Essays with the gift of optimism; Peripheral Visions, by Phyllis Theroux. New York: William Morrow & Co. 136 pp.

Phyllis Theroux is a mother of three, a gardener in a neighborhood cooperative, and a survivor of what she calls ''perilous times.'' Because she is also an essayist, one with the gift for gleaning bits of wisdom and insight out of the tide of everyday events, she is able to share the other aspects of her life in a humorous, affecting way.

In this book of essays, Theroux spends quite a bit of time looking at childhood, her own and that of her children. She recalls how her father instilled her with the gift of optimism, making her the promise that ''ahead of me was dry land - a bright, marshless territory, without chuckholes or traps, where one day I would walk easily and as befitting my talents. The fact that I didn't know what my talents were did not put my father off in the slightest.'' While the raising of her own children has not exactly been the smooth territory her father promised, it has nevertheless provided some of her best moments--in these essays as well as in life.

In an especially well written essay called ''In Defense of Children,'' she takes a few jabs at the ''National Organization for Nonparents,'' and takes issue with the premise that children are usurpers of personal fulfillment and a cause of the high divorce rate. On the contrary, she writes, ''children stand like immovable sequoias in the middle of one's life, daily upgrading the quality of one's thinking, the extent of one's selfishness, and the depth of one's love.''

But being a mother is only one of the sources from which her observations on life spring. Even tilling a small garden plot in a neighborhood cooperative yields more sustenance than just carrots and peas, a fact evidenced by her essay ''The Call of the Soil.'' At first baffled by mulch and the correct way to rake, she soon finds her hobby providing an unfathomable joy.

At other times she casts her eye on her urban neighborhood in much the same way another essayist, Annie Dillard, recorded the rural surroundings at Tinker Creek. There are friends, neighborhood characters, and others who make it possible to cope with life in the 1980s. Juggling inflation and dodging financial doom, she shops at secondhand stores and arms herself with wry humor. Retrieving the morning mail, she overlooks the overdue bills and asks, ''Can someone who still gets The New Yorker go broke?''

Surely not, it would seem, with the wealth of good writing and good sense that this volume provides.