Enquiry for Science Major/Minor/Programme Requirements
MATH1013 University mathematics II (6 credits) Academic Year 2025
Offering Department Mathematics Quota 500
Course Co-ordinator Dr T W Ching, Mathematics < lmtching@maths.hku.hk >
Teachers Involved (Dr A Lefebvre de Saint Germain,Mathematics)
(Dr R La,Mathematics)
(Dr T W Ching,Mathematics)
(Dr W Zhang,Mathematics)
Course Objectives This course aims at students with Core Mathematics plus Module 1 or Core Mathematics plus Module 2 background and provides them with basic knowledge of calculus and some linear algebra that can be applied in various disciplines. It is expected to be followed by courses such as MATH2012, MATH2101, MATH2102, MATH2211, and MATH2241.
Course Contents & Topics - Functions; graphs; inverse functions.
- Limits; continuity and differentiability.
- Mean value theorem; Taylor's theorem; implicit differentiation; L'Hopital's rule.
- Higher order derivatives; maxima and minima; graph sketching.
- Radian, calculus of trigonometric functions.
- Definite and indefinite integrals; integration by substitutions; integration by parts; integration by partial fractions.
- Complex numbers, polar form, de Moivre's formula.
- Applications: Solving simple ordinary differential equations.
- Basic matrix and vector (of orders 2 and 3) operations, determinants of 2x2 or 3x3 matrices.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 describe properties of functions and inverse functions
CLO 2 evaluate limits, and determine continuity and differentiability of functions
CLO 3 apply advanced rules/techniques of differentiation and integration to compute derivatives and integrals; sketch graphs of functions; approximation of functions
CLO 4 solve problems involving complex numbers
CLO 5 solve simple first and second order ordinary differential equations
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 Level 2 or above in Module 1, or Module 2 of HKDSE Mathematics or equivalent, or
Pass in MATH1009 or MATH1011; and
Not for students who have passed MATH1821, or (MATH1851 and MATH1853), or have already enrolled in this course.
Course Status with Related Major/Minor /Professional Core 2025 Major in Chemistry (Intensive) ( Disciplinary Elective )
2025 Major in Mathematics ( Core/Compulsory )
2025 Major in Mathematics (Intensive) ( Core/Compulsory )
2025 Major in Molecular Biology & Biotechnology (Intensive) ( Disciplinary Elective )
2025 Major in Physics (Intensive) ( Disciplinary Elective )
2025 Minor in Computational & Financial Mathematics ( Core/Compulsory )
2025 Minor in Mathematics ( Core/Compulsory )
2025 Minor in Operations Research & Mathematical Programming ( Core/Compulsory )
2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory )
2024 Major in Chemistry (Intensive) ( Disciplinary Elective )
2024 Major in Decision Analytics ( Core/Compulsory )
2024 Major in Mathematics ( Core/Compulsory )
2024 Major in Mathematics (Intensive) ( Core/Compulsory )
2024 Major in Molecular Biology & Biotechnology (Intensive) ( Disciplinary Elective )
2024 Major in Physics (Intensive) ( Disciplinary Elective )
2024 Major in Risk Management ( Core/Compulsory )
2024 Major in Statistics ( Core/Compulsory )
2024 Minor in Actuarial Studies ( Disciplinary Elective )
2024 Minor in Computational & Financial Mathematics ( Core/Compulsory )
2024 Minor in Mathematics ( Core/Compulsory )
2024 Minor in Operations Research & Mathematical Programming ( Core/Compulsory )
2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory )
2023 Major in Chemistry (Intensive) ( Disciplinary Elective )
2023 Major in Decision Analytics ( Core/Compulsory )
2023 Major in Mathematics ( Core/Compulsory )
2023 Major in Mathematics (Intensive) ( Core/Compulsory )
2023 Major in Molecular Biology & Biotechnology (Intensive) ( Disciplinary Elective )
2023 Major in Physics (Intensive) ( Disciplinary Elective )
2023 Major in Risk Management ( Core/Compulsory )
2023 Major in Statistics ( Core/Compulsory )
2023 Minor in Actuarial Studies ( Disciplinary Elective )
2023 Minor in Computational & Financial Mathematics ( Core/Compulsory )
2023 Minor in Mathematics ( Core/Compulsory )
2023 Minor in Operations Research & Mathematical Programming ( Core/Compulsory )
2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory )
2022 Major in Chemistry (Intensive) ( Disciplinary Elective )
2022 Major in Decision Analytics ( Core/Compulsory )
2022 Major in Mathematics ( Core/Compulsory )
2022 Major in Mathematics (Intensive) ( Core/Compulsory )
2022 Major in Molecular Biology & Biotechnology (Intensive) ( Disciplinary Elective )
2022 Major in Physics (Intensive) ( Disciplinary Elective )
2022 Major in Risk Management ( Core/Compulsory )
2022 Major in Statistics ( Core/Compulsory )
2022 Minor in Actuarial Studies ( Disciplinary Elective )
2022 Minor in Computational & Financial Mathematics ( Core/Compulsory )
2022 Minor in Mathematics ( Core/Compulsory )
2022 Minor in Operations Research & Mathematical Programming ( Core/Compulsory )
2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory )
