In the homestretch of its 2014-15 season, the Detroit Symphony Orchestra is going out with a couple of blockbusters.

Next week finds music director Leonard Slatkin leading the orchestra and a gaggle of guests through a complete concert version of Puccini's "Tosca." This weekend, however, Slatkin and his charges are tackling Gustav Mahler's hefty Symphony No. 1, which anchors a rewarding program that also includes music by DSO composer-in-residence Gabriela Lena Frank and Jean Sibelius.

Frank's "Concertino Cusqueño" (2012) marks the first time in her tenure that the DSO has performed one of her pieces at Orchestra Hall. On Thursday, it revealed itself to be a terrific 11-minute curtain raiser, whetting the appetite for the large-scale concerto for orchestra she's writing for the DSO for next season.

What was best about the concertino was the way Frank funneled a melting pot of cultural and musical influences into music that still sings with her own voice. (The California-born composer herself is a melting pot of ethnic heritages, including Peruvian and Chinese on her mother's side and a father of Lithuanian-Jewish descent.)

To start, Frank quotes the knocking-at-the-door timpani rhythm that opens Benjamin Britten's Violin Concerto before blending into a religious tune from Cusco, once the Inca capital in the Peruvian Andes. A colorful piccolo-and-bass clarinet duet immediately captures the ear before the music launches into a series of fetching episodes rich with folkloric melody, snappy dance rhythms and clearly delineated forms.

Strumming strings evoke guitars, and the shadow of Bartok hovers here and there. The piccolo and bass clarinet duet return at the close to complete the frame. Slatkin led a vibrant performance.

The star violinist Midori was originally supposed to play William Walton's Violin Concerto this week with the DSO, but she had to withdraw for medical reasons. She was replaced Thursday by fast-rising young Taiwanese-American violinist Paul Huang, who has already received a 2015 Avery Fisher Career Grant. The rarely heard Walton isn't the kind of repertory work that would be under the fingers of most violinists — the DSO last programmed it in 1989 — so Huang played Sibelius' beloved Violin Concerto instead.

Huang's initial entrance was so whispered that I at first wondered whether there would ultimately be enough projection to his sound. No need to worry. He quickly shifted into high gear, producing a canon-like sound that filled the hall. (His bio says he plays a 1742 Guarneri del Gesu violin on loan from the Stradivari Society of Chicago.) Huang played with a striking technique, sure intonation and a lyrical, legato way of shaping phrases.

After intermission, Slatkin and the DSO turned their attention to Mahler. The 1889 premiere of the First Symphony did not go well. The music's patchwork quilt — evocations of nature, gnarly complexities, folk and dance tunes, brassy ecstasies and a lachrymose klezmer-like funeral march — was too unconventional, too rustic and, especially in anti-Semitic Vienna, too Jewish.

My favorite performances manage to maintain a sense of the music's bizarre qualities and heightened emotional state without slipping into eccentric mannerism. It's a thin line, and there were times Thursday in the opening movements that I wanted deeper emotional revelations from Slatkin and the ensemble. Still, Slatkin's clear-eyed, balanced approach to the score paid dividends in the leisurely flow of the second movement's traditional landler (Austrian waltz) and the unified, gradual building of momentum that carried through the finale's blaze of brass and horns.

The DSO's young principal bassist Kevin Brown brought an especially gentle and heartfelt lyricism to the brooding variation on "Frère Jacques" that opens the funeral march, and principal horn Karl Pituch's gorgeous solos stood out among the many wind players who stepped in and out of the spotlight in this remarkable score.