Independent Study--decided each semester
This course is an introduction to vector calculus as well as application of differentiation and integration to functions of several variables. Topics include partial derivatives, directional derivatives, motion in space, line integrals, and multiple integration. IAI: MTH 903 Mathematics. IAI: M1 900-3.
MATH 2524 with a grade of C or better - Must be completed prior to taking this course.
Course Alignment
General Education Outcomes are the knowledge, skills, abilities, attitudes, and behaviors that students are expected to develop as a result of their overall experiences with any aspect of the college, including courses, programs, and student services, both inside and outside of the classroom. The General Education Outcomes specifically learned in this course are:
- Critical Thinking
Calculus 3 is a continuation of calculus topics from the previous two courses and will also be connected to physics, engineering, chemistry, and other STEM topics and courses.
Faculty Contact Information
12-1 MWF
Email is the best way to get hold of me: aharwood@kcc.edu
Course Information
At the end of this course, students will be able to:
- Use the mathematics of vectors to find directed derivatives, arc length, and curvature, and apply them to applications in physics.
- Solve problems involving partial derivatives using, but not limited to, chain rules and differentials
- Evaluate multiple integrals in rectangular, polar, and spherical coordinates
- Use line integrals in applications in areas of vector fields.
- Parametric Equations
- Polar Coordinate System
- Calculus of Polar Functions
- Conic Sections
- Lines and Curves in Space
- Calculus of Vector-Valued Functions
- Motion in Space
- Lengths of Curves
- Curvature and Normal Vectors
- Planes and Surfaces
- Graphs and Level Curves
- Limits and Continuity
- Partial Derivatives
- The Chain Rule
- Directional Derivatives and the Gradient
- Maximum/Minimum Problems
- Lagrange Multipliers
- Double Integrals over Rectangular Regions
- Double Integrals over General Regions
- Double Integrals in Polar Coordinates
- Triple Integrals
- Triple Integrals in Cylindrical and Spherical Coordinates
- Integrals in Mass Calculations
- Vector Fields
- Line Integrals
- Conservative Vector Fields
- Green's Theorem
- Divergence and Curl
- Surface Integrals
- Stokes' Theorem
- Divergence Theorem
Calculus Early Transcendentals 3rd Edition (optional) Briggs, Cochran, Gillett and Schulz. Pearson Publishing.
The same text is used for the entire Calculus sequence.
MyMathLab access code--includes e-text, included with tuition for this course
Graphing Calculator—TI-84 preferred (Available to borrow for free from the library)
Homework
Homework is an essential part of any math class. The homework for this class will be given via MyMathLab. Each section of homework is worth 5 points. You may attempt each homework problem an unlimited amount of times with only the highest of the scores counting towards your grade (additional practice is also available). When you registered for this course, you were enrolled in the MyMathLab course.
There may also be homework that will be turned in on paper. Points for these will be determined as the class progresses. These may be done in groups, but each person should be responsible for their own work and everyone will be required to turn in their own papers.
Quizzes
There will be numerous quizzes given throughout the semester. The quizzes will be given in class and the lowest quiz score will be dropped at the end of the semester. Each student can make up one quiz per semester, but notification to your professor ahead of time is required.
Final Exam
There will be a comprehensive final exam given the 17th week of the semester. There are no makeup opportunities for the final exam. The final exam represents 20% of your final grade.
Grading Scale by percentage
90-100 A
80-89 B
70-79 C
60-69 D
Below 60 F
Liberal Arts & Sciences
Dean, Jennifer Huggins; 815-802-8484; R310; jhuggins@kcc.edu; Division Office- W102; 815-802-8700
Attendance
Attendance is mandatory. To be successful in this course, a student must attend class every day. You are responsible for work missed due to absence. There will be no distinction between “excused” and “unexcused” absences. Attendance will not be counted for a grade, but will factor into your overall success in the class.
**Note: Math can be taught in the classroom, but can only be learned through practice, critical thinking, and more practice. Please ask questions to help further your understanding, either in class or during office hours. Calculus requires your knowledge of algebraic procedures but also creative, critical thinking that needs to be developed. You are expected to be in attendance all semester.
Cell Phones, Other Distractions
Please refrain from using cell phones for calls, texting, etc… while in class. If it is an emergency, please leave the classroom. Using cell phones or other electronic devices on or during the taking of tests/quizzes will be considered cheating and will be subject to the guidelines below.
Cheating/Plagiarizing
Students found cheating on any assessments will earn a grade of zero on the assessment after the first occurrence and a grade of F for the entire course after the second occurrence. Using AI tools, such as ChatGPT and photomath, will be considered cheating.
Calculator Usage
Graphing calculators will be required throughout this course, except on specific items chosen by your instructor. You cannot share calculators during quizzes or exams. More specific instructions about allowed calculators will be given in class.
Integrity and Respect for everyone involved in the course is expected. If you have any questions about expectations, please let your professor know.
Week 1 | 12.1 Parametric Equations 12.2 Polar Coordinates |
2 | 12.3 Calculus in Polar Coordinates 12.4 Conic Sections (hand-out only) 13.3 The Dot Product |
3 | 13.4 The Cross Product 13.5 Lines and Planes in Space 13.6 Cylinders and Quadric Surfaces |
4 | 14.1 Vector-Valued Functions 14.2 Calculus of Vector-Valued Functions 14.3 Motion in Space 14.4 Length of Curves |
5 | 14.5 Curvature and Normal Vectors |
6 | 15.1 Graphs and Level Curves 15.2 Limits and Continuity (Introduction only) 15.3 Partial Derivatives 15.4 The Chain Rule |
7 | 15.5 Directional Derivatives and the Gradient 15.6 Tangent Planes and Linear Approximation |
8 | 15.7 Maximum/Minimum Problems 15.8 Lagrange Multipliers |
9 | 16.1 Double Integrals over Rectangular Regions 16.2 Double Integrals over General Regions |
10 | 16.3 Double Integrals in Polar Coordinates 16.4 Triple Integrals |
11 | 16.5 Triple Integrals in Cylindrical and Spherical Coordinates 16.6 Integrals for Mass Calculations |
12 | 17.1 Vector Fields 17.2 Line Integrals |
13 | 17.2 Line Integrals 17.3 Conservative Vector Fields |
14 | 17.4 Green’s Theorem 17.5 Divergence and Curl |
15 | 17.6 Surface Integrals |
16 | 17.7 Stokes’ Theorem 17.8 Divergence Theorem |
17 | Final Exam |
College Policies, Resources and Supports
For information related to the Student Code of Conduct Policy, Withdrawal Policy, Email Policy, and Non- Attendance/Non-Participation Policy, please review the college’s Code of Campus Affairs and Regulations webpage, which can be found at catalog.kcc.edu under the Academic Regulations & Conduct Guide.
KCC offers various academic and personal resources for all students. Many services are offered virtually, as well as in person. Please visit Student Resources - Kankakee Community College to access student resources services such as:
- Clubs and organizations
- Counseling and referral services
- Office of disability services
- Student complaint policy
- Transfer services
- Tutoring services, etc.
The materials on this course are only for the use of students enrolled in this course for purposes associated with this course. Further information regarding KCC's copyright policy is available at https://kcc.libguides.com/copyright.
|Course syllabus/calendar is subject to change.