Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH029
Module Title: Calculus (Mathematical Sciences)
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, 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.
 Syllabus Part 1 Functions, limits and continuity1. Basic concepts and graphs of functions2. Even and odd functions, periodical functions, inverse functions3. Composite functions4. Mathematical models of real world problems, examples5. Concept of limit, finding limits, one-sided limits6. Limits involving infinity and infinitesimal7. Continuity and the types of discontinuity, Intermediate Value TheoremPart 2 Derivatives of single variable functions 1. Definition, notations and geometric interpretation of derivatives2. Derivatives of products and quotients3. Derivatives of simple functions4. The chain rule, higher order derivatives5. Derivatives of implicit functions and the functions determined by parametric equations6. Linearization and differentials, application in approximations 7. Mean value theoremsPart 3 Applications of Derivatives1. The behaviour of a function: increasing and decreasing, point of inflection, concavity2. Local and global minimum or maximum3. L’Hospital’s RulePart 4 Integration of single variable functions1. Indefinite and definite integrals2. Integration table of simple functions, rules for integration, integration by substitution3 Antiderivative and separable differential equation4. Integration by parts5. Fundamental Theorems of Calculus, Newton-Leibniz formula6. First order differential equation and its application7. Improper integralPart 5 Applications of integrals1. Areas of plane regions bounded by curves2. Length of a curve3. Volumes by slicing and rotation about an axis4. Probability and Random Variables
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 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