United were held to 15 league draws last season, more than any other team in the top division, and one of them was against Swansea.
An emphatic 4-0 victory over West Ham in their opening game suggested United have shaken off a tendency to draw matches they should be winning, putting them in good spirits for the trip to south Wales.
United were held to 15 league draws last season, more than any other team in the top division, and one of them was against Swansea at Old Trafford in April.
Jose Mourinho's side look much better equipped now to deal with sides who sit deep and try to frustrate them; their attacking verve was too much for a defensively minded Hammers side last Sunday.
The British record £75 million ($96 million) fee paid to Everton for Romelu Lukaku already looks like money well spent, with the Belgium striker scoring twice on his league debut, while Nemanja Matic, a £40 million recruit from Chelsea, was outstanding in midfield.
Mourinho's men look well set to improve on last season's sixth place finish and the United manager has even spoken of a title challenge this season.
He has won the domestic title in his second season in each of his last five managerial positions – at Porto, Chelsea twice, Inter Milan and Real Madrid.
With Chelsea faltering at home to Burnley last weekend, Mourinho's hopes of marking his second season at Old Trafford by winning the Premier League may just have grown a little.
Not that it's time to start dreaming of future glory just yet, according to United striker Martial, who scored against West Ham after coming off the bench.
"As a squad, we haven't really talked about specific aims for the season too much so far, but the goal is to win as many titles as possible," he said.
"That is what we tried to do last year and it's what we are going to try to do this year."
Mourinho does have long-term injuries to contend with; Ashley Young's hamstring problem will keep him out until October, while defenders Luke Shaw and Marcos Rojo are still some way off full fitness.
Mourinho confirmed last week that he is in discussions to re-sign Zlatan Ibrahimovic, but the former Paris Saint-Germain striker's cruciate knee ligament damage still requires several more months of rehabilitation.
One bonus for United is that they will not have to face the player who scored Swansea's goal at Old Trafford last season after Gylfi Sigurdsson's drawn-out transfer to Everton finally went through on Wednesday
Last season's 15-goal top scorer Fernando Llorente could return for Swansea, having completed his recovery from a broken arm, but midfielders Ki Sung-Yeung and Nathan Dyer are still injured.
Paul Clement, who guided Swansea to safety with a game to spare last season after arriving at the club in January, plans to use the Sigurdsson money to bring in up to three signings.
"It's a big challenge to replace Gylfi Sigurdsson. There's no question about that," he said.
"But what we hope to be able to do is bring in two or three players who will strengthen our squad in various positions. It's not just going to be one for one."