Math2351: Introduction to Differential Equations  

Syllabus: Refer to Canvas for details and updated information

Instructor

Mo Mu

Contact Details: Rm 3457; phone: 2358-7446; e-mail: mamu@ust.hk

Course Description

Credits: 3 units; Topic: Differential equations

Exclusions: MATH 2350, MATH 2352

Prerequisites: AL Pure Mathematics/AL Applied Mathematics; or MATH 1014; or MATH 1018; or MATH 1020; or MATH 1024

Textbook:

Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems, Global Ed., Wiley

 

Course Topics:

·  Introduction(Chapter 1)

o   Mathematical models; Direction Fields (1.1)

o   Solution of Some DEs(1.2)

 

·  First Order Equations(Chapter 2)

o   Linear equations; Method of Integrating Factors (2.1)

o   Separable equations (2.2)

 

·  Second Order Linear Equations(Chapter 3)

o   Homogeneous Equations with constant coef. (3.1, 3.3 and 3.4)

o   Solutions of linear homogeneous equations; the Wronskian (3.2)

o   Nonhomogeneous equations; undetermined coef. (3.5)

·  Series Solutions of Second Order Linear Equations (Chapter 5)

o   Power series (5.1)

o   Series solutions near an ordinary point (5.2)

o   Euler Equations; Regular Singular Points (5.4)

 

·  Laplace Transform (Chapter 6)

o   Laplace transform (6.1)

o   Initial value problems (6.2)

o   Step functions (6.3- 6.4)

o   Impulse functions (6.5)

 

·  Systems of First Order Linear Equations (Chapter 7)

o   Introduction (7.1)

o   Basic theory (7.4)

o   Homogeneous linear systems with constant coefficients (7.5, 7.6)

 

·  Partial Differential Equations and Fourier Series (Chapter 10, optional)

o   Two-Point Boundary Value Problem (10.1)

o   Fourier Series (10.2, 10.4)

o   Separation of Variables; Heat Conduction in a Rod (10.5)

o   Laplace Equation (10.8)