Study Guide CC2030 Mathematics

Dr Anthony Loh

Dr Chun-Man Chan Dr Kenneth Lo

Dr Roy Ng

• Subject Syllabus • Teaching Plan • Learning Outcomes Matrix • Assessment Criteria • Chapter 1—Linear Algebra • Chapter 2—Function, Limit and Continuity • Chapter 3—Differentiation • Chapter 4—Application of Differentiation I • Chapter 5—Application of Differentiation II • Chapter 6—Indefinite Integral • Chapter 7—Definite Integral • Chapter 8—Application of Integration • Chapter 9—Double Integral • Chapter 10—Complex Numbers

CC2030 MathematicsLevel 2 Credits 3 Nature Science Medium of Instruction English Teaching Pattern 28 hours of Lecture

14 hours of Tutorial Prerequisites Nil Exclusions CC2003 Quantitative Methods & CC2026 Numerical Skills Assessment 50% Coursework

50% Examination Aims This subject introduces students to the fundamentals of algebra and calculus. It provides students with practices in applying mathematical concepts to solve scientific and engineering problems. Studying the subject will also help students to develop their analytical and logical thinking for their further study in other engineering subjects. Learning Outcomes On successfully completing this subject, students will be able to: • understand fundamental mathematical concepts in algebra and calculus • extend their knowledge of mathematical techniques and adapt known solutions to

different situations • apply the appropriate mathematical techniques to solve problems in science and

engineering • think analytically and logically Indicative Contents • Basic Algebra

Linear functions and quadratic functions; Binomial theorem; Simple inequalities; System of Linear equations in two and three variables; Elimination method; Matrix and matrix operations; Use of matrices to solve systems of linear equations.

• Complex Number

Complex numbers; Geometrical representation; n-tb root of complex number. • Calculus

Basic concepts of limits and derivatives; Gradient of tangent and rate of change; Second order derivatives; Maximum and minimum; Curve sketching; Optimization problems; Definite and indefinite integrals; Integration methods; Applications of integration (e.g. properties of area, volume and mass); Double integrals.

Teaching/Learning Approach Lectures focus on the introduction and explanation of fundamental mathematical concepts in algebra and calculus, and demonstrate how they can be applied to solve scientific and engineering problems. Tutorials provide students with the opportunity to deepen their understanding of the concepts taught in lectures and to apply appropriate mathematical techniques to solve problems in science and engineering. Assessment Approach A variety of assessment tools may be used, including assignments, tests and an examination designed to develop and assess students’ achievement of the subject expected learning outcomes. Indicative Readings Recommended Textbook Smith, Robert T. and Minton, Roland B. Calculus: Concepts and Connections. McGraw Hill. (latest ed.). References Anton, Howard. Calculus. Wiley. (latest ed.). Anton, Howard. Contemporary Linear Algebra. John Wiley & Sons. (latest ed.). Barnett, Raymond and Ziegle, Michael. College Algebra. McGraw Hill. (latest ed.). Bostock, L. Core Maths for Advanced Level. Stanley Thornes. (latest ed.). Thomas, G.B., Finney, R.L., Hass, J.R. and Giordano, F.R. Thomas’ Calculus. Addison Wesley. (latest ed.).

Hong Kong Community College CC2030 Mathematics

Tentative Teaching Plan

Subject Leader Dr Anthony Loh (Office: Rm HHB1537, Tel: 3746-0238, email: ccccaloh@hkcc-polyu.edu.hk) Subject Lecturer Dr Kenneth Lo (Office: Rm HHB1625, Tel: 3746-0101, email: ccchlo@hkcc-polyu.edu.hk) Dr Anthony Loh (Office: Rm HHB1537, Tel: 3746-0238, email: ccccaloh@hkcc-polyu.edu.hk) Objectives: On successfully completing this subject, students will be able to:

understand fundamental mathematical concepts in algebra and calculus. extend their knowledge of mathematical techniques and adapt known solutions to

different situations. apply the appropriate mathematical techniques to solve problems in science and

engineering. think analytically and logically.

Tentative Teaching Schedule

Lecture Tutorial

No Content Remarks No Content Remarks

1

System of Linear equations in two and three variables; Elimination method

1

2 Matrix and matrix operations 2

System of Linear equations in two and three variables; Elimination method

3 Use of matrices to solve systems of linear equations

3 Matrix and matrix operations

4

Linear functions and quadratic functions; Binomial theorem; Simple inequalities

4 Use of matrices to solve systems of linear equations

5

Basic concepts of limits and derivatives; Gradient of tangent and rate of change

Submission of Assignment 1

5

Linear functions and quadratic functions; Binomial theorem; Simple inequalities

6 Second order derivatives; Maximum and minimum 6

Basic concepts of limits and derivatives; Gradient of tangent and rate of change

7 Curve sketching; Optimization problems 7 Second order derivatives;

Maximum and minimum

8 Definite integrals 8 Curve sketching; Optimization problems

9 Test Lectures 1-7 9 Definite integrals

10 Indefinite integrals 10 Indefinite integrals

11 Integration methods 11 Integration methods

12 Applications of integration

Submission of Assignment 2

12 Applications of integration

13 Multiple integrals 13 Multiple integrals

14 Complex numbers; Geometrical representation; n-th root

14 Complex numbers; Geometrical representation; n-th root

Assessment Weighting

Coursework: 50% Examination: 50% 100%

Assessment Methods for Coursework Test 60% Assignment 1 20% (Individual) Assignment 2 20% (Individual) 100%

Attendance and other rules / regulations The attendance requirement and all other rules and regulations in the HKCC Student Handbook and in the respective Definitive Programme Document apply. Please refer to these documents for details. Lecture/Tutorial Notes and Assignments Students are required to download lecture/tutorial notes and assignments from the SMILE e-Learning System.

Learning Outcome Matrix Subject Learning Outcomes (a) understand fundamental mathematical concepts in algebra and calculus. (b) extend their knowledge of mathematical techniques and adapt known solutions to different

situations. (c) apply the appropriate mathematical techniques to solve problems in science and

engineering. (d) think analytically and logically. Learning Outcome Matrix

Learning Outcomes Chapter (a) (b) (c) (d) Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5 Chapter 6 Chapter 7 Chapter 8 Chapter 9 Chapter 10

Assessment Criteria: Quality of Assignment Required performance Standard Quality of

calculations Quality of reasoning

Understanding of tools and concepts

Formulation of solution or conclusion

Unsatisfactory Inaccurate and incomplete calculations

Absence of argument; isolated steps without connections

Failure to use the tools selected; unsound approach and analysis

Fail to formulate a solution; conclusions illogical or not supported by evidence and critical argument

Satisfactory Slightly inaccurate and slightly incomplete calculations

Logically flawed and unclear argument

Some faults in the use of tools and concepts, overall sound approach

Attempt to formulate a solution to the problem and draw conclusions; flawed argument

Good Accurate and slightly incomplete calculations

Logically correct argument with some unclear areas

Effective use of a range of relevant tools and concepts

Attempt to formulate a solution to the problem and draw sensible conclusions with logical argument

Excellent Accurate and complete calculations

Logically correct argument clear in all important aspects

Clearly explanation and effectively use the tools and concepts

Clear solution and conclusions; demonstration of critical and creative thinking and originality