Describing the origin and basic knowledge of differential equations, Laplace transforms and Linear algebra

Developing problem solving skills on differential equations, Laplace transforms and Linear algebra

Studying the existence-uniqueness and other behaviors of solutions of a large class of differential equations, Laplace transforms and Linear algebra

Describing the solution procedure of differential equation using inverse Laplace transform

Discussing the application of differential equations, Laplace transforms and Linear algebra in various fields

To introduce students to the origin and use of differential equations, Laplace transform and Linear algebra

To provide the basic knowledge about differential equations, Laplace transform and Linear algebra

To provide the standard methods for solving differential equations, as well as methods based on the use of matrices or Laplace transforms

To demonstrate how differential equations can be useful in solving many types of problems

To develop numerical methods for solving differential equations

have an enhanced knowledge and understanding of differential equations, Laplace transforms and Linear algebra

be better able to use differential equation models to solve practical problems

be able to apply Laplace transforms for any real problem and data

be able to solve differential equations using Laplace transform methods

Differential Equation: Basic concept, classification, origin and application of differential equation (DE), Nature and methods of solution, Initial and boundary value problems, Existence of solutions.

First-Order Differential Equation: Standard forms of first-order and exact DEs,  Integrating factors, Separable and homogeneous equations, Linear DE, Bernoulli equations, Applications of first-order DE- orthogonal and oblique trajectories.

Higher-Order Differential Equation: Definition and basic existence theorem, Homogeneous equations, Reduction of order, Non-homogeneous equations, Homogeneous linear equation with constant coefficients, Method of undetermined coefficients, Variation of parameters, Cauchy- Euler equation, Application of DE in statistics.

Laplace and Inverse Laplace Transformation: Introduction, General properties, Function – Piecewise continuous, gamma, Bessel, Heaviside, Dirac delta, Periodic, Change of scale properties, Derivatives, Integrals, Multiplication by power, Initial and final value problems, Laplace transforms of systems, Applications of Laplace transformation to differential equations, and in statistics.

1)

Boelkins, M. R., J. L., Goldberg & M. C. Potter (2009). Differential equations with linear algebra. Oxford University Press USA.

2)

Ross, S.L. (1989). Differential Equations, 4th ed., Wiley, N.Y. [Solution]

3)

Arendt, W., C. J. Batty, M. Hieber, & F. Neubrander (2011). Vector-valued Laplace transforms and Cauchy problems. Springer.

4)

Ayres, F. (1997). Differential Equations, Schaum’s Outline Series, McGraw-Hill, NY.

5)

Goodge, S.M. (2000). Differential Equations and Linear Algebra, Prentice Hall, N.J., USA.

6)

Hirsch, M. W., S. Smale and R. L. Devaney (2004). Differential Equations, Dynamical Systems, and an Introduction to Chaos, Amsterdam, Elsevier.