# Multivariable Calculus

Maynooth University

## Course Description

• ### Course Name

Multivariable Calculus

• ### Host University

Maynooth University

• ### Location

Dublin, Ireland

Calculus

• ### Language Level

Taught In English

• ### Prerequisites

MT231P, MT241P, and MT243P or (MT102S and MT112A) or equivalent modules.

• ### Course Level Recommendations

Upper

ISA offers course level recommendations in an effort to facilitate the determination of course levels by credential evaluators.We advice each institution to have their own credentials evaluator make the final decision regrading course levels.

### Hours & Credits

• ECTS Credits

5
• Recommended U.S. Semester Credits
2
• Recommended U.S. Quarter Units
3
• ### Overview

Module Objective:
To introduce the student to rigorous multivariate calculus and its uses.

Functions from R^n to R. Examples. Quadrics. Visualisation. Limits and continuity. Partial Derivatives. Gradients, directional derivatives, mean-value theorem, chain rules, Tangent lines and planes, level surfaces, max-min, Hessian, 2nd Derivative Test. Double and triple integrals.

Learning Outcomes:

On successful completion of the module, students should be able to:
-Draw level curves for functions of two variables.
-Find the partial derivatives and gradient vector of a function.
-Obtain tangents and normals to surfaces.
-Solve max-min problems in several variables.
-Obtain solutions to double and triple integrals. Use double, triple and surface integrals in applications.
-Use double and triple integrals in applications
-Use the methods from the course to solve problems. State definitions and theorems covered in the course.

Teaching & Learning Methods
24 lecture hours, 5 tutorial hours, 51 private study hours.

Assessment:
Continuous Assessment: 30%
University scheduled written examination: 70%

Pre-requisites:
24 lecture hours, 5 tutorial hours, 51 private study hours.

### Course Disclaimer

Courses and course hours of instruction are subject to change.

Credits earned vary according to the policies of the students' home institutions. According to ISA policy and possible visa requirements, students must maintain full-time enrollment status, as determined by their home institutions, for the duration of the program.

ECTS (European Credit Transfer and Accumulation System) credits are converted to semester credits/quarter units differently among U.S. universities. Students should confirm the conversion scale used at their home university when determining credit transfer.

Please reference fall and spring course lists as not all courses are taught during both semesters.

Please note that some courses with locals have recommended prerequisite courses. It is the student's responsibility to consult any recommended prerequisites prior to enrolling in their course.