National Taiwan Normal University Course Outline
 Spring , 2026

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I.Course information
Serial No. 2668 Course Level Undergraduate / Master
Course Code MAC0133 Chinese Course Name 偏微分方程導論（二）
Course Name Introduction to Partial Differential Equations (II)
Department Department of Mathematics
Two/one semester 1 Req. / Sel. Sel.
Credits 3.0 Lecturing hours Lecture hours: 3
Teach in English Y Teach in National Languages
Prerequisite Course
Comment
Course Description
Day & Class Period/Location Fri. 2-4 Gongguan M311
Curriculum Goals Corresponding to the Departmental Core Goal
1.　Let students understand some basic theories of partial differential equations Master:
　1-1 Equipped with professional mathematics competences
　1-2 Being able to reason and induct with mathematical logic
　1-4 Possessing the abilities to propose and solve questions in advanced mathematics
　3-1 Being able to seek out answers with the attitudes of patience, diligence, concentration, and curiosity
　3-4 Having insights, intuitions, and senses of mathematics
2.　Recognize equations derived in other fields and understand the meaning of the original problem by the mathematical analysis Master:
　1-5 Being able to use mathematics as tools to learn other subjects
　4-4 Possessing global views from both scientific and humanistic perspectives, and being able to appreciate the values of other knowledge fields

II. General Syllabus
Instructor(s) CHERN, Jann-Long/ 陳建隆
Schedule

This is one of the EMI courses. In this course I and II, we will conduct an in-depth investigation into the fundamental principles and techniques used in partial differential equations (PDEs).

Partial differential equations arise in many scientific and engineering modeling processes. With a history spanning over two centuries, PDEs have evolved from the study of physical and geometric problems into an independent branch of mathematics, encompassing a wide range of topics and diverse methods. The problems discussed in PDEs are connected to fields such as physics, mechanics, biology, geometry, and chemistry. Modern tools are often employed to solve these problems. In recent years, research in this field has flourished, making it a valuable course for undergraduate and graduate students in science and engineering disciplines to learn and explore.

1. After a brief review of the ordinary differential equations knowledge used in this course, we will begin with the motivation: the origin and derivation of partial differential equations in three basic forms (heat conduction, wave, and gravitational). Furthermore, in the Course II, we will study the topics: Sobolev Spaces; 2nd-Order Elliptic PDE; Linear Evolution equations; introduction of the Calculus of Variations (if the studying time is enough).
2. If the studying time is enough,  after learning the basic theory and properties of each type of equation, we will quickly explore their individual applications. 

Below is our tentative learning schedule for  these PDE Course I and Course II, and the courses content and schedule may be adjusted based on students' actual learning progress and outcomes:

Part I.  Four important linear partial differential equations and their basic propertiesend   cccccccc
1. Transport Equation 
2. Laplace's Equation 
3. Heat Equation 
4. Wave Equation 

Part II: Theory for linear partial differential equations

  • Sobolev spaces

  •  Second-order elliptic equations

  •  Linear evolution equations

  •  Introduction of the calculus of variations (if the studying time is enough) 
Instructional Approach
Methods Notes
Formal lecture In this course: (1) After a brief review of the ordinary differential equations knowledge used in this course, we will begin with the motivation: the origin and derivation of partial differential equations in three basic forms (heat conduction, wave, and gravitational); (2) After learning the basic theory and properties of each type of equation, we will quickly explore their individual applications.
Group discussion The key points of the related studying topics are discussed in groups by students, TA and teacher.
Grading assessment
Methods Percentage Notes
Assignments 20 % The students of the course will report in groups the related properties and theorems for each selected mathematical models.
Final exam 30 % We plan to give a final test for this course.
Class discussion involvement 20 % We will ask the group discussions and seminar to test the students for the study of basic related mathematical models and knowledge.
Presentation 30 % For each group students will read and give a report of selected exercises and related topics.
Adjustment methods for students
Required and Recommended Texts/Readings with References

References:

1. L.C. Evans, Partial Differential equations
2. F. John, Partial Differential Equations

 

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