The episode begins with Sheldon and Leonard in their apartment, where Sheldon is excitedly discussing his plans to attend a conference in 2003. He reminisces about how he was a different person back then, particularly in his social interactions. Leonard, however, is more focused on the present and is less enthusiastic about Sheldon's nostalgia.

Meanwhile, Penny and Amy are at the apartment, and they are discussing their relationships. Penny expresses her frustration about