Module Catalogues, Xi'an Jiaotong-Liverpool University   
Module Code: MTH029
Module Title: Calculus (Mathematical Sciences)
Module Level: Level 0
Module Credits: 5.00
Academic Year: 2019/20
Semester: SEM1
Originating Department: Mathematical Sciences
Pre-requisites: N/A
To give students a broad education in calculus, which include the topics usually covered in a course on single-variable calculus;

To give students a solid mathematical foundation for the modules in year two and above;

To give students an appreciation of the applications of calculus in other fields of science;

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

Learning outcomes 
A Have a good mathematical understanding of the basic concepts of calculus.

B Have a good understanding of the application of calculus in other fields of science.

C Solve problems by calculation.

D Establish mathematical models for simple practical problems.

Method of teaching and learning 
Students will be expected to attend 3 hours of lectures and 1hour of tutorial in a typical week. In lectures, students will learn the concepts, theories and calculation skills of calculus. In tutorials, students can practice these skills.

In addition to the lectures and tutorials, students will be expected to devote the unsupervised time to private study. Private study will provide time for reflection and consideration of lecture material and background reading. Online resources will be provided to the students to support their active learning.

Continuous assessment including home assignments and online exercises will be used to assess the learning outcomes. Written examination in the middle and at the end of the semester constitutes the major part of the assessment of the academic achievement of students.
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 infinitesimal

7. Continuity and the types of discontinuity, Intermediate Value Theorem

Part 2 Derivatives of single variable functions

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 function: increasing and decreasing, point of inflection, concavity

2. Local and global minimum or maximum

3. L’Hospital’s Rule

Part 4 Integration of single variable functions

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

4. Probability and Random Variables

Delivery Hours  
Lectures Seminars Tutorials Lab/Prcaticals Fieldwork / Placement Other(Private study) Total
Hours/Semester 39    13      98  150 


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

Module Catalogue generated from SITS CUT-OFF: 12/9/2019 11:57:37 PM