Help me understand Math by studying on my own without a lecturer

[grand666]

Hi guys,

I just registered before I go to work so I hope I'm allowed to ask this question here. If not I apologise, I'm quite in a hurry before work.

Homework Statement

I am completing my bachelors in Telecommunication through a distance education University from my home country. Why don't I study in the states? Well it will be more expense and have to transfer subjects etc etc.

I'm doing Engineering Mathematics IV and haven't done math in a while. Please if someone knows of some good resources on the web where I can learn the below sections it will be appreciated. I have a textbook but they use "higher english" if that makes sense. English is my second language and I'm fluent but the way the textbook is written is confusing.

I'm not looking for a spoon feed or anything, I study at least 3hrs a day and watch a lot of videos on subjects. The below ones I can't really seem to find any good sources that explain what they are and how to compute them.
Maybe if it's possibe, can you tell me what I need to know before I attempt these type of questions? I'm not totally lost but it takes time to tackle a new subject so if I can know what I need to know before hand then it will speed things up. I love math, just not when I'm stuck. :)

Here are some sections I need info on.

Complex Anaysis - mapping onto the w-plane from z-plane
Laurent Expansion
Show that the integral has a contour integral for a suitable path
How to find the transfer function of a given differential equation
The state space model using Laplace
How to determine the response of a system if a forcing function is applied at t=0
Write down the transfer function of a system initially in a quiescent state, and
show that it is not stable using the Ruth-Hurwitz criterion.
What is the state space model ex. x= AX + Bu; y = Cx
Method of convolution
Write down the difference equation if given a z-transform
How to solve state space equations by taking z-transforms and inverse matrix


Sorry I know it's a lot and probably confusing, I'm trying to finish this before work. It feels like I'm in over my head even though I'm studying every day like a book worm. I have to do a lot of catching up regarding simple calculus too coz I haven't done it in 6years.

Any advice would help. Thanks guys.

Homework Equations

The Attempt at a Solution

 

[lippyka]

For complex analysis, you can try looking at resources from Khan Academy, they have some helpful videos that explain the basics of complex analysis. For Laurent Expansion, you can check out the wikipedia page on Laurent Series, which will provide a good overview of the topic. For finding the transfer function of a differential equation, you can check out some online tutorials and videos that will explain the concept in detail. For the state space model using Laplace, you can refer to the textbook that you have or take a look at some online tutorials and videos that explain the concept in detail. For determining the response of a system if a forcing function is applied at t=0, you can refer to some online tutorials or videos that explain the concept in detail. You can also refer to your textbook for this topic. For the transfer function of a system initially in a quiescent state, you can refer to some online tutorials or videos that explain the concept in detail. You can also use the Ruth-Hurwitz criterion to determine the stability of the system. For the state space model, you can refer to the equation x= AX + Bu; y = Cx and understand how it works by referring to some online tutorials or videos. For the method of convolution, you can refer to some online tutorials or videos that explain the concept in detail. For writing down the difference equation if given a z-transform, you can refer to some online tutorials or videos that explain the concept in detail. For solving state space equations by taking z-transforms and inverse matrix, you can refer to some online tutorials or videos that explain the concept in detail.