The death of Steve Jobs at age 56 comes at a crucial period in the history of personal computing — an industry he almost single-handedly created, first with the Apple II, then the Macintosh, then iTunes and the iPod, and now the iPhone and the iPad.

Apple has $76 billion in the bank, but it faces challenges from seemingly every corner.

Google wants to crush the iPhone with its Android system. Netflix wants to dominate the world’s living rooms, leaving iTunes behind. Facebook wants to be the window to the Internet, controlling just about everything. And now Amazon is jumping into the tablet business.

Apple comes at this battle not with Jobs, who gave up day-to-day control in August, but with a Southern, soft-spoken gentleman named Tim Cook, who debuted the new iPhone this week to mostly tepid — and even some harsh — reviews.

Cook will battle Google and the other challengers with Jobs’s legacy stalking his every move — on Wall Street, in Apple’s stores, and in the hearts and minds of technology users around the world. No executive in the history of American business was more closely tied to a company’s brand than Jobs was with Apple.

“The world rarely sees someone who has had the profound impact Steve has had, the effects of which will be felt for many generations to come,” longtime rival Bill Gates, the co-founder of Microsoft, wrote Wednesday night on his personal blog.

A newer generation of tech titans also lionized Jobs, with Facebook founder Mark Zuckerberg posting a note on his Facebook page: “Steve, thank you for being a mentor and a friend. Thanks for showing that what you build can change the world. I will miss you.”

The White House released a statement from President Obama that said, in part: “Steve was among the greatest American innovators — brave enough to think differently, bold enough to believe he could change the world, and talented enough to do it.”

And Google co-founder Larry Page wrote on his Google Plus account: “I am very, very sad to hear the news about Steve. . . . He was very kind to reach out to me as I became CEO of Google and spend time offering his advice and knowledge even though he was not at all well. My thoughts and Google’s are with his family and the whole Apple family.”

With Jobs gone, the pressure on Cook will be relentless. There already were rumblings in the tech world this week that there wouldn’t have been such a tepid response to the new iPhone if Jobs, not Cook, had been onstage.

To be fair, Apple maps out its projects years in advance, so Jobs was involved with this announcement and probably many to come.

Still, it is not hard to imagine this constant refrain: “Well, it’s because Steve is gone.”

Where Jobs was a visionary who could make the details of a new mouse sound almost religious, Cook is an operations guru who made sure Apple pummeled competitors for the best component prices. Nobody is expecting Cook to stand on a stage anytime soon and articulate computing’s future.

Apple’s defenders will say that Cook has a deep and talented executive team — which is true — with luminaries such as industrial design master Jonathan Ive. But the company recently lost its head of retail to J.C. Penney, and it remains to be seen whether Apple, without Jobs, will have the same power to attract other executives.

Jobs seemed to know how much he would be missed.Fortune recently reportedthat he had set up a mini-university inside the company to teach up-and-comers how Apple thinks and makes decisions. But the way Apple thinks and makes decisions is really the way Jobs thought and made decisions. Can that be taught?

The new iPhone, dubbed the 4S, will hit stores on Oct. 14. People will camp out for days in advance to get one. Lines will snake around malls.

But for Apple without Jobs, the question is: Will they line up someday for the iPhone 5?

Staff writer Hayley Tsukayama contributed to this report.

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