Southern Utah University

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Southern Utah University
Southern Utah University
Fall Semester 2025

Calculus III (Face-to-Face)

MATH 2210-01

Course: MATH 2210-01
Credits: 4
Term: Fall Semester 2025
Department: MATH
CRN: 31665

Course Description

Vectors in two and three-dimensional space, quadric surfaces, cylindrical and spherical coordinates, calculus of vector-valued functions, partial derivatives and the gradient, limits and continuity of functions of several variables, vector fields and line integrals, multiple integrals and evaluation theorems. (Fall, Spring, Summer) [Graded (Standard Letter)] Prerequisite(s): MATH 1220 or adequate test score - Prerequisite Min. Grade: C, P Prerequisite Test: AP Calculus B/C - Prerequisite Test Score: 5 Registration Restriction(s): None

Required Texts

Calculus: Eartly Transcendentals, by James Stewart, Daniel Clegg and Saleem Watson (9th edition), Cengage Learning, ISBN   978-1337613927

Learning Outcomes

Students should improve in the following university Essential Learning Outcomes: Quantitative Literacy, Problem Solving. Additionally, students should improve in the following course-specific content areas:

1) Three-space, distance, and spheres; vectors, work and torque; lines, planes, and quadric surfaces.

2) Space curves, vector-valued functions and their calculus; position, velocity and acceleration.

3) Multivariable functions and level curves, limits, continuity, and partial derivatives; the gradient, tangent planes, steepest ascent/descent; optimization and Lagrange multipliers.
 4) Multiple integrals in two- and three-spaces and in polar, cylindrical, and spherical coordinates; volumes and centers of mass; the Jacobian and change of variables.

5) Vector fields, line integrals, work, divergence and curl; conservative vector fields and the fundamental theorem of line integrals; Green's theorem.

6) Parametric surfaces, area, and surface integrals; flux of a vector field through a surface.

7) Finding work by Stokes' theorem and flux using the divergence theorem.

Course Requirements

Students are expected to be present in class regularly.  Students are to complete weekly homework, a weekly quiz, three midterm exams and a final exam. 

Course Outline

The following is tentative and subject to change. 
| Week 1   | ·       Three Dimensional Coordinates o   Rectangular coordinates in three space o   Measuring distance o   Equations of spheres ·       Vectors in Two and Three Dimensions o   Geometry of sums and differences of vectors o   Algebraic properties of vector arithmetic
 | Week 2 | ·       Vector Dot and Cross Products o   Angles between vectors o   Parallel and perpendicular vectors o   Vector projections o   Applications ·       Lines and Planes in Three Space o   Parametric equations for lines o   Cartesian equations of planes o   Angles between planes and parallel planes o   Distances between points, lines and planes
| Week 3 | ·       Quadric Surfaces in Three Space o   Generalized cylinders o   Cartesian equations for ellipsoids, cones, paraboloids and hyperboloids ·       Vector Valued Functions and Space Curves o   Parametric equations for curves in three space o   Limits and continuity of vector valued functions
| Week 4 | ·       Derivatives and Integrals of Vector Functions o   Tangent lines and tangent vectors to parametric curves in three space o   Product rule and chain rule for derivatives o   Velocity and acceleration of vector valued functions o   Definite integrals of vector valued functions ·       Differential Geometry of Space Curves o   Arc length and curvature 
| Week 5 | ·       Functions of Several Variables o   Domain, range, graphs o   Level sets/contours o   Limits and continuity ·       Partial Derivatives o   Definitions and notation o   Geometric meaning o   Higher order derivatives
| Week 6 | ·       Tangent Planes and Linear Approximations ·       Chain Rule o   Derivatives of compositions of multivariable functions, vector valued functions, and multivariable vector valued functions o   Implicit differentiation in two and three variables ·       Gradient Vectors o   Directional derivatives of functions of two and three variables o   Tangent spaces to level sets of multivariable functions
| Week 7 | ·       Computing Extreme Values of Functions of Two Variables Using First and Second Order Partial Derivatives. ·       Optimization of Multivariable Functions Under Restraints Using the Method of Lagrange Multipliers
| Week 8 | ·       Double Integrals Over Rectangles and General Regions o   Double Riemann sums o   Midpoint rule for double integrals o   Iterated integrals and Fubini’s theorem o   Determining bounds of integration o   Changing the order of integration o   Average value of a function of two variables
| Week 9  | ·       Double Integrals in Polar Coordinates o   Polar rectangles o   Change of variables formula ·       Applications of Double Integrals o   Area o   Volume o   Surface area o   Center of mass o   Probability and expected value
 | Week 10 | ·       Triple Integrals o   Cartesian coordinates o   Cylindrical coordinates o   Spherical coordinates o   Linear change of variables
| Week 11 | ·       Vector Fields o   Motivating examples (gravitational fields, electric fields, force fields) o   Conservative vector fields and potential functions o   Gradient fields ·       Line Integrals o   Integrating functions of two or three variables along curves with respect to a coordinate variable or arc length o   Integrating vector fields in two and three space along curves. o   Fundamental theorem of line integrals ·       Green’s Theorem o   Oriented curves o   Simple regions o   Annular regions
| Week 12 | ·       Curl and divergence of vector fields o   Relation between curl and conservative vector fields o   Incompressible vector fields o   Vector forms of Green’s theorem ·       Parametric Surfaces o   Parametric equations of surfaces o   Grid curves o   Surfaces of revolution o   Tangent planes o   Surface area
| Week 13 | ·       Surface Integrals o   Oriented surfaces o   Integrals over surfaces defined parametrically and as the graph of a function o   Integrals of vector fields on oriented surfaces o   Flux
| Week 14 | ·       Stokes’s Theorem o   A fundamental theorem for integrals of vector fields on oriented surfaces ·       Divergence Theorem o   A fundamental theorem for integrals of vector fields on solid regions of three space
 

