Intercollegiate Classes
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- Lecturer: Profile: Peter Howell
Course information
General prerequisites:
Differential Equations 1 and Differential Equations 2 from Part A are prerequisites, and the material in these courses will be assumed to be known. Calculus of Variations and Fluids and Waves from Part A are desirable but not essential. Integral Transforms from Part A is strongly desirable.
Course term: Michaelmas
Course lecture information: 16 lectures
Course weight: 1
Course level: H
Assessment type: Written Examination
Course overview:
This course continues the Part A Differential Equations courses. In particular, first-order conservation laws are solved and the idea of a shock is introduced; general nonlinear and quasi-linear first-order partial differential equations are solved, the classification of second-order partial differential equations is extended to systems, with hyperbolic systems being solved by characteristic variables. Then Riemann's function, Green's function and similarity variable methods are demonstrated.
Learning outcomes:
Students will know a range of techniques to characterise and solve PDEs including non-linear first-order systems, and second-order. They will be able to demonstrate various principles for solving PDEs including the method of characteristics, Green's functions, similarity solutions and Riemann functions.
Course synopsis:
First-order equations; applications. Characteristics, domain of definition. [2 lectures]
Weak solutions, conservation laws, shocks. [2 lectures]
Non-linear equations; Charpit's equations; eikonal equation. [3 lectures]
Systems of partial differential equations, characteristics. Shocks; weak solutions. [3 lectures]
2nd order semilinear equations. Hyperbolic equations, Riemann functions. [2 lectures]
Elliptic equations, parabolic equations. Well-posed problems, Green's function, similarity solutions. [4 lectures]
Weak solutions, conservation laws, shocks. [2 lectures]
Non-linear equations; Charpit's equations; eikonal equation. [3 lectures]
Systems of partial differential equations, characteristics. Shocks; weak solutions. [3 lectures]
2nd order semilinear equations. Hyperbolic equations, Riemann functions. [2 lectures]
Elliptic equations, parabolic equations. Well-posed problems, Green's function, similarity solutions. [4 lectures]
Section outline
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Work submission deadline is 72 hours before each class.
- Class 1 Tutor: Andreas Münch; TA: Renjing Wang
- 15.30-17.00 Wednesday weeks 3,5,7 in room C3; 14:00-15:30 Thursday week HT1 in room C3
- Class 2 Tutor: Andreas MΓΌnch; TA: Ellen Li
- 15.30-17.00 Thursday weeks 3,5,7 in room C3; 15:30-17:00 Thursdays week HT1 in room C3
- Class 3 Tutor: Peter Howell; TA: Emma Johnson
- 9-10:30 Friday weeks 3,5,7 in room C1; 9-10:30 Friday week HT1 in room C2
- Class 4 Tutor: William Gillow; TA: Mohamed Yalaoui
- 15:30-17:00 Monday weeks 4,6,8 in room C2 and 15:30-17:00 Monday week HT1 in room C2
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Registration start: Monday, 5 October 2026, 12:00 PMRegistration end: Friday, 6 November 2026, 12:00 PM
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Class Tutor's Comments Assignment
Class tutors will use this activity to provide overall feedback to students at the end of the course.