# Prerequisites for learning Linear Differential Equations, Transforms, Vector Calculus & Complex Variables?

I am going into Computer Science undergrad level Math this semester and it's been a while since High School. Could someone advice on what kind of prerequisites is needed for learning the following:

Linear Differential Equations (LDE)
- LDE of nth order with constant coefficients
- Method of variation of parameters
- Cauchy's & Legendre's LDE
- Simultaneous & Symmetric Simultaneous DE
- Modelling of Electric Circuits

Transforms
- Fourier Transforms
- Complex exponential form Fourier series
- Fourier Integral Theorem
- Fourier Sine & Cosine Integrals
- Fourier Sine & Cosine transforms & their inverses
- Z Transform (ZT)
- Standard Properties - ZT of standard sequences & their inverse

Vector Calculus
- Vector differentiation
- Directional derivative
- Solenoid and Irrigational fields
- Vector identities. Line, Surface and Volume integrals
- Green‘s Lemma, Gauss‘s Divergence theorem and Stoke‘s theorem

Complex Variables
- Functions of Complex variables
- Analytic functions
- Cauchy-Riemann equations
- Conformal mapping
- Bilinear transformation
- Cauchy‘s integral theorem & Cauchy‘s integral formula
- Laurent‘s series, and Residue theorem

That's straight out of the "contents" page.

I can imagine I would need to learn concepts of Limits & Continuity, Derivation, Integration. Some basic Algebra, quadratic equations, differential equations. That much is obvious.

But...
Do I need things like 3D Geometry & Conic Sections? (equations of Ellipse, Parabola, Hyperbola etc)
Do I need to learn Sequences and Series (Arithmetic Progressions, Geometric Progressions?)
Matrices? Determinants? Binomial Theorem?
I had all that in High School. And more..

For Linear Differential Equations, you will need basic calculus (differentiation and integration in one variable) and linear algebra (matrices, determinants, eigenvalues and eigenvectors).

For Vector Calculus you will need linear algebra and basic calculus as well.

For Complex Variables, you will need basic calculus and sequences and series (more specifically, Taylor series, and geometric series might be desirable).

For Fourier Series, you will need basic calculus, sequences and series and complex variables.

• That's strange. In my book.. Fourier Series is a chapter before Complex Variables...how did they expect us to comprehend Fourier if we hadn't first studied complex variables. May 10, 2019 at 20:08
• Some measure theory is helpful for Complex Analysis, imo
– user515599
May 10, 2019 at 20:09
• @badatmath In my experience, Riemann-Stieltjes integration is often enough to understand basic Complex Analysis (at least what OP will probably see). May 14, 2019 at 17:59
• @BhooshanAJ You can understand Fourier Series as just a series using sines and cosines, but I think the theory is much richer using Complex Analysis, if you use complex exponentials and such. May 14, 2019 at 18:02