Calculus 3

Syllabus

handouts videos syllabus pdf flier photographs

Office Hours

Office hours are by appointment: email me and we will find a time for us to meet. I will be glad to answer all of your questions about the course material, go over some problems together with you, check your assignment work, review together for an exam, or discuss any course content you may have questions about.

Textbook

No texbook required. Handouts with course material and practice problems and review sheets are on this website.

Technology

All students are required to have a graphing calculator.

Topics Covered

1. Three Dimensional Coordinate System. Introduction to Surfaces in Space
2. Vectors. The Dot and Cross Products
3. Equations of Lines and Planes
4. Space Curves. Tangent lines. Arc Length
5. Partial Derivatives
6. Tangent Planes. Gradient Vector. Linear Approximations
7. Partial Derivatives. Chain Rule
(Exam 1)

8. Maximum and Minimum Values
9. Lagrange Multipliers
10. Double Integrals. Double Integrals in Polar Coordinates
11. Surface Area. Applications
(Exam 2)

12. Parametric Surfaces
13. Triple Integrals. Substitution in Triple Integrals
14. Line Integrals
15. Fundamental Theorem.
16. Green's Theorem. Curl and Divergence
(Exam 3)

17. Sequences. Series
18. Convergence of Series and Convergence Tests
19. Power Series
20. Taylor Series

(Final Exam)

Tentative exam dates

Exam 1: During the 4th week of classes
Exam 2: During the 7th week of classes
Exam 3: During the 11th week of classes
Final Exam: During the Finals week.

Grading

Exams 1, 2 and 318% each
Final Exam24%
Assignments11%
Projects/Presentation11%
TOTAL100%
Grades are computed according to the following system:
A A- B+ B B- C+ C C- D+ D F
grade 93-100 90-92 87-89 83-86 80-82 77-79 73-76 70-72 67-69 60-66 0-59

Number of credits

4

Prerequisites

Calculus 2.

Attendance

It is important that students attend classes. Students are responsible for all material covered in class, even if attendance is not checked or assignments collected.
Recordings of the lectures are available on my website. To stay on track, it is highly recommended that students attend the classes and use the recordings just for reference.

Exams

There will be three semester exams and a cumulative final exam. No makeup exam will be given unless the excuse for missing the scheduled exam is acceptable to the instructor. Any makeup exam must be taken before the next regularly scheduled exam. No exam grade will be dropped.

Assignments and Projects

There will be four assignments and two Matlab projects during the semester. There will be no makeup assignments. Assignments turned in after their due date will receive an automatic reduction in grade. No assignment, project or exam grade will be dropped.

Course Objectives

  • Students will obtain a well rounded introduction to the area of multivariable function calculus and number and power series.
  • Students will further develop problem solving techniques required for successful application of mathematics obtained in previous calculus courses.
  • Students will competently use appropriate technology to model data, implement mathematical algorithms and solve mathematical problems.

Learning outcomes

  • Students will demonstrate knowledge of the analytical methods used within a specific mathematical field, and distinguish between effective and faulty reasoning.
  • Students will formulate problems, obtain their solutions, and be familiar with modeling techniques required for successful application of mathematics to a variety of fields.
  • Students will develop an understanding of multivariable function calculus and number and power series.
  • Students will be able to differentiate and integrate multivariable functions and use multivariable calculus in problem solving.
  • Students will develop an understanding of and proficiency in using mathematical software and appropriate technology.

Academic integrity

Saint Joseph's University encourages the free and open pursuit of knowledge; we consider this to be a fundamental principle and strength of a democratic people. To this end, SJU expects its students, its faculty, its administrators, and its staff to uphold the highest standards of academic integrity. The University expects all members of the University community to both honor and protect one another's individual and collective rights.

Student with Disabilities Statement

Reasonable accommodations are provided to eligible students by the Office Student Disability Services (SDS). For more information, please contact SDS at sds@sju.edu or 610.660.1774, or visit the website at www.sju.edu/sds.

Statement on AI use

The assignments in this course should be completed without any use of artificial intelligence platforms. Note that students will not have access to such platforms on in-class exams.