Instructor's policies on late assignments and/or makeup work

 Not accepted except in cases of school sponsored activities (e.g. sports teams), or emergent circumstances out of the student's control, or if an agreement has been made with the instructor in advance.  Two quiz scores are dropped at the end of the semester, and the reason for this is that sometimes you just don't want to be in class because you have a family vacation or a camping trip or similar that you'd rather be doing; these do not count as excused absences for the purpose of accepting late work, so please don't ask.  

There is no flexibility whatever regarding the time you take the final exam except in cases of extreme circumstances (e.g. medical emergencies, car crash on the way to school).  This does NOT include things like you have plane tickets for the day before to go home for Winter break or Summer break.

Attendance Policy

Attendance is expected and not formally recorded.

Course Fees

$5

ADA Statement

Students with medical, psychological, learning, or other disabilities desiring academic adjustments, accommodations, or auxiliary aids will need to contact the Disability Resource Center, located in Room 206F of the Sharwan Smith Center or by phone at (435) 865-8042. The Disability Resource Center determines eligibility for and authorizes the provision of services.

If your instructor requires attendance, you may need to seek an ADA accommodation to request an exception to this attendance policy. Please contact the Disability Resource Center to determine what, if any, ADA accommodations are reasonable and appropriate.

Academic Credit

According to the federal definition of a Carnegie credit hour: A credit hour of work is the equivalent of approximately 60 minutes of class time or independent study work. A minimum of 45 hours of work by each student is required for each unit of credit. Credit is earned only when course requirements are met. One (1) credit hour is equivalent to 15 contact hours of lecture, discussion, testing, evaluation, or seminar, as well as 30 hours of student homework. An equivalent amount of work is expected for laboratory work, internships, practica, studio, and other academic work leading to the awarding of credit hours. Credit granted for individual courses, labs, or studio classes ranges from 0.5 to 15 credit hours per semester.

Academic Freedom

SUU is operated for the common good of the greater community it serves. The common good depends upon the free search for truth and its free exposition. Academic Freedom is the right of faculty to study, discuss, investigate, teach, and publish. Academic Freedom is essential to these purposes and applies to both teaching and research.

