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dm84z28
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Hello alll. i am enrolled in Differential Equation Calc this semester. i was wondering what kind of stuff will i be doing and what should i expect in terms of difficulty etc. thanks in advance
I assume you've had basic algebra so you should be familiar with classical equation in 1 or more variables. I also assume that you've had basic calculus, derivatives and integrals. With differential equations, these two fundamental concepts of calculus meet each other. In these equations, the unknown is no longer just 'x' (or more variables) but a function y and its derivatives (y', y'', ...).dm84z28 said:Hello alll. i am enrolled in Differential Equation Calc this semester. i was wondering what kind of stuff will i be doing and what should i expect in terms of difficulty etc. thanks in advance
dicerandom's comment reminds me of the nickname our instructor had for DiffEQ. He called the course "Difficult Equations".dm84z28 said:Hello alll. i am enrolled in Differential Equation Calc this semester. i was wondering what kind of stuff will i be doing and what should i expect in terms of difficulty etc. thanks in advance
HallsofIvy said:I honestly don't know what "Differential Equation Calc" means. Normally you take several courses in calculus before taking "Differential Equations" because you have to really know calculus well before you can understand differential equations. I would have thought an engineering course would do more than just teach you how to use a program to solve differential equations!
[tex]y[x]=c_1-c_2Cos[x]+1/2e^x\left(Sin[x]-Cos[x]\right)[/tex]
[tex]y^{''}[x]-\frac{1}{Tan[x]}y^{'}[x]==e^x Sin[x]\text{//Simplify}[/tex]
A differential equation is a mathematical equation that describes the relationship between a function and its derivatives. It involves the use of derivatives to express the rate of change of a function at any given point.
Differential equations are used in calculus to model real-world phenomena and predict how they will change over time. They are also used to solve problems involving rates of change, such as in physics, engineering, and economics.
There are various methods for solving differential equations, depending on its type and order. Some common techniques include separation of variables, substitution, and using integrating factors. Computer software and numerical methods can also be used to solve more complex equations.
Ordinary differential equations (ODEs) involve a single independent variable, while partial differential equations (PDEs) involve multiple independent variables. ODEs also have a single derivative, while PDEs can have multiple derivatives of different variables.
Differential equations have many applications in various fields, such as physics, engineering, biology, economics, and finance. They are used to model and understand natural phenomena, such as population growth, heat transfer, and fluid flow. They are also used in designing and optimizing systems and processes, such as in control theory and signal processing.