Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH013
Module Title: Calculus (Science and Engineering)
Module Level: Level 0
Module Credits: 5.00
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 functions2. Even and odd functions, periodical functions, inverse functions 3. Composite functions 4. Mathematical models of real world problems, examples5. Concept of limit, finding limits, one-sided limits 6. Limits involving infinity and infinitely small quantities 7. Continuity and the types of discontinuityPart 2 Derivatives of functions of a single variable 1. Definition, notations and geometric interpretation of derivatives2. 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 equations6. Linearization and differentials, application in approximations 7. Mean value theorems Part 3 Applications of Derivatives1. The behaviour of a graph: increasing and decreasing, point of inflection, concavity2. Local and global minimum or maximum 3. L’Hospital’s RulePart 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 equation4. Integration by parts5. Fundamental Theorems of Calculus, Newton-Leibniz formula6. First order differential equation and its application 7. Improper integral Part 5 Applications of integrals1. Areas of plane regions bounded by curves2. 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: 12/9/2019 11:31:16 PM