Academic Freedom in the realm of teaching is fundamental for the protection of the rights of the faculty member and of you, the student, with respect to the free pursuit of learning and discovery. Faculty members possess the right to full freedom in the classroom in discussing their subjects. They may present any controversial material relevant to their courses and their intended learning outcomes, but they shall take care not to introduce into their teaching controversial materials which have no relation to the subject being taught or the intended learning outcomes for the course.

As such, students enrolled in any course at SUU may encounter topics, perspectives, and ideas that are unfamiliar or controversial, with the educational intent of providing a meaningful learning environment that fosters your growth and development. These parameters related to Academic Freedom are included in SUU Policy 6.6.

Academic Misconduct

Scholastic honesty is expected of all students. Dishonesty will not be tolerated and will be prosecuted to the fullest extent (see SUU Policy 6.33). You are expected to have read and understood the current SUU student conduct code (SUU Policy 11.2) regarding student responsibilities and rights, the intellectual property policy (SUU Policy 5.52), information about procedures, and what constitutes acceptable behavior.

Please Note: The use of websites or services that sell essays is a violation of these policies; likewise, the use of websites or services that provide answers to assignments, quizzes, or tests is also a violation of these policies. Regarding the use of Generative Artificial Intelligence (AI), you should check with your individual course instructor.

Emergency Management Statement

In case of an emergency, the University's Emergency Notification System (ENS) will be activated. Students are encouraged to maintain updated contact information using the link on the homepage of the mySUU portal. In addition, students are encouraged to familiarize themselves with the Emergency Response Protocols posted in each classroom. Detailed information about the University's emergency management plan can be found at https://www.suu.edu/emergency.

HEOA Compliance Statement

For a full set of Higher Education Opportunity Act (HEOA) compliance statements, please visit https://www.suu.edu/heoa. The sharing of copyrighted material through peer-to-peer (P2P) file sharing, except as provided under U.S. copyright law, is prohibited by law; additional information can be found at https://my.suu.edu/help/article/1096/heoa-compliance-plan.

You are also expected to comply with policies regarding intellectual property (SUU Policy 5.52) and copyright (SUU Policy 5.54).

Mandatory Reporting

University policy (SUU Policy 5.60) requires instructors to report disclosures received from students that indicate they have been subjected to sexual misconduct/harassment. The University defines sexual harassment consistent with Federal Regulations (34 C.F.R. Part 106, Subpart D) to include quid pro quo, hostile environment harassment, sexual assault, dating violence, domestic violence, and stalking. When students communicate this information to an instructor in-person, by email, or within writing assignments, the instructor will report that to the Title IX Coordinator to ensure students receive support from the Title IX Office. A reporting form is available at https://cm.maxient.com/reportingform.php?SouthernUtahUniv

Non-Discrimination Statement

SUU is committed to fostering an inclusive community of lifelong learners and believes our university's encompassing of different views, beliefs, and identities makes us stronger, more innovative, and better prepared for the global society.

SUU does not discriminate on the basis of race, religion, color, national origin, citizenship, sex (including sex discrimination and sexual harassment), sexual orientation, gender identity, age, ancestry, disability status, pregnancy, pregnancy-related conditions, genetic information, military status, veteran status, or other bases protected by applicable law in employment, treatment, admission, access to educational programs and activities, or other University benefits or services.

SUU strives to cultivate a campus environment that encourages freedom of expression from diverse viewpoints. We encourage all to dialogue within a spirit of respect, civility, and decency.

For additional information on non-discrimination, please see SUU Policy 5.27 and/or visit https://www.suu.edu/nondiscrimination.

Pregnancy

Students who are or become pregnant during this course may receive reasonable modifications to facilitate continued access and participation in the course. Pregnancy and related conditions are broadly defined to include pregnancy, childbirth, termination of pregnancy, lactation, related medical conditions, and recovery. To obtain reasonable modifications, please make a request to title9@suu.edu. To learn more visit: https://www.suu.edu/titleix/pregnancy.html.

Disclaimer Statement

Information contained in this syllabus, other than the grading, late assignments, makeup work, and attendance policies, may be subject to change with advance notice, as deemed appropriate by the instructor.