# Calculus 3

### Syllabus

handouts videos syllabus pdf flier photographs

## Office Hours

Office hours for Spring 2023 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.

 Exams 1, 2 and 3 18% each Final Exam 24% Assignments 11% Projects/Presentation 11% TOTAL 100%
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

4

Calculus 2.

## Attendance

It is imperative that students attend all classes. Students are responsible for all material covered in class, even if attendance is not checked or assignments collected.

## 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.

## Response time

The assignments, projects and exams are typically graded in three days after they are turned in. Special circumstances like snow days, school closing or holidays, may occasionally delay the response time. Barring special circumstances, students’ emails are usually responded to within one working day.

## Course Objectives

• Obtain a well rounded introduction to the area of multivariable function calculus and number and power series.
• Deepen students' knowledge of problem formulation and problem solving techniques required for successful application of mathematics obtained in previous calculus courses.
• Competently use appropriate technology to model data, implement mathematical algorithms and solve mathematical problems.
• Cultivate the analytical skills required for the efficient use and understanding of mathematics.

## Learning outcomes

Students will:
• demonstrate proficiency in multivariable function calculus and number and power series,
• be able to differentiate and integrate multivariable functions,
• be able to use multivariable calculus in problem solving,
• demonstrate proficiency in using mathematical software,
• know how to use appropriate technology to solve problems applying calculus techniques.