CEO Margaret (Meg) Whitman of Hewlett-Packard Co. (NYSE: HPQ), the world’s biggest computer company, scheduled her first full-day briefing with security analysts Wednesday, after slightly more than a year at the helm.

Under Whitman, 56, the former CEO of eBay Inc. (Nasdaq: EBAY) (the No. 1 online auctioneer) and defeated Republican nominee for governor of California in 2010, the Palo Alto, Calif.-based company has been coasting.

Its shares are down 24 percent, lowering its market value below $34 billion, compared with the $239 billion market value for smaller rival International Business Machines Corp. (NYSE: IBM) and $615 billion for Apple (Nasdaq: AAPL), the world's most valuable technology company.

For the nine-month period ended July 31, HP reported a net loss of $5.79 billion, or $2.93 a share, compared with the year-earlier’s net income of $6.84 billion, or $3.16 a share, on revenue that dipped 5 percent to $90.4 billion.

Whitman has replaced several top managers, merged the world’s largest PC and printer units and implemented a restructuring plan that will see layoffs of as many as 30,000 employees, or 8 percent of the payroll, over two years.

Here are five things Whitman must do now:

Prove she has a vision for the company. Back in 1993, when Louis V. Gertsner, a nonengineer like Whitman, was brought in to lead IBM, which was near bankruptcy, he famously declared that he didn’t need a vision to get the job done. Within a single quarter, Gerstner slashed costs and put IBM on the technology-services path that has made it hugely profitable.

Whitman’s been on the job for a year, though, and has only spoken in general terms of HP’s promise and technology. Well, what’s the vision or mission, especially as technology migrates to the cloud and onto mobile devices in the age of the cloud?

Break the outsider jinx at HP. Until Lew Platt retired as CEO, HP had only been run by internal bosses, starting with co-founders David Packard and William R. Hewlett, followed by the legendary John A. Young, now 80. But Platt’s outside successors -- Carly Fiorina, Mark Hurd and Leo Apotheker -- were each disasters in their own right.

Whitman, a Princeton economics graduate with a master’s degree in business administration from Harvard, had only been a HP director a few months before stepping up. Can she get the ball rolling again and make HP the earnings powerhouse it could be?

Deal with HP’s finances. Of the 31 analysts covering HP, only eight recommend the company as a “buy,” according to estimates carried by Thomson Reuters; seven rate it either “sell” or “strong sell,” while the remainder are neutral.

They also expect HP to report fiscal year net income of $4.05 a share on revenue of $121 billion for the year ending Oct. 31. That compares with $3.38 a share on revenue of $127.2 billion last year.

But HP’s long-term debt now exceeds $20 billion, compared with $12 billion a year ago. Its credit rating was slashed two notches from A to BBB+ or slightly above investment grade.

Analyst Steven Milunovich of UBS has proposed that Whitman merge the company’s finance arm with that of Dell Inc. (Nasdaq: DELL), the No. 3 PC maker. That would greatly lower HP’s overall debt, although it would likely encounter major regulatory obstacles.

In her earlier comments to analysts, Whitman has said she’s confident HP can meet all financial challenges. Chief Financial Officer Cathie Lesjak has been in her job since 2007, when she was promoted from treasurer, so she is respected by outsiders.

Deliver compelling new products for consumers and enterprises. In the consumer space, HP needs to introduce and deliver a range of products running Microsoft (Nasdaq: MSFT) Windows 8 for desktops and laptops, as well as photo services and multimedia that leverage the prowess of Autonomy, the UK company it acquired last year because it specialized in the sector.

As well, HP needs to mount major challenges to Apple, Microsoft, Samsung Electronics (Seoul: 005930) and Inc. (Nasdaq: AMZN), the No. 1 e-retailer, in the tablet space. The company has announced the HP ElitePad 900 tablet for business, but only for January shipment. Will there be an HP rival to the iPad?

For enterprises, HP needs to announce where it will battle new lines of servers from IBM as well as Oracle (Nasdaq: ORCL), the No. 1 database developer, in the “big data” space. Will HP maintain its good relations with Intel (Nasdaq: INTC), the No. 1 chipmaker, now its primary supplier of chips, or revert to internal supply?

Make HP products "must have" items. HP products and services are generally well-regarded, well-engineered and well-serviced. But they don’t have the cult following of Apple and aren’t as successful in the consumer sector as products from Samsung, and somehow they have lost their pop.

There’s plenty at HP Laboratories that Whitman could unleash, provided management knows how to leverage it. Given HP’s tradition of quality, the brand can be built up and new products and services can be offered, especially as “big data” proliferate.

HP, for sure, doesn’t have to offer a smartphone, but it has to move into mobility. It also needs a platform. That’s for Whitman to lay out starting on Wednesday.

HP shares traded late Tuesday at $17.05, down 16 cents.