# BDIC1032J Maths (Engineering) 4

This module is the forth module of calculus, about multi-variable calculus. The main contents include differential calculus for multi-variable functions and multiple integrals. By learning multi-variable calculus, where the contents change from one to three-dimensional questions, students can receive training on non-objective and special imagination.

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Curricular information is subject to change

Learning Outcomes:

Students are expected to achieve the following competence:
• Find limits,continuity, total differential of multi-variable functions
• Finding gradients of multi-variable functions;
• Using gradients to find greatest increasing and decreasing directions of multi-variable function.
• Optimizing a function under constraints in terms of the method of Lagrangian multiplier;
• Computing double integrals in right coordinates, especially iterated integrals;
• Computing double integrals in polar coordinates;
• Computing triple integrals in right coordinates;
• Computing triple integrals in cylindrical and spherical coordinates.

Indicative Module Content:

week 9 Partial derivatives of composite functions and implicit functions.
week 10 Tangent lines of curves and tangent planes of surfaces in space.
week 11 Gradients and directional derivatives.
week 12 Lagrangian multiplier method, double integrals in Right coordinates.
week 13 Double integrals in polar coordinates, triple integrals in Right coordinates.
week 14 Triple integrals in Right, cylindrical and spherical coordinates.
week 15 Revision.

Student Effort Hours:
Student Effort Type Hours
Lectures

32

Tutorial

16

Autonomous Student Learning

48

Online Learning

34

Total

130

Approaches to Teaching and Learning:
Face-to- face lectures , tutorials , office hours and on-line question -and-answer as well as peer instruction, all kinds of approaches are applies to achieve positive teaching outcome.
Requirements, Exclusions and Recommendations

Not applicable to this module.

Module Requisites and Incompatibles
This module is delivered overseas and is not available to students based at the UCD Belfield or UCD Blackrock campuses

Assessment Strategy
Description Timing Component Scale Must Pass Component % of Final Grade In Module Component Repeat Offered
Exam (In-person): 2 hour final exam Week 15 Graded Yes

100

Yes

Carry forward of passed components
No

Resit In Terminal Exam
Summer Yes - 2 Hour
Feedback Strategy/Strategies

• Feedback individually to students, on an activity or draft prior to summative assessment
• Feedback individually to students, post-assessment
• Group/class feedback, post-assessment
• Online automated feedback

How will my Feedback be Delivered?

Assignment feedback individually , and the feedback will give the marks of the assignment by students' performances. Group feedback will be used when there is a team work given. Online feedback happens when online question and answers exist, the students' performance will be marked as assessments.

Name Role
Enchang Sun Tutor
Wenying Wu Tutor