Module Catalogues, Xi'an Jiaotong-Liverpool University   
Module Code: MTH008
Module Title: Multivariable Calculus (Science and Engineering)
Module Level: Level 0
Module Credits: 5.00
Academic Year: 2019/20
Semester: SEM2
Originating Department: Mathematical Sciences
Pre-requisites: MTH013ORMTH017ORMTH019ORMTH021ORMTH023ORMTH025ORMTH027MTH023MTH021MTH008
To give students a broad education in calculus of multivariable functions, differential equations and infinite series, which includes the topics usually covered in a standard course of advanced calculus.

To give students an appreciation of the application of mathematics to science and engineering

To introduce the mathematical modeling for solving practical problems.

To develop students' ability to work independently and to acquire the skill of problem solving.

Learning outcomes 
On successful completion of this module, students are expected to”

"have a good understanding of the basic concepts which are the subject of this module;

"have a good appreciation of the link between mathematics and other subjects;

"have the basic skills of problem solving;

“be able to establish mathematical models for simple practical problems.
Method of teaching and learning 
Students will be expected to attend about five hours of formal lectures and supervised problem classes/tutorials and group discussions in a typical week. Lectures and tutorials will introduce students to the academic content and practical skills which are the subject of the module, while problem classes and tutorials will allow students to practice those skills.

In addition to contact hours, students will be expected to devote sufficient unsupervised time to private study. Private study will provide time for reflection and consideration of lecture material and background reading.

Continuous assessment, including home assignment marking will be used to test to what extent practical skills have been learnt. Written examinations in the middle and at the end of the module constitute the major part of the assessment of the academic achievement.

In order to facilitate the smooth transition to the English delivery of all modules from year 2, this module will be delivered in dual languages (Chinese and English).
Part 1 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. Vector equation for a straight line and a plane

6. Cylinders and quadric surfaces

7. Examples of application

Part 2 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. Direction derivatives and gradient vectors

4. Concepts of divergence and curl. Applications

5. Linearization and total differentials

6. Extreme values and saddle points

7. Lagrange’s multiplier method and applications

Part 3 Multiple integrals

1. Double integral: concept and calculation

2. Areas, moments and center of mass

3. Concept and calculation of triple integrals in rectangular, cylindrical and spherical coordinates

Part 4 Infinite series

1. Concepts and properties of the infinite series

2. Geometric series and harmonic series

3. Comparison test for the series with positive terms

4. Ratio test and root test

5. Alternating series, absolute convergence and conditional convergence

6. Power series, radius and interval of convergence

7. Taylor formula and Taylor series

8. Sum of power series and the power series expansions of functions

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


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: 12/9/2019 11:13:43 PM