DIFFERENTIAL EQUATIONS

Compulsory course 3 Credits.

Theory +Practice: 3 credits

I. Overview This course provides: - First- order Differential Equations.Higher-order Differential . Equations. Linear Differential Equations. Systems of Differential Equations. Existence and Uniqueness Theory.

II. Prerequisites. Analysis1, Analysis 2

III. Contents

Chapter 1: FIRST ORDER DIFFERENTIAL EQUATIONS

1.1 Separation of variables.

1.2 Linear equation.

1.3 Existence- uniqueness theorem for solution of Cauchy problem..

1.4 Kinds of solutions.

1.5 Solving a homogeneous equation of degree zero.

1.6 Solving an exact differential equation.

1.7 Solving Bernoulli equations, Riccati equations.

1.7 Using Maple and Mathematica to solve a differential Equation.

1.8 Strange solutions.

.Chapter 2: SECOND- AND HIGHER- ORDER LINEAR DIFFERENTIAL EQUATIONS

2.1 Existence- uniqueness theorem for linear initial-value problems.

2.2 Fundamental solutions of a homogeneous linear equation.

2.3 Wronskian determinant of solutions. Ostrogradski-Liouville formula.

3.3 Finding a particular solution.

3.4 Solutions of non- homogeneous linear equations.

3.5 Some special equations.

3.6 Laplace transforms.

Chapter 3: SYSTEMS OF FIRST ODER DIFFERENTIAL EQUATIONS

3.1 Linear operators for systems of first-order equations.

3.2 Writing a higher-order linear differential equation as a first-order system.

3.3 Existence- uniqueness theorem for solution of an initial-value problem.

3.4 Fundamental solutions of a homogeneous first-order linear system.

Wronskian determinant of solutions.

3.5 Solving a first-order linear system by using matrix eigenvalues.

3.5 Solving a first-order linear system by using exponential matrix.

3.6 Stability of first-order linear systems.

IV. References

[1] Hoang Huu Duong – Vo Duc Ton- Nguyen The Hoan, Differential equations (Vietnamese), University Publisher 1970.

[2] Edwards & Penny, Differential equations, , Pearson Education, Inc., 2004.

[3] Bruce P. Conrac , Differential equations, Pearson Education, Inc., 2003.

[4] Elementary Differential Equations, William R. Derrick – Stanley I. Grossman, 1997.