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