Financial markets rebounded sharply yesterday on news that President Reagan is expected to recover rapidly and fully from a shooting attack on Monday. "You'd have to say we're back to normal," said analyst David Jones at Aubrey G. Lanston & Co. of New York.

While the shock of another presidential assassination attempt continued to dominate talk in the investment community, the uncertainty that caused markets to be shut down abruptly in this country and Canada Monday afternoon was erased.

In response, stock prices and the value of the U.S. dollar recovered, after declining Monday (and early yesterday in Japan and Europe) on news that Reagan was wounded in the chest and headed for surgery. "A steadier tone developed in the dollar as confidence returned," said a dealer for Barclay's Bank International, describing the initial dollar setback.

Commodities trading also was back to normal yesterday, there was some easing of interest rates and the bond market was firmer with prices moving higher.

At the New York Stock Exchange, buyers were active from the opening bell as advancing issues topped declining stocks by a 3-to-1 margin in what analysts said was an extension of a rally that had been in progress prior to news reports on Monday of the shooting in Washington.

The composite index of Big Board stocks rose 0.91 point to 78.27 and the American Stock Exchange index soared 3.95 points to 360.60, in moderately heavy trading. The Dow Jones average of industrial stocks topped the 1,000-mark again and the Johnston, Lemon & Co. index of 30 Washington-area stocks rose to a record 167.381 compared with 166.802 last Friday and under 100 a year ago.

Overall, over-the-counter stocks were particularly strong as the National Association of Securities Dealers composite index hit a 1981 high of 210.18, up 1.36 points. Another broad market indicator, the Standard & Poor's index of 500 stocks jumped 1.72 points to 136.

Anthony Ludovaci, of Tucker Anthony & R. L. Day in New York, said the stock market was strong before the attack on Reagan and that otherwise basic market factors haven't changed, including a slowdown in the economy that points to reduced inflation.

"But psychologically, the world is more sympathetic to President Reagan and it may soften opposition in Congress to his programs," he added.

Initial relief that the assassination attempt had failed also got an extra boost from the new strength in bonds, said Jerry Hinkle, manager of the trading department of Sanford Bernstein & Co. in New York. Bond gains were noted in all sectors as the federal funds rate charged by banks for overnight lending between institutions eased to 14 1/4 percent from 15 percent. In addition, Citicorp commercial paper (corporate IOU interest fell to an average of 13.436 percent from 13.663 percent last week.

Citibank, the commerical banking subsidiary of Citicorp reduced its broker loan rate to 15 1/2 percent from 16 percent while competitor/ Manufacturers Hanover Bank & Trust cut its broker loan, rate to 16 percent from 16 1/4 percent.

The U.S. dollar declined in early European trading, in reaction to the Reagan shooting, but in late New York trading, the dollar was selling for 2.1090 German marks compared with 2.26 marks following the assassination attempt and 2.2460 marks prior to news of the shooting. The pound fell to $2.2340 in New York compared with $2.25-$2.26 after the Reagan attack.

In Tokyo, the U.S. currency slipped from 212.85 yen to 208.80 yesterday morning but recovered sharply to close at 211.40. Stock prices also fell initially in Tokyo but rebounded sharply, with one market index there hitting a record high.

Gold closed at $514.50 in New York, up slightly from $514 in a quiet market. The Comex settlement price was $513.80, up from $512.10, while silver was settled at $11.895 compared with $12.150. Suspension of the national strike in Poland was said to be the main factor in gold trading, with bullion down $15 an ounce in London to $507.50 compared with $522.50 on Monday.

The Dow Jones average of 30 industrial blue chip stocks on the New York exchange closed at 1003.87, up 11.71 points for the day and just below its best level of the day. In the previous two sessions, the Dow barometer had closed below the 1,000 market after reaching an eight-year high rank of 1,015.22 last Wednesday. The Dow transportation stock average also gained ground yesterday, up 6.97 points to 437.62 -- above the level it reached a week ago.

Volume on the Big Board was 51.3 million shares yesterday compared with 33.5 million in Monday's abbreviated session. Nationwide trading in NYSE-listed stocks on all exchanges and in the over-the-counter market rose to 58.67 million from 38 million. There were 1,145 advancing issues, 422 on the downside and 351 unchanged.

On the Amex, volume rose to 6.17 million shares from 4.34 million with 383 advancing issues, 226 declining and 203 unchanged.

Texaco was the most active NYSE issue, up 1 to 37 1/2 on a volume of 666,700. Eastman Kodak, which announced a new line of color film products for home use, rose 5/8 to 81 5/8.