Dingqun Deng's personal website
As a tutor or teaching assistant
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Spring 2023, Interacting Particle Systems and Their Large Scale Behavior II, BSIMA, TA
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Fall 2023, Interacting Particle Systems and Their Large Scale Behavior I, BSIMA, TA
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Spring 2022, Geometric numerical methods for dynamical systems, BSIMA, TA
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Fall 2022, Symplectic Geometric Method of Hamiltoian Systems, BSIMA, TA
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Spring 2021, MA2181 Mathematical Methods for Engineering, CityU, Tutor & TA
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Fall 2021, MA2177 Engineering Mathematics and Statistics, CityU, Tutor & TA
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Spring 2020, MA3515 Introduction to Optimization, CityU, Tutor & TA
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Fall 2020, MA1201 Calculus and Basic Linear Algebra II, CityU, Tutor & TA
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Spring 2019, MA1200 Calculus and Basic Linear Algebra I, CityU, Tutor & TA
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Fall 2019, MA3001 Differential Equations I, CityU, Tutor & TA
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Spring 2018, MA1200 Calculus and Basic Linear Algebra I, CityU, Tutor & TA
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Fall 2018, MA1201 Calculus and Basic Linear Algebra II, CityU, Tutor & TA
Some notes
Contents:
1. Approximation by smooth functions;
Partition of unity; Green formula;
2. Extension theorem;
3. Trace theorem (building);
4. Embedding theorem (building);
5. Poincare and Hardy inequality;
6. Differential quotient;
7. Dual space;
8. Time-dependent spaces;
Teaching
2018.2
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2018.9
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2019.1
Contents:
1. Basic Properties of Resolvent and Spectrum.
2. Fredholm Operator
3. Essential Spectrum
4. Perturbation of Fredholm
5. Some index theory
5. Riesz projection and functional calculus
6. Riesz projection and eigenvalues
7. Essential Specturm and Eigenvalues by using complex analysis
Contents:
1. Unbounded linear operator, Graph norm
2. Ajoint of unbounded operator
3. Riesz projection and functional calculus
4. Perturbation of Fredholm
Contents: (maybe finished)
1. Semigroup to generator;
2. Generator to semigroup (Hille-Yoshida);
3. Perturbation of generator/semigroup;
4. Inversion Formula;
5. Disspative operator;
Contents:
1. Derivation of the linearized collision operator L = -\nu + K
2. Properties of the function \nu and operator K
3. Spectrum of the cut-off L
4. Solution on an interval [T, T+1]
5. Global solution with initial data having exponential decay