１年次開講の『大学生のための表現法』と２年次開講の『食品化学』の２科目を担当しています。

『』『』。

I teach two courses: 'Expression Techniques for University Students' offered in the first year, and 'Food Chemistry' offered in the second year.

Literal

1st-year-enrollment [possessive-の] 'University-students for expression-method' [and-と] 2nd-year-enrollment [possessive-の] 'Food chemistry' [possessive-の] 2 courses [object-を] in-charge-am-doing.

Academic faculty self-introduction. 次 (じ) is a counter for 'year, order' in academic contexts: 1年次 ('first year'), 2年次 ('second year'). 開講 ('opening a course') is a formal education term. 担当する ('to be in charge of') is the standard verb for 'to teach/handle' a course or responsibility. Note the structure: each course name is a modifier of the main noun 科目 ('subject, course'), all stacked before the final verb.