Highlights: December 25-31

Nature at 7 p.m. Sunday presents “Christmas in Yellowstone,”  an exploration of the great winter world of Yellowstone through images of the spectacular landscape and wildlife.

Masterpiece Classic at 8 p.m. Sunday presents part two  and three of Oscar-winning writer Julian Fellowes‘ “Downtown Abbey”, a depiction of the lives of the noble Crawley family and the staff who serve them, set at their Edwardian country house in 1912.

Jerusalem: Center of the World at 9 p.m. Monday draws on religious texts, the science of archaeology and oral traditions to determine why this small city has occupied the minds of so many for so long.

The Botany of Desire at 7 p.m Tuesday brings Michael Pollan’s best-selling book of the same name to television, showing how human desires are an essential, intricate part of natural history. The program explores the natural history of four plants and the corresponding human desires that link their destinies to our own.

Frontline at 9 p.m. Tuesday profiles Thomas Lynch, a poet and undertaker whose family has cared for the dead in a small town in central Michigan for three generations. In “The Undertaking,” a critically acclaimed book, Lynch offered unique and profound insight into what he called the “dismal trade.” In an intimate and revealing film, Lynch helps makes sense of the ways Americans cope with death, grief and life.

Independent Lens at 10 p.m. Tuesday presents “Lioness,” an intimate look at war through the eyes of the first women in U.S. history sent into direct ground combat, despite a policy that bans them from doing so.

Nature at 7 p.m. Wednesday takes an exclusive look into the worlds of Arctic bears such as polar bears and grizzlies.

In collaboration with National Geographic, Nova at 8 p.m. Wednesday follows the exploits of acclaimed photojournalist James Balog and a scientific team as they deploy time-lapse cameras in risky, remote locations in the Arctic, Alaska, and the Alps.

Nova at 9 p.m. investigates the collapse of an immense, 200 meter-thick ice shelf into the ocean off the Antarctic Peninsula in 2002, shocking scientists and raising the alarming possibility that we may be heading toward an ice-free Antarctica — last seen a million years ago.

Austin City Limits at 10 p.m. Wednesday and 10:30 p.m. Friday presents a classic Tom Waits performance from 1979.

Emmy-winning actress Holland Taylor discusses her long and varied career on Overheard with Evan Smith at 7 p.m. Thursday.

World-renowned classical guitarist Jorge Caballero performs the classic work Pictures At An Exhibition by Modest Mussorgsky on Arts In Context at 7:30 p.m. Thursday.

Independent Lens at 9 p.m. Thursday presents “These Amazing Shadows,” a program that looks at the work of the National Film Preservation Board and the cinematic treasures it strives to save, from Hollywood blockbusters to avant-garde gems, and from the earliest days of film to today.

On PBS Arts From San Francisco: The Little Mermaid at 8 p.m. Friday, John Neumeier — the American-born chief choreographer for Hamburg Ballet — blends dance, dramatic storytelling and spectacle into this interpretation of Hans Christian Andersen’s classic fable.

In this special Central Texas Gardener conversation at noon and 4 p.m. Saturday, get the CTG team’s perspective on drought, hard freezes, what we learned this year, and the changes we’ll make in 2012.

The New York Philharmonic’s New Year’s Eve concert kicks off with Bernstein’s Overture to Candide and promises to delight with more Bernstein and two Gershwin masterpieces on “Live From Lincoln Center: Bernstein and Gershwin” at 7 p.m. Saturday.

American Masters at 9 p.m. Saturday chronicles the rise of a new breed of musicians in the 1960s Los Angeles whose raw emotions and simple instrumentation bridged the gap between singers and the songs they wrote in “Troubadors: Carole King/James Taylor & The Rise.”

Modern rock giants Coldplay ring in the new year with a very special episode of Austin City Limits at 11 p.m. Saturday highlighting their hits and songs from their newest LP, “Mylo Xyloto.”