Module Catalogues, Xi'an Jiaotong-Liverpool University   
 
Module Code: MTH014
Module Title: Multivariable Calculus (Architecture)
Module Level: Level 0
Module Credits: 5.00
Academic Year: 2019/20
Semester: SEM2
Originating Department: Mathematical Sciences
Pre-requisites: MTH013ORMTH019ORMTH023ORMTH027
   
Aims
To give students an education in calculus of multivariable functions, differential equation and geometry in space and vectors, which includes the basic topics usually covered in an elementary course of multivariable calculus.

To give students an appreciation of the application of mathematics to architecture.

To introduce the concept of modelling and various mathematical models in practical problems.

Learning outcomes 
A Demonstrate an understanding of the concepts of derivative and integral of functions with multiple variables;

B Demonstrate an understanding of vector, line, plane and surface in three space and their equations;

C Calculate the derivative and integral of different functions with multiple variables;

D Apply their knowledge of differentiation to determine critical features of functions including extreme values;

E Apply their knowledge of multiple integration, including calculating the volume of solids;

F Understand the mathematical models for simple practical problems.


Method of teaching and learning 
This module will be delivered through a combination of formal lectures and tutorials.
Syllabus 
Part 1 Conics and polar coordinates

1. Basic of parabola, ellipse and hyperbolas

2. Translation and rotation of axes

3. Polar coordinates, graphs of polar equations and calculus in polar coordinates

Part 2 Vectors and solid geometry

1. Concept of a vector, rectangular coordinates and vectors in space

2. Equal vectors, sum of vectors, subtraction of two vectors

3. Dot and cross products, parallel vectors and orthogonal vectors

4. Unit vectors, direction cosine, vectors expressed in terms of unit vectors in rectangular coordinates and their operations

5. Equations for a straight line and a plane

6. Equations for surfaces of revolution, cylinders and quadric surfaces

7. Curvature, cylindrical and spherical coordinates

Part 3 Multivariable functions and their derivatives

1. Functions of several variables and partial derivatives

2. The chain rule and partial derivatives of composite functions, higher order derivatives 3. Linearization and total differentials

4. Extreme values and saddle points

5. Lagrange’s multiplier method and applications

Part 4 Multiple integrals

1. Double integral: concept and calculation

2. Areas and volumes

3. Concept and calculation of triple integrals in rectangular coordinates and other coordinates


Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 52    13      85  150 

Assessment

Sequence Method % of Final Mark
1 Written Examination 70.00
2 Mid-Term Test 20.00
3 Course Work 10.00

Module Catalogue generated from SITS CUT-OFF: 12/16/2019 7:34:26 AM