MATH20290 Multivariable Calculus for Eng

Academic Year 2021/2022

This module is an introduction to calculus of several variables. In addition, the study of linear ordinary differential equations is extended from first order (seen in stage 1) to higher order. The module is currently divided into nine chapters on the following topics (details below): 1. Functions of several variables; 2. Partial derivatives, chain rule, linear approximation; 3. Gradient and directional derivatives; 4. Second order partial derivatives and the Hessian matrix; 5. The Jacobian matrix, chain rule and inverse function theorem; 6. Maxima and minima, classification of critical points; 7. Constrained optimization and Lagrange multipliers; 8. Higher order linear differential equations with constant coefficients; 9. (Time permitting) The Laplace transform.

[Disclaimer: module content and assessment strategies may be subject to minor changes during the trimester. These changes may not be reflected in this module descriptor at that time, but will be clearly communicated to all students via other means.]

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Curricular information is subject to change

Learning Outcomes:

On successful completion of this module the student should be able to:1. Calculate first and second order partial derivatives. 2. Find equations of tangent lines to curves and tangent planes to surfaces.3. Determine rates of change using the chain rule. 4. Find approximate values of functions and percentage changes. 5. Calculate directional derivatives.6. Find and classify critical points of functions of several variables.7. Solve constrained extremum problems using the method of Lagrange multipliers. 8. Solve linear constant coefficient differential equations by various methods. 9. (Time permitting) Compute Laplace transforms. Determine simple inverse Laplace transforms. Use Laplace transforms to solve differential equations.

Indicative Module Content:

1. Functions of several variables; 2. Partial derivatives, chain rule, linear approximation; 3. Gradient and directional derivatives; 4. Second order partial derivatives and the Hessian matrix; 5. The Jacobian matrix, chain rule and inverse function theorem; 6. Maxima and minima, classification of critical points; 7. Constrained optimization and Lagrange multipliers; 8. Higher order linear differential equations with constant coefficients; 9. (Time permitting) The Laplace transform.

Student Effort Hours: 
Student Effort Type Hours
Lectures

36
Tutorial

12
Specified Learning Activities

20
Autonomous Student Learning

32
Total

100
Approaches to Teaching and Learning:
Given the size of the class (300+ students) and the requirement that for classes of more than 250 students on-line materials need to be provided, the primary source of teaching materials will consist of pre-recorded videos.

In addition to these there will be a face-to-face lecture each week on campus where I will give an overview of the material for that week and will answer any questions. This lecture will be simultaneously broadcast via zoom for students who cannot attend in person, and a recording will be made available in Brightspace.

The class will also be split into 2 tutorial groups. Each group will get one tutorial per week, starting in Week 2 (or possibly Week 3 -- to be confirmed). These will be F2F on campus, and most likely also broadcast and recorded. Precise details will be provide at the beginning of term. 
Requirements, Exclusions and Recommendations
Learning Requirements:

The student must have taken modules in Calculus of a single variable whose content includes the basics of differential and integral calculus. The student should also have taken an Algebra module whose learning outcomes include a working knowledge of vector geometry in 2 and 3 dimensions as well as an appreciation of matrix techniques.


Module Requisites and Incompatibles
Pre-requisite:
MATH10250 - Intro Calculus for Engineers , MATH10260 - Linear Algebra for Engineers

Incompatibles:
ECON10030 - Intro Quantitative Economics, MATH20060 - Calculus of Several Variables, MATH20140 - Multivariable Calculus (Sci)., MATH20240 - Mathematics for Engineers IV, MST20070 - Multivariable Calculus


 
Assessment Strategy  
Description Timing Open Book Exam Component Scale Must Pass Component % of Final Grade
Examination: Final exam 2 hour End of Trimester Exam No Standard conversion grade scale 40% No

85
Class Test: In-term test. Unspecified n/a Standard conversion grade scale 40% No

15

Carry forward of passed components
No
 
Resit In Terminal Exam
Spring 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.

Name Role
Assoc Professor Thomas Unger Lecturer / Co-Lecturer