I need advice in building self-study courses?

Question

My course covers topics on calculus. Having looked at what I built, it will be a long process, I think that it is worth cutting down some topics of the topic that would not take too much time to study. I actually only have 30-120 minutes to study the subject per day.

My plan for the moment: 1)Precalculus 2)Differential calculus 3)Integral calculus 4)Ap Calculus BC 5)Calculus 1 6)Calculus 2 7)Multivariable calculus

I am engaged in Khan Academy. And in general, having spent two weeks on drawing up a plan a year ago, I think that it is worth reducing as certain topics between themselves recur. In general, I would like to hear from those who study at the Khan Academy. But I would also be grateful to those who simply have already studied and mastered all these topics. What could you give advice on what can be removed and what can be studied. I will be grateful.

PS I am 21 years old and at the moment I speak only the basics of algebra, now I have mastered 67% of the course of algebra 1. The basic course consists of: 1)algebra basic 2)algebra 1 3)algebra 2 3)Trigonometry 4)Precalculus

Answer 1

It is rather redundant to first study differential and integral calculus, followed by AP Calculus BC, only to then return to calculus 1 and 2. These courses are essentially equivalent to the first three and unless you would like to review there is not much point in studying them again.

Your plan otherwise seems fine, although knowing the context of why you are studying calculus would help in creating a more detailed plan. You may, for example, be interested in including a course in differential equations in your study. Differential equations are prevalent throughout the sciences, particularly physics. Complex analysis after differential equations may be useful as well for applications to other fields. If you are more interested in math for its own sake, consider a course in real analysis as well. This will put the calculus you study on Khan Academy on a rigorous foundation.

Answer 2

I would recommend searching for a good textbook to work from. A quick Google search on multivariable calculus brought up Single and Multivariable Calculus Early Transcendentals by David Guichard. This textbook appears to introduce the reader to the basics in the introductory chapters, and then goes on to explore the more advanced material.

I suspect that textbook writers, who spend a lot of time researching pedagogical techniques, are your best allies on this one. In many of my calculus classes, the first 1 to 4 chapters were skipped because they were introductory material. I think those chapters are written for individuals like you. In this way, you will not miss any material: the later chapters will reference only material that you had learned previously in the book.

I don't think you need to reinvent the wheel by outlining an order of attack when many textbook writers have already done so for you. You'll need to find a textbook which starts from a place that you feel confident, but for this level, I do not think that is too difficult.

Of course, not everyone learns best from a textbook. If that is the case, consider then using the exercises which end each chapter in a good textbook, and use your other sources to help you learn the material in order to solve the problems. If you intend to read the content of the textbook, you should still attempt some of the problems until you feel comfortable with the task.

Depending on the textbook that you pick, you might find that the exercises can be very dry or unnecessarily time consuming. This does happen, and if you feel comfortable with the material, I would encourage you to skip such questions.