BDIC1042J Maths 3

Academic Year 2021/2022

This module is the third module of calculus, about multi-variable differential calculus. The main contents include curves and surfaces in space in terms of vectors, introduction to differential calculus of multi-variable functions, (higher order) partial derivatives, chain rule, gradients, tangent line (plane, resp.) for a curve (surface, resp.), classification of extrema of surfaces, the Lagrangian multiplier method, and so on.
By learning multi-variable calculus, students will receive the training of extending the techniques of single-variable calculus to the multi-variable case, by combining calculus and the knowledge of linear algebra.

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Curricular information is subject to change

Learning Outcomes:

Students are expected to achieve the following competence:
• Computing dot and cross products of vectors;
• Finding equations of tangent lines of curves and tangent planes of surfaces;
• Understanding the geometric meaning of partial derivatives;
• Computing (higher) partial derivatives;
• Computing total differentials;
• 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.

Indicative Module Content:

Teaching Plan

Week 1 Review of vectors and geometry in space.
Week 2 Tangent lines and normal planes of curves, tangent planes and normal lines of surfaces.
Week 3 Multi-variable functions, limits and continuity.
Week 4 Partial derivatives, higher order partial derivatives.
Week 5 Total differentials, with applications in approximate computations; partial derivatives of composite functions and implicit functions.
Week 6 Tangent lines of curves and tangent planes of surfaces in space.
Week 7 Gradients and directional derivatives, and the Lagrangian multiplier method.
Week 8 Revision and final exam.

* Tutorials will be held every week from Week 2.

Student Effort Hours: 
Student Effort Type Hours
Lectures

48
Practical

17
Total

65
Approaches to Teaching and Learning:
Lecturing (face-to-face teaching) + tutorials + close-book examinations. 
Requirements, Exclusions and Recommendations

Not applicable to this module.


Module Requisites and Incompatibles
Not applicable to this module.
 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Assignment: Academic poster based on group work. Unspecified n/a Alternative linear conversion grade scale 40% No

15
Continuous Assessment: Attendence recording and tutorial participation. Throughout the Trimester n/a Pass/Fail Grade Scale No

20
Examination: Final Exam.
90 minutes of examination, at the end of the module.		 Unspecified No Alternative linear conversion grade scale 40% No

65

Carry forward of passed components
No
 
Resit In Terminal Exam
Summer Yes - 2 Hour
Please see Student Jargon Buster for more information about remediation types and timing. 
Feedback Strategy/Strategies

• Group/class feedback, post-assessment

How will my Feedback be Delivered?

Not yet recorded.