Enquiry for Science Major/Minor/Programme Requirements
MATH4406 Introduction to partial differential equations (6 credits) Academic Year 2025
Offering Department Mathematics Quota ---
Course Co-ordinator Dr H Y Zhang, Mathematics < hyzhang@maths.hku.hk >
Teachers Involved (Dr H Y Zhang,Mathematics)
Course Objectives This course introduces students to the basic techniques for solving partial differential equations as well as the underlying theories.
Course Contents & Topics - Laplace, heat and wave equations. Classification of partial differential equations. Boundary-value, initial-value and eigenvalue problems. Separation of variables, Fourier series, linearity and superposition, Duhamel's principle, characteristic method.
- Green's function, generalized functions and fundamental solutions.
- Maximum principle, existence, uniqueness and continuous dependence on data.
- If time permits Cauchy-Kowalevski theorem, variational method, nonlinear partial differential equations.
Course Learning Outcomes
On successful completion of this course, students should be able to:

CLO 1 apply the tools of calculus, linear algebra, mathematical analysis in a coherent way to PDE problems
CLO 2 understand the basic theory of partial differential equations and the methods to solve them
CLO 3 apply the knowledge of partial differential equations to physical sciences and engineering
Pre-requisites
(and Co-requisites and
Impermissible combinations)		 Pass in MATH2101, MATH2102, MATH2241; and
Pass in MATH3405, or already enrolled in this course.
Course Status with Related Major/Minor /Professional Core 2025 Major in Mathematics ( Disciplinary Elective )
2025 Major in Mathematics (Intensive) ( Core/Compulsory )
2025 Minor in Mathematics ( Disciplinary Elective )
2024 Major in Mathematics ( Disciplinary Elective )
2024 Major in Mathematics (Intensive) ( Core/Compulsory )
2024 Minor in Mathematics ( Disciplinary Elective )
2023 Major in Mathematics ( Disciplinary Elective )
2023 Major in Mathematics (Intensive) ( Core/Compulsory )
2023 Minor in Mathematics ( Disciplinary Elective )
2022 Major in Mathematics ( Disciplinary Elective )
2022 Major in Mathematics (Intensive) ( Core/Compulsory )
2022 Minor in Mathematics ( Disciplinary Elective )
2021 Major in Mathematics ( Disciplinary Elective )
2021 Major in Mathematics (Intensive) ( Core/Compulsory )
2021 Minor in Mathematics ( Disciplinary Elective )
Course to PLO Mapping 2025 Major in Mathematics < PLO 1,2,3 >
2025 Major in Mathematics (Intensive) < PLO 1,2,3 >
2024 Major in Mathematics < PLO 1,2,3 >
2024 Major in Mathematics (Intensive) < PLO 1,2,3 >
2023 Major in Mathematics < PLO 1,2,3 >
2023 Major in Mathematics (Intensive) < PLO 1,2,3 >
2022 Major in Mathematics < PLO 1,2,3 >
2022 Major in Mathematics (Intensive) < PLO 1,2,3 >
2021 Major in Mathematics < PLO 1,2,3 >
2021 Major in Mathematics (Intensive) < PLO 1,2,3 >
Offer in 2025 - 2026 Y        1st sem    Examination Dec     
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 100.0
Assessment Methods
and Weighting
Methods Details Weighting in final
course grade (%)		 Assessment Methods
to CLO Mapping
Assignments 10.0 1,2,3
Examination 50.0 1,2,3
Test 40.0 1,2,3
Required/recommended reading
and online materials		 - W.A. Strauss: Partial Differential Equations: An Introduction, Hoboken, N.J. : Wiley c2008 2nd ed.
- R. Haberman: Applied partial differential equations: with Fourier series and boundary value problems, Boston : Pearson c2013 5th ed.
- D. Bleecker & G. Csordas: Basic partial differential equations, Cambridge, Mass. : International Press c1996
- L.C. Evans: Partial differential equations, Providence, R.I. : American Mathematical Society c2010 2nd ed.
Course Website http://moodle.hku.hk/
Additional Course Information


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