Learn Hardcore German: Ich muss heute meine Aufgabe erfüllen.

muss is the first-person singular of the modal verb müssen, meaning “must” or “have to.” It expresses that you are obliged or required to do something.

Why is muss placed directly after Ich?

German main clauses follow the verb-second (V2) rule: the conjugated verb must occupy the second position. Since Ich is the subject in position one, muss comes immediately after.

Why do we place heute between muss and meine Aufgabe?

Time adverbials (like heute) typically appear right after the finite verb and before objects. The order here is:

Subject (Ich)
Verb (muss)
Time adverbial (heute)
Object (meine Aufgabe)
Infinitive at the end (erfüllen)

Why is meine Aufgabe in the accusative case?

The verb erfüllen takes a direct object, and direct objects in German take the accusative. Because Aufgabe is feminine, the possessive mein becomes meine in the accusative.

Is erfüllen a separable verb? How can I tell?

erfüllen is inseparable. Prefixes such as er-, be-, ver-, ent-, and zer- never detach from the verb and always stay attached in all tenses and clauses.

What’s the difference between erfüllen and erledigen when talking about tasks?

erfüllen implies fulfilling a duty, promise, requirement or expectation.
erledigen simply means handling or finishing a task without the sense of “meeting conditions.”

Can I say Ich muss heute meine Aufgabe machen instead? Would it be correct?

Yes, it’s grammatically fine and more colloquial. machen is more general (“do/make”), whereas erfüllen emphasizes completing or satisfying an assignment or obligation.

How would I express the same idea in the perfect tense?

With modal verbs in the perfect you use haben plus a double infinitive:
Ich habe heute meine Aufgabe erfüllen müssen.
In simple past you’d say:
Ich musste heute meine Aufgabe erfüllen.