Differential Equations: why given after calculus 3?

nycfunction

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I have never taken differential equations. Why is this course given after calculus 3?
 
Re: Differential Equations

It may depend on the school. For example, If DE is considered "advanced hours", it would logically come after the calculus sequence. In reality, it can be taught after the second semester of calculus. What is now covered in Calc III is similar to what used to be considered as "Advanced Calculus", which was an elective in junior colleges (as was DE) and would not transfer to a 4-year college as "advanced" or upper division hours.

Some of the topics in a DE course can be taught as part of other advanced courses in math. For example, solution by Laplace transform, linear differential operators, and possibly series solutions could be covered in other courses.
 
Just a question (if you don't mind nycfunction), what do Calc I, II, and III courses consist of? It seems to be a standard US thing to call them as such ...

Also, what would come after your standard calculus classes? I'm going into pharmacy next year but I'd like to keep up with undergraduate math on my own time. Would analysis come up next? Where would linear algebra, topology, tensor calculus, etc. (words that have no meaning to me at the moment) fit in ?
 
o_O said:
Just a question (if you don't mind nycfunction), what do Calc I, II, and III courses consist of? ...Also, what would come after your standard calculus classes? ...Where would linear algebra, topology, tensor calculus, etc. (words that have no meaning to me at the moment) fit in ?
Calculus 1: Limits, derivatives, differentiation of functions of one variable; applications to motion problems, maximum-minimum problems, curve sketching, and mean-value theorems and a few other topics.

Calculus 2: Inverse functions; logarithmic and exponential functions; integration of functions; and applications of the definite integral, including area, volume, and arc length.

Calculus 3: Vectors in two and three dimensions, equations of lines and planes, functions of several variables, partial differentiation, directional derivatives, and multiple integration; line integrals; and infinite series and power series in one variable.

Some colleges teach Linear Algebra after calculus 3 but most go right into Differential Equations.

Linear Aglebra: Vector spaces, systems of linear equations, determinants, linear transformations, and matrices.

Topology has now become an elective and NOT a requirement for math majors. Students who take topology do so after taking at least 10 math courses in the math major program. Topology, even at its basic level, is mind boggling, to say the least. What does it cover?

Topology: Sets functions, metric spaces, topological spaces, neighborhoods, continuity, connectedness, homotopy, fundamental groups, and compactness.

Math analysis is taught between Linear Algebra and Differential Equations. Math analysis is usually taught in two semesters: They call it Analysis 1 and 2.

Math Analysis 1: Introduction to real analysis, the real number system, limits, continuity, differentiation, the mean value and Taylor's theorems and applications. Riemann integration and improper integrals.

Math Analysis 2: Infinite series and power series, pointwise and uniform convergence, ndimensional Euclidean space, metric spaces, functions from Rn to Rm, continuity, and the differential as a linear map: inverse and implicit function theorems.

Of course, every college has their own set of courses and when to take them.
 
o_O said:
Just a question (if you don't mind nycfunction), what do Calc I, II, and III courses consist of? It seems to be a standard US thing to call them as such ...

Also, what would come after your standard calculus classes? I'm going into pharmacy next year but I'd like to keep up with undergraduate math on my own time. Would analysis come up next? Where would linear algebra, topology, tensor calculus, etc. (words that have no meaning to me at the moment) fit in ?

Calc I is differentiation, Calc II is integration, Calc III can be multi-dimensional applications, including surfaces of revolution, etc., infinite series, and many more topics. Either real or complex analysis courses may follow. Linear algebra may or may not explicitly need concepts from calculus, depending on the text and the syllabus. Topology is a generalization of geometry but usually needs analysis as a pre-requisite. Tensor calculus, also called differential geometry, can contain linear algebra and calculus as well as elements of non-Euclidean geometry and other topics. It is quite useful in physics, since general relativity is traditionally explained in these terms.
 
nycfunction said:
I have never taken differential equations. Why is this course given after calculus 3?
Generally, First order linear ordinary differential equation is taught right after teaching antiderivatives - as in AP calculus AB (may be BC). This is generally taught as rate problems - a practical application of anti-derivatives..
 
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