Should I Take Advanced ODE Without Completing Algebra 2?

[JG89]

Hey guys, I am currently going into my second year at U of T (Toronto).

In my first semester, I have to take a course called "Advanced Ordinary Differential Equations". Its course description is: "First-order equations. Linear equations and first-order systems. Non-linear first-order systems. Existence and uniqueness theorems for the Cauchy problem. Method of power series. Elementary qualitative theory; stability, phase plane, stationary points. Examples of applications in mechanics, physics, chemistry, biology and economics.".

I HAVE to take it first semester, because it isn't offered second semester. The thing is, I haven't taken the pre-requisite for it, Algebra 2, which I was suppose to take last year but couldn't due to other reasons. Here is the course description for Algebra 2: "A theoretical approach to real and complex inner product spaces, isometries, orthogonal and unitary matrices and transformations. The adjoint. Hermitian and symmetric transformations. Spectral theorem for symmetric and normal transformations. Polar representation theorem. Primary decomposition theorem. Rational and Jordan canonical forms. Additional topics including dual spaces, quotient spaces, bilinear forms, quadratic surfaces, multilinear algebra. Examples of symmetry groups and linear groups, stochastic matrices, matrix functions."

Now, the math department doesn't care about pre-requisites. I can take the ODE course first semester and its pre-req, Algebra 2, second semester. Their philosophy is to let us go ahead and take the courses, and if we fail then we fail. I'm just worried about taking the ODE course this coming september, when I haven't covered Algebra 2. I mean, in the month that I have left until September I could try to cover as much as I can, but there's no way I am going to complete it by September. Keep in mind that I need to take the ODE course in September if I want to keep on track with my studies. I will have to stay behind an extra year if I don't take this course.

What should I do?

 

[Newtime]

Hey guys, I am currently going into my second year at U of T (Toronto).

In my first semester, I have to take a course called "Advanced Ordinary Differential Equations". Its course description is: "First-order equations. Linear equations and first-order systems. Non-linear first-order systems. Existence and uniqueness theorems for the Cauchy problem. Method of power series. Elementary qualitative theory; stability, phase plane, stationary points. Examples of applications in mechanics, physics, chemistry, biology and economics.".

I HAVE to take it first semester, because it isn't offered second semester. The thing is, I haven't taken the pre-requisite for it, Algebra 2, which I was suppose to take last year but couldn't due to other reasons. Here is the course description for Algebra 2: "A theoretical approach to real and complex inner product spaces, isometries, orthogonal and unitary matrices and transformations. The adjoint. Hermitian and symmetric transformations. Spectral theorem for symmetric and normal transformations. Polar representation theorem. Primary decomposition theorem. Rational and Jordan canonical forms. Additional topics including dual spaces, quotient spaces, bilinear forms, quadratic surfaces, multilinear algebra. Examples of symmetry groups and linear groups, stochastic matrices, matrix functions."

Now, the math department doesn't care about pre-requisites. I can take the ODE course first semester and its pre-req, Algebra 2, second semester. Their philosophy is to let us go ahead and take the courses, and if we fail then we fail. I'm just worried about taking the ODE course this coming september, when I haven't covered Algebra 2. I mean, in the month that I have left until September I could try to cover as much as I can, but there's no way I am going to complete it by September. Keep in mind that I need to take the ODE course in September if I want to keep on track with my studies. I will have to stay behind an extra year if I don't take this course.

What should I do?

IMO you'll be fine either way. From the descriptions you gave, I can't picture you needing anything more than basic liner algebra for your ODE course (although I haven't heard of Elementary qualitative theory, so I can't say for sure).

 

[Monocles]

You should be fine taking differential equations. Some things will seem a bit more mysterious from a conceptual point of view than they would have otherwise, but the only linear algebra used in a first class on differential equations is finding the eigenvalues/eigenvectors of a matrix, which is a very straightforward mechanical process that they will probably teach you in the course anyways (if only as a review). Plus, most students do not yet understand what the significance of eigenthings when they take differential equations anyways! I know I didn't.