- #1
awholenumber
- 200
- 10
what is a good book to learn first order differential equations ??
MidgetDwarf, what are the topics that you found lacking in the book by Simmons?MidgetDwarf said:Ross: Differential Equations
Maurris Terrabaun (Not sure how this is spelled): It is a dover title.
Zill or Boyce/Prima: These are the standard textbooks used at universities. Generic, but get the job done.
I would purchase Ross and supplement it with either Boyce/Prima or Zill.
The Terrabaun book is also nice, but for some reason I prefer Ross.
My only complaint with Ross, is that the operator method section can be hard to read for some people. A few of my friends found that section to be incoherent. I found it readable. Laplace Transform is explained well, but Zill gives a bit more explanation. That is the only thing I liked about ZIll.
Zill/Boyce have harder plug and chug problems.
The book by Simmons: Differential Equations with Applications and Historical Notes, is also nice. I found it to concise for my needs. Lots of thinking problems. It is an interesting read, like all of Simmons books. Found the coverage lacking.
A first-order differential equation is a mathematical equation that involves an unknown function and its derivative. The derivative in this case is a first derivative, which means it is the rate of change of the function with respect to the independent variable.
The general form of a first-order differential equation is dy/dx = f(x,y), where y is the dependent variable and x is the independent variable. The function f(x,y) represents the relationship between the two variables and can be expressed in various forms, such as algebraic, trigonometric, or exponential.
There are several methods for solving first-order differential equations, including separation of variables, integrating factors, and substitution. Each method has its advantages and is used depending on the specific form of the equation.
First-order differential equations have numerous applications in various fields, including physics, chemistry, engineering, and economics. They are used to model and predict the behavior of dynamic systems, such as population growth, chemical reactions, and electrical circuits.
One common mistake when solving first-order differential equations is not checking for initial conditions. These are necessary to find the particular solution of the equation. Another mistake is not simplifying the final solution, which can lead to incorrect answers. It is also essential to check for any algebraic or arithmetic errors while solving the equation.