# Calculus III: Multivariable Calculus and Geometry

Universidad Antonio de Nebrija

## Course Description

• ### Course Name

Calculus III: Multivariable Calculus and Geometry

• ### Host University

Universidad Antonio de Nebrija

• ### Area of Study

Calculus, Mathematics

• ### Language Level

Taught In English

### Hours & Credits

• Contact Hours

45
• Recommended U.S. Semester Credits
3
• Recommended U.S. Quarter Units
4

## Calculus III: Multivariable Calculus and Geometry

Hours: 45

Prerequisites: basic calculus and algebra

Instructor name:

E-mail: @nebrija.es

Office hours: to be communicated the first day of class

1. Course Description

A standard third course in calculus. Topics include polar coordinates and polar curves; vectors and analytical geometry in three dimensions; vector-valued functions and curvature; components of acceleration; functions of several variables; limits and continuity in three-space; partial and directional derivatives; gradients, tangent planes, and extreme of functions of two variables; multiple integrals in rectangular, polar, spherical, and cylindrical coordinates; applications of multiple integrals to area, volume, moments, centroids, and surface area.

2. Learning Objectives

Students who successfully complete this course will be able to:

· demonstrate the ability to analyze and visualize curves, surfaces, and regions in 2 and 3 dimensions, in Cartesian, polar, cylindrical, and spherical coordinate systems;

· perform calculus operations on vector-valued functions including limits, derivatives, integrals, curvature, and the description of motion in space;

· perform calculus operations on functions of several variables including limits, partial derivatives, directional derivatives, and multiple integrals;

· find and classify extrema and tangent planes of functions of two variables;

· apply some of the theorems of vector calculus, such as the Fundamental Theorem of Line Integrals, Green’s Theorem, the Divergence Theorem, and Stokes’ Theorem, to simplify integration problems;

· apply the computational and conceptual principles of calculus to the solutions of various engineering applications.

3. Methodology

The majority of the course syllabus follows the main methodological guidelines of the Communicative Approach, based on the core principles of procedure conception and constructive acquisition of knowledge. The methodology is based on the teaching-learning procedures, focused on the learner, which encourages active participation and results in the development of general and specific competencies that prove knowledge, capacities and attitudes for their future professional careers.

4. Evaluation

The form of assessment is based on the core principles of the educational assessment, i.e., an active and participative teaching-learning process focused on the learner. The instructor uses numerous and differentiated forms of assessment to calculate the final grade received for this course. For the record, these are listed below. The content, criteria and specific requirements for each assessment category will be explained in greater detail in class.

In the Spanish educational system, it is required to quantitatively express the result of each student’s evaluation. In order to do so, Nebrija faculty uses different strategies and instruments such as: papers,

exams, tests, projects, self-evaluation activities, etc. In order to issue a final grade for the Spanish Plus programs the following scale is established:

• 30 % Attendance and active participation in class
• 30% Daily work/ Papers/ Essays
• 40% Exams/ Final papers or projects*

Therefore, the final grade is the average between attendance and participation, daily work and exams, presentations, projects and essays.

Active participation in class is evaluated by means of different activities such as:

• Activities and exercises correction;
• Reflection upon the different contents in the course;
• Oral activities (individual, in pairs or in groups). Fluency, correction, adequacy and relevance are taken into account.

Daily work makes reference to any activity or task that is done inside or outside of the classroom, whether during the class time or at any other time.

Exams/ Final papers or projects

The course includes a midterm and a final written exam on theoretical concepts and course facts. If a student, unjustifiably, does not do or submit an exam, paper or project, it will be graded with a ‘0’.

* A minimum grade of 5 must be obtained in a final exam/ final project in order to pass the course.

5.2. Attendance, participation and grading policies

5.2.1. Attendance policy

Attendance is mandatory. In case of missing 5 or more sessions in one course, the student will receive a zero in his/her participation and attendance grade. In addition, not attending classes will not excuse the student from handing in in any homework, papers or essays previously assigned.

The following situations must be considered:

• Each session of class will count as an absence.
• Two delays of more than 15 minutes will be considered an absence. The entrance to class will not be allowed after 30 minutes once it has started.
• There are no excused absences. E.g.: Not attending class because of sickness will count as an absence. The student is responsible for catching up with any homework done while absent.
• Exams dates have been officially approved by the University, therefore, they will not be changed.*

*Except for those courses where the professor will set up specific dates and inform the students at the beginning of the program.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Eligibility for courses may be subject to a placement exam and/or pre-requisites.

Availability of courses is based on enrollment numbers. All students should seek pre-approval for alternate courses in the event of last minute class cancellations