Die Ärztin sieht die kleine Wunde an meinem Knie und gibt mir einen Verband.

Ärztin means female doctor. German often uses:

• Arzt = male doctor / doctor (masculine form)
• Ärztin = female doctor

The ending -in is a very common way to make a noun specifically feminine in German.

Also notice the vowel change:

• Arzt
• Ärztin

That change is part of the normal feminine form here.

Because both nouns are feminine singular.

• die Ärztin = the doctor
• die Wunde = the wound

But they are not doing the same job in the sentence:

• die Ärztin is the subject
• die kleine Wunde is the direct object

In this case, the form die happens to be the same for feminine nominative and feminine accusative.

So even though the case is different, the article still looks the same.

Because the adjective ending must match the noun phrase pattern.

Here you have:

• die = definite article
• Wunde = feminine singular
• the phrase is in the accusative

After a definite article, adjectives usually take weak endings. For feminine singular nominative and accusative, that ending is -e.

So:

• die kleine Wunde = correct

This is the same pattern you see in:

• die kleine Katze
• ich sehe die kleine Katze

Because an here is followed by the dative case when it shows location.

The phrase an meinem Knie means the wound is located on / at my knee.

Why dative?

With two-way prepositions like an, German uses:

• accusative for movement toward a place
• dative for location

Here there is no movement. The wound is simply located there. So German uses dative:

• an meinem Knie

Also:

• Knie is neuter
• mein in dative neuter singular becomes meinem

So the full form is:

• an meinem Knie

In natural English, the best translation is usually on my knee.

But German an can cover meanings that English splits up differently, such as on, at, or sometimes by, depending on context.

Here it refers to the location of the wound on the body, so on my knee is the most natural English meaning.

Because mir is the dative form of ich, and here it means to me.

With geben (to give), German usually has:

• someone who gives = subject
• thing being given = accusative direct object
• person receiving it = dative indirect object

So in:

• gibt mir einen Verband

you have:

• mir = to me
• einen Verband = a bandage / dressing

Compare:

• Sie sieht mich. = She sees me. (mich = direct object)
• Sie gibt mir einen Verband. = She gives me a bandage. (mir = indirect object)

Because Verband is a masculine noun, and here it is the direct object of gibt.

The indefinite article for:

• masculine nominative = ein
• masculine accusative = einen

So:

• ein Verband = a bandage/dressing
• sie gibt einen Verband = she gives a bandage

That is why the sentence has:

• einen Verband

Here Verband means a bandage or dressing used for a wound.

It does not mean a verb form. It is a noun, which is why it is capitalized.

Be aware that Verband can also mean association or organization in other contexts, but in a medical sentence like this, it clearly means bandage/dressing.

Because German, like English, can leave out the subject in the second clause when it is clearly the same as the first one.

So instead of saying:

• Die Ärztin sieht die kleine Wunde an meinem Knie und die Ärztin gibt mir einen Verband.

German normally says:

• Die Ärztin sieht ... und gibt ...

English does the same:

• The doctor sees the wound and gives me a bandage.

You usually would not repeat the doctor there either.

Because und does not change the normal word order of the clause.

German main clauses normally put the conjugated verb in second position. In the second clause, the subject is understood, so the verb comes early:

• und gibt mir einen Verband

You can think of it as short for:

• und sie gibt mir einen Verband

So the normal main-clause pattern is still there.

No. Here an belongs to the phrase an meinem Knie, which describes where the wound is.

So the structure is basically:

• Die Ärztin sieht
• die kleine Wunde
• an meinem Knie

That means:

• The doctor sees the small wound
• the wound is on my knee

This is important because German also has the separable verb ansehen:

• Sie sieht die Wunde an. = She looks at the wound.

But that is not what is happening here. In your sentence, an is a preposition, not a separable verb particle.

Because all nouns are capitalized in German.

So in this sentence:

• Ärztin
• Wunde
• Knie
• Verband

are all capitalized because they are nouns.

This is one of the most noticeable spelling differences between German and English.

These are the third-person singular present-tense forms of the verbs:

• sehen → sie sieht = she sees
• geben → sie gibt = she gives

The subject is die Ärztin, which is she, so both verbs must match that subject.

These two verbs are also a bit irregular in the present tense:

• sehen changes from e to ie: er/sie sieht
• geben changes from e to i: er/sie gibt

So the forms are not seht or gebt here, because those would be you plural forms.