2021 Major in Chemistry (Intensive) ( Disciplinary Elective )
2021 Major in Decision Analytics ( Core/Compulsory )
2021 Major in Mathematics ( Core/Compulsory )
2021 Major in Mathematics (Intensive) ( Core/Compulsory )
2021 Major in Molecular Biology & Biotechnology (Intensive) ( Disciplinary Elective )
2021 Major in Physics (Intensive) ( Disciplinary Elective )
2021 Major in Risk Management ( Core/Compulsory )
2021 Major in Statistics ( Core/Compulsory )
2021 Minor in Actuarial Studies ( Disciplinary Elective )
2021 Minor in Computational & Financial Mathematics ( Core/Compulsory )
2021 Minor in Mathematics ( Core/Compulsory )
2021 Minor in Operations Research & Mathematical Programming ( Core/Compulsory )
Course to PLO Mapping 2025 Major in Chemistry (Intensive) < PLO 4,5 >
2025 Major in Mathematics < PLO 1,2,3 >
2025 Major in Mathematics (Intensive) < PLO 1,2,3 >
2025 Major in Molecular Biology & Biotechnology (Intensive) < PLO 3,4 >
2025 Major in Physics (Intensive) < PLO 2,3,4 >
2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 3,4 >
2024 Major in Chemistry (Intensive) < PLO 4,5 >
2024 Major in Decision Analytics < PLO 1,3 >
2024 Major in Mathematics < PLO 1,2,3 >
2024 Major in Mathematics (Intensive) < PLO 1,2,3 >
2024 Major in Molecular Biology & Biotechnology (Intensive) < PLO 3,4 >
2024 Major in Physics (Intensive) < PLO 2,3,4 >
2024 Major in Risk Management < PLO 2,3 >
2024 Major in Statistics < PLO 1 >
2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 3,4 >
2023 Major in Chemistry (Intensive) < PLO 4,5 >
2023 Major in Decision Analytics < PLO 1,3 >
2023 Major in Mathematics < PLO 1,2,3 >
2023 Major in Mathematics (Intensive) < PLO 1,2,3 >
2023 Major in Molecular Biology & Biotechnology (Intensive) < PLO 3,4 >
2023 Major in Physics (Intensive) < PLO 2,3,4 >
2023 Major in Risk Management < PLO 2,3 >
2023 Major in Statistics < PLO 1 >
2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 3,4 >
2022 Major in Chemistry (Intensive) < PLO 4,5 >
2022 Major in Decision Analytics < PLO 1,3 >
2022 Major in Mathematics < PLO 1,2,3 >
2022 Major in Mathematics (Intensive) < PLO 1,2,3 >
2022 Major in Molecular Biology & Biotechnology (Intensive) < PLO 3,4 >
2022 Major in Physics (Intensive) < PLO 2,3,4 >
2022 Major in Risk Management < PLO 2,3 >
2022 Major in Statistics < PLO 1 >
2021 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 3,4 >
2021 Major in Chemistry (Intensive) < PLO 4,5 >
2021 Major in Decision Analytics < PLO 1,3 >
2021 Major in Mathematics < PLO 1,2,3 >
2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
2021 Major in Molecular Biology & Biotechnology (Intensive) < PLO 3,4 >
2021 Major in Physics (Intensive) < PLO 2,3,4 >
2021 Major in Risk Management < PLO 2,3 >
2021 Major in Statistics < PLO 1 >
Offer in 2025 - 2026 Y        1st sem    2nd sem    Examination Dec    May     
Offer in 2026 - 2027 Y
Course Grade A+ to F
Grade Descriptors
A Demonstrate an excellent understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, clearly and elegantly presenting correct logical reasoning and argumentation and being able to carry out computations carefully and correctly, and with some innovative approaches to solving problems.
B Demonstrate a good understanding of key concepts and ideas by being able to identify the appropriate theorems and their applications through correctly analysing problems, but with some minor inadequacies in arguments, identifying the appropriate theorems or their applications and presentation or with some minor computational errors.
C Demonstrate an acceptable understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with some inadequacies in applying the theorems through incorrectly analysing problems with poor argument and presentation or a number of minor computational errors.
D Demonstrate some understanding of key concepts and ideas by being able to correctly identify appropriate theorems, but with substantial inadequacies in applying the theorems through incorrectly analysing problems with poor argument or presentation or with substantial computational errors.
Fail Demonstrate poor and inadequate understanding by not being able to identify appropriate theorems or their applications, or not being able to complete the solution.
Communication-intensive Course N
Course Type Lecture-based course
Course Teaching
& Learning Activities
Activities Details No. of Hours
Lectures 36.0
Tutorials 12.0
Reading / Self study Students are expected to watch videos online before classes. 100.0
Assessment Methods
and Weighting
Methods Details Weighting in final
course grade (%)		 Assessment Methods
to CLO Mapping
Assignments 10.0 1,2,3,4,5
Examination 50.0 1,2,3,4,5
Test 40.0 1,2,3,4,5
Required/recommended reading
and online materials		 Adrian Banner: The Calculus Lifesaver: All the Tools You Need to Excel at Calculus (Princeton University Press, 2007)
George B. Thomas, Maurice D. Weir and Joel Hass: Thomas' Calculus (12th edition, Addison Wesley)
Course Website http://moodle.hku.hk/
Additional Course Information


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