Course Name Year Term Period Faculty / Graduate School All Instructors Credits
34757:Computing Mathematics (G1) 2019 Spring Mon2 College of Information Science and Engineering BAI YANG 2

Campus

BKC

Class Venue

Prism109

Language

English

Course Outline and Method

The goal of this course is to bring fundamental knowledge of differentiation and integration to students. Specifically, this course covers some basic contents of Calculus, including limit, continuity, derivative and its applications, indefinite integral and definite integral, multiple integral, curvilinear integral, surface integral, series, and so on. This course lays the foundation for learning future courses such as differential equation.

Student Attainment Objectives

After this course, students should understand the importance of Calculus as one of the fundamental subjects for most of the engineering programs. Also, students will be able to explain the basic concepts of limit, differentiation and integration. At the same time, they will gain the skills of computing derivatives and integrals, as well as applying these skills to solve concrete problems such as calculating areas and volumes, or optimization problems.

Recommended Preparatory Course

Pre-calculus: limits, continuity, and derivatives

Course Schedule

Lecture/Instructor（When there are multiple instructors) Theme
Keyword, References and Supplementary Information
1

Preliminaries

Limits and continuity, tangents and the derivative at a point
2

Differentiation (1)

The derivative as a function, differentiation rules, the derivative as a rate of change
3

Differentiation (2)

Derivatives of trigonometric functions, derivatives of transcendental functions
4

Differentiation (3)

The chain rule, implicit differentiation, linearization and differentials
5

Differentiation (4)

Applications of derivatives: indeterminate forms and L’Hôpital’s Rule, extreme values of functions
6

Differentiation (5)

Applications of derivatives: the mean value theorem, optimization
7

Mid-term Exam

Lasts 90 min. and covers topics of Weeks 1 through 6
8

Integration (1)

Pre-calculus: area and estimating with finite sums, the definite integral, indefinite integrals
9

Integration (2)

Techniques of integration: substitution, integration by parts, trigonometric Integrals, etc.
10

Integration (3)

Applications of definite integrals: calculation of area, volume, and arch length, etc.
11

Integration (4)

Multiple integrals: double integrals, triple integrals, moments and centers of mass
12

Integration (5)

Integrals and vector fields: line integrals, surface integrals, etc.
13

Infinite Sequences and Series (1)

Infinite series, the integral test, comparison tests, the ratio and root tests
14

Infinite Sequences and Series (2)

Power series, Taylor and Maclaurin series, the binomial series
15

Course Overview

Covers topics of Weeks 1 through 14

Class Format

Recommendations for Private Study

Students are recommended to read relevant chapters before class. This will be helpful for them to better and faster understand the contents of the lecture. Homework will be assigned within each lecture and is due on the next lecture. Collaboration on homework is encouraged because discussion with other students is an efficient way of solving challenging problems. However, it is not allowed to copy solutions from other students directly.

Grade Evaluation Method

Kind Percentage Grading Criteria etc.
Final Examination (Written) 50

Ability to solve the questions provided in the final exam
Report Examination
(A report to be submitted by the unified deadline)		 0

Exams and/or Reports other than those stated above, and Continuous Assessment　
(Evaluation of Everyday Performance in Class)		 50

Attendance, assignments and the mid-term exam

Grade Evaluation Method （Note）

Software such as Mathematica, Matlab, and so on, is recommended to use for checking the answers to your homework problems. However, solutions to these problems need to be clearly understood and written in steps by yourself.

Advice to Students on Study and Research Methods

Students are recommended to review the contents of the lecture after each class. Although the slides used in the lecture will be provided, taking notes is considered to be necessary, since the slides may not cover everything in the lecture. The example problems given during the class are recommended to be re-studied by yourselves after class.

Textbooks

Title Author Publisher ISBN Code Comment
Thomas’ Calculus 13th Ed. George B. Thomas, Jr., Maurice D. Weir, Joel Hass, Christopher Heil Pearson Education 978-0-321-87896-0

Textbooks （Frequency of Use, Note）

Reference Books

Reference Books （Frequency of Use, Note）

Web Pages for Reference

How to Communicate with the Instructor In and Out of Class(Including Instructor Contact Information)

Talk with Students,Other (Separate instructions will be provided)

Other Comments

This course describes the theory of some very practical and immensely useful parts of computer science. Students are encouraged to deepen their understanding of the principles learned by implementing those principles as working programs. For example, understanding binary arithmetic makes possible the implementation of functions providing arbitrary-precision arithmetic (where overflow never occurs). Understanding state machines makes possible the implementation of pattern recognisers. These are challenging, but realistic, projects to undertake while studying the 'Introduction to Programming' course. Your instructors will be more than happy to help you attempt any such project that you feel is at, or even just beyond, your level of programming competence.