Enquiry for Course Details
MATH2014 Multivariable calculus and linear algebra (6 credits) Academic Year 2026
Offering Department Mathematics Quota ---
Course Co-ordinator Dr H Y Zhang, Mathematics < hyzhang@maths.hku.hk >
Teachers Involved (Dr H Y Zhang,Mathematics)
(Dr M Zindulka,Mathematics)
Course Objectives To provide students with a solid foundation in calculus of several variables and linear algebra, which they will need in the study of mathematics related subjects.
Course Contents & Topics - Vectors and Matrices: Vectors in space, dot product and cross product, determinants (with geometric interpretations).
- Partial Derivatives: Functions of several variables, partial derivatives, extreme values and Lagrange multipliers, Taylor's formula.
- Multiple Integrals: Double and triple integrals, substitution in multiple integrals.
- Matrix Algebra: Matrix addition and multiplication, system of linear equations as a matrix equation.
- Vector Spaces: The Euclidean spaces as vector spaces, its subspaces, span of vectors, linear independence, basis and dimension.
- Eigenvalues and Eigenvectors: Diagonalization and computing powers.
- Numerical Methods: Bisection method and Newton's method for finding roots of equations, Simpson's rule and Trapezoidal rule for numerical integration.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 understand the geometric meaning of partial and directional derivatives
CLO 2 optimize multivariate objective functions (with/without constraints)
CLO 3 evaluate integrals over curvilinear regions in space
CLO 4 understand the concept of vector spaces, basis, dimension
CLO 5 solve simple eigenvalue problems and apply the theory to practical problems
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 Pass in MATH1013 or (MATH1851 and MATH1853) or MATH1861.
Not for students who have passed MATH2822 or (MATH2101 and MATH2211), or have already enrolled in these courses.
Course Status with Related Major/Minor /Professional Core 2U000C00 Course not offered under any Major/Minor/Professional core
2026 Minor in Computational & Financial Mathematics ( Disciplinary Elective )
2026 Minor in Mathematics ( Disciplinary Elective )
2026 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective )
2025 Minor in Computational & Financial Mathematics ( Disciplinary Elective )
2025 Minor in Mathematics ( Disciplinary Elective )
2025 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective )
2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory )
2024 Major in Decision Analytics ( Core/Compulsory )
2024 Major in Risk Management ( Core/Compulsory )
2024 Major in Statistics ( Core/Compulsory )
2024 Minor in Computational & Financial Mathematics ( Disciplinary Elective )
2024 Minor in Mathematics ( Disciplinary Elective )
2024 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective )
2023 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory )
2023 Major in Decision Analytics ( Core/Compulsory )
2023 Major in Risk Management ( Core/Compulsory )
2023 Major in Statistics ( Core/Compulsory )
2023 Minor in Computational & Financial Mathematics ( Disciplinary Elective )
2023 Minor in Mathematics ( Disciplinary Elective )
2023 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective )
2022 Bachelor of Arts and Sciences in Applied Artificial Intelligence ( Core/Compulsory )
2022 Major in Decision Analytics ( Core/Compulsory )
2022 Major in Risk Management ( Core/Compulsory )
2022 Major in Statistics ( Core/Compulsory )
2022 Minor in Computational & Financial Mathematics ( Disciplinary Elective )
2022 Minor in Mathematics ( Disciplinary Elective )
2022 Minor in Operations Research & Mathematical Programming ( Disciplinary Elective )
Course to PLO Mapping 2024 Bachelor of Arts and Sciences in Applied Artificial Intelligence < PLO 3,4 >
2024 Major in Decision Analytics < PLO 1,3 >
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 Decision Analytics < PLO 1,3 >
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 Decision Analytics < PLO 1,3 >
2022 Major in Risk Management < PLO 2,3 >
2022 Major in Statistics < PLO 1 >
Offer in 2026 - 2027 Y        1st sem    2nd sem    Examination Dec    May     
Offer in 2027 - 2028 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 analyzing 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 analyzing 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 analyzing 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 analyzing 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 100.0
Assessment Methods
and Weighting
Methods Details Weighting in final
course grade (%)		 Assessment Methods
to CLO Mapping
Assignments assignments, tutorials, participation, etc 5.0 1,2,3,4,5
Examination 50.0 1,2,3,4,5
Test 3 tests 45.0 1,2,3,4,5
Required/recommended reading
and online materials		 TBC
Course Website http://moodle.hku.hk/
Additional Course Information


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