How to self study effectively post graduation? I would like to know details about how one self studies entire courses or new areas of research post graduation? For example, I am an experimentalist with little exposure to numerical analysis (finite volume or element methods) and would like to develop sound understanding of the subject so as to expand my research area. I intend to start with variational calculus, matrix algebra, numerical methods for integration/differentiation from textbooks. 

However, I am curious, how does one self study effectively without assignments/exams which is typical of any structured coursework in academic setting? Do you solve all the problems in a book? Solve selected once? Search for online courses and attempt their assignments and questions? Do you also cover the entire books or just the topics you are interested in pursuing during future research?

Also, am curious, as an academic, how often do you have to learn a new course or subject through self-study to progress your research skills or career?

Any suggestions or advice would be most helpful!
This is a great question and just the mere fact that you are posing it indicates that you are serious about your pursuit in academia. Many students simply study for exams or for specific minimal requirements. "True" learning however occurs when the person freely seeks out knowledge, not to pass some arbitrary exam but to learn more about a subject. It reminds me of the old quote attributed to Mark Twain (although some dispute this) "I have never let my schooling interfere with my education".

If you're studying for self-study, try to be structured about it. One way is to create a KWL chart - it's a system to organize your studies. You divide a piece of paper or a page on a notebook to three parts:


What I Know | 2. What I Want to know | 3. What I Learned


By doing this, you can chart out what knowledge you possess of the topic currently, identify which gaps you have in your knowledge and then finally summarize what you have learned after you finished your study session. It's a good way of keeping track of what you're learning and systematizing your thoughts.