You may love your job and admire and respect your boss, but you are certainly not getting much in the way of love, admiration, or respect in return. Your boss is a bully, and her little apology notes are meaningless. A true apology is a statement of regret, an admission of wrong, and a commitment to refrain from the inappropriate actions in the future.
One strategy is for you to meet with your boss after she has calmed down. Both of you should be sitting when you talk, since people tend to be more calm when seated. Tell her that her yelling, cursing, and public insults are hurtful and deeply upsetting to you, and they have to stop. If she has a problem with your work, you want it addressed in a businesslike way and in private.
Another strategy is for you to hold your ground and be assertive when she goes into her tirade. A show of strength can cause some bullies to put on the brakes. With either approach, your boss's reaction will help you determine your next step which can include resources inside and outside the company.
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