Module Catalogues, Xi'an Jiaotong-Liverpool University   
 
Module Code: MTH013
Module Title: Calculus (Science and Engineering)
Module Level: Level 0
Module Credits: 5.00
Academic Year: 2019/20
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: N/A
   
Aims
To give students a broad education in calculus and linear algebra, which include the topics usually covered in a course on single-variable calculus;

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

To develop the students' ability to work independently and to acquire the skill of problem solving.
Learning outcomes 
A. have a good understanding of the basic concepts which are the subject of this module;

B. have a good appreciation of the link between mathematics and Science and Engineering;

C. be skilful of problem solving;

D. be able to establish mathematical models for simple practical problems.

E. train students’ ability in learning academic contents using English

Method of teaching and learning 
Students will be expected to attend 3 hours of formal lectures and 1 hour of tutorial in a typical week. In lectures, teachers will introduce the academic content and practical skills which are the subject of the module. In the tutorials, the students can practice those skills.


In addition to the formal lectures and tutorials, students are expected to devote the unsupervised time to study the lecture materials and background readings. Online resources will be provided to the students to promote their active learning and self-leaning. Continuous assessment including online home assignments will be used to assess the learning outcomes. Written examinations in the middle and at the end of the semester constitute the major part of the assessment of the academic achievement of students.

Syllabus 
Part 1 Functions, limits and continuity

1. Basic concepts and graphs of functions

2. Even and odd functions, periodical functions, inverse functions

3. Composite functions

4. Mathematical models of real world problems, examples

5. Concept of limit, finding limits, one-sided limits

6. Limits involving infinity and infinitely small quantities

7. Continuity and the types of discontinuity

Part 2 Derivatives of functions of a single variable

1. Definition, notations and geometric interpretation of derivatives

2. Derivatives of products and quotients

3. Derivatives of simple functions

4. The chain rule, higher order derivatives

5. Derivatives of implicit functions and the functions determined by parametric equations

6. Linearization and differentials, application in approximations

7. Mean value theorems

Part 3 Applications of Derivatives

1. The behaviour of a graph: increasing and decreasing, point of inflection, concavity

2. Local and global minimum or maximum

3. L’Hospital’s Rule

Part 4 Integration of functions of a single variable

1. Indefinite and definite integrals

2. Integration table of simple functions, rules for integration, integration by substitution

3 Antiderivative and separable differential equation

4. Integration by parts

5. Fundamental Theorems of Calculus, Newton-Leibniz formula

6. First order differential equation and its application

7. Improper integral

Part 5 Applications of integrals

1. Areas of plane regions bounded by curves

2. Length of a curve

3. Volumes by slicing and rotation about an axis

Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 39    13      98  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: 8/20/2019 6:19:10 PM