- #1

Hall

- 351

- 88

**Differential Equations and Boundary Value Problem ( Computing and Modelling)**by Edwards and Penney. There are several things in the book which I don't like

- Too much focus is given to modelling, almost every topic is explained not from mathematical point of view but from application point of view.
- Improved Euler's Method is not well explained, it has been made a kinda gravy of.
- Here is how they do separable differential equations:

**separable**provided that ##H(x,y)##

can be written as the product of a function of ##x## and a function of ##y##: ## \frac{dy}{dx} = g(x) h(y) = g(x)/f(y)##

where ##h(y) = 1/f(y)##. In this case the variables ##x## and ##y## can be separated [...] by writing informally the

equation ##f(y) dy = g(x) dx## which we understand to be concise notation for the differential equation ## f(y) \frac{dy}{dx} = g(x)##. It is easy to solve this type of differential equation simply by integrating both sides with respect to ##x##:

## \int f( y (x) ) \frac{dy}{dx} dx = \int g(x) dx +C##.

I mean to say that, first of all converting ##h(y)## to ##1/f(y)## was really not needed, we could simply take ##h(x)## to the denominator of LHS. And why not to simply integrate ## f(y) dy ## and ## g(x) dx##, (Prof. Jerison taught to do it that way only) why to take that ##dx## back again? Well, it may be due to some rules in academia or whatever, but I find it not very easy to understand and remember.

- The notation ##D_x## is used quite a lot, like ## D_x \left( \int P(x) dx \right) = P(x)## and has not been explained anywhere that it stands for ##\frac{d}{dx}##.

I've decided to change my book. I would like to you to recommend be books on differential equations which would help in self-teaching, books like Late. Prof. Mattuck's Introduction to Analysis, or books of Prof. Strong. Please make sure the books recommended should have following in its content:

- First-Order Differential Equations (Slope Fields, Method of Separation, Linear-first Order equations, Substitution Method)
- Numerical Methods and Mathematical models (Euler's Method, RK2, RK4)
- Linear Equations of Higher Order
- System of Differential Equations
- Laplace Transform Methods
- Eigenvalues method
- Intro to PDE

Thank you.