Module Catalogues, Xi'an Jiaotong-Liverpool University

Module Code: MTH019
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 an appreciation of the application of mathematics to business, finance and social sciences;To train the students' ability to work independently and to acquire the skill of problem solving.
 Learning outcomes A To understand all the key concepts of Limit, Continuity, Derivative and Integration for the function of polynomial, exponential, logarithmic, and trigonometric functions; B To have a good appreciation of the link between mathematics and business, finance and social sciences;C To be able to calculate the limits, derivatives and integrations of the polynomial, exponential, logarithmic, and trigonometric functions.D To be able to establish simple mathematical models using the idea of differential, integration and first order differential equation.
 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 Preliminaries (review) 1. Basic concepts and graphs of functions 2. Even and odd functions, periodical functions, inverse functions, composite functions 3. Exponential and logarithmic functions 4. Trigonometric functions Part 2 Limits 5. Concept of limit, finding limits, one-sided limits 6. Limits involving infinity and infinitely small quantities 7. Continuity Part 3 Derivatives of a single variable functions 8. Definition, notation and geometric interpretation of derivatives 9. Derivatives of products and quotients 10. Derivatives of simple functions 11. The chain rule, higher order derivatives 12. Derivatives of implicit functions 13. Related rates and applications 14. Derivatives of exponential, logarithmic and trigonometric functions 15. Differential and approximations Part 4 Applications of Derivatives 16. Maxima and minima 17. Monotonicity and concavity . 18. Local extrema and extrema on open intervals 19. Practical applications 20. Mean value theorem for derivatives 21. Antiderivatives and introduction to differential equations 22. Indeterminate forms and the L’Hospital’s Rule Part 5 The definite integral 23. Definite integrals 24. The 1st and 2nd fundamental theorems of Calculus. Part 6 Applications of integrals 25. Areas of plane regions bounded by curves 26. Length of a curve 27. Volumes by slicing and rotation about an axis Part 7 Techniques of integration and differential equations 28. Integration by substitutions 29. Integration by parts 30. First order differential equation and its application in interest model, logistic model.
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: 1/26/2020 10:50:33 PM