Having finished the homework是现在分词的完成式做状语=after I had finished the homework ,I went home 在状语从句中主句的主语与从句的主语相同时 从句主语可以省略,再把动词改成分词.主动用现在分词,被动用过去分词.动作先发生用完成式.
Given more time ,I can do my work better =if I am given more time ,I can do my work better
相当于条件状语从句.