oct

5.6: Calculating Centers of Mass and       Moments of Inertia

 

29

29 Oct

5.7: Change of Variables in Multiple Integrals

 

30

31 Oct*

Quiz #8: Covering 5.4 – 5.5

5.3 & 5.4 & 2.7 & 5.5

31

03 Nov

Quiz #9: Covering 5.6 – 5.7

Review 3

 

32

05 Nov

Test 3

 

33

07 Nov*

6.1: Vector Fields

6.2: Line Integrals

5.6 & 5.7

34

10 Nov

6.3: Conservative Vector Fields

 

35

12 Nov

6.4: Green’s Theorem

 

36

14 Nov*

Quiz #10: Covering 6.1 – 6.4

Review 3 & 6.1 & 6.2

37

17 Nov

6.5: Divergence and Curl

 

38

19 Nov

6.6: Surface Integrals

 

39

21 Nov*

QUIZ #11: Covering 6.5 – 6.6

6.3 & 6.4

 

 

THANKSGIVING BREAK

28 Nov: 6.5 & 6.6

40

01 Dec

6.7: Stokes’ Theorem

 

41

03 Dec

6.8: The Divergence Theorem

 

42

05 Dec*

Review for the FINAL

6.7 & 6.8

43

08 Dec

Quiz #12: Covering 6.7 – 6.8

Review 4

 

44

10 Dec

Test 4

 

45

12 Dec*

Review for the FINAL

Review 4

46

16 Dec

MAT 2431 FINAL

 

 

* DENOTES AN ALL DAY

 

Student Syllabus Confirmation and Agreement

 

Rock Canyon High School Concurrent Enrollment with

Arapahoe Community College

 

Course: MAT 2431 Fall 2025

 

 

 

Initial the box indicating you have read, understood, and have agreed to each line item.

1

I understand what types of assignments will be completed throughout the course.

2

I understand how assignments will be submitted and graded.

3

I have reviewed the course schedule and made note of important dates, such as homework, quiz, test, and final exam dates

4

I am aware of what online materials are required for the course, AND I know where and how to access them.

5

I understand the technology requirements for the course.

6

I understand that there are technology skills needed for this course, and it is my responsibility to get support on any prerequisite technology skills.

7

I have visited the Math Support Center website for information on math tutoring.

 

8

I know how to log into MyACC and Canvas

9

I acknowledge that all email communication between me and my instructor must be done through my RCHS student email address.

10

I have emailed any disability accommodations to my instructor if applicable.

 

 

 

 

Student Printed Name: __________________________________________________

 

 

 

Student Signature: ______________________________________ Date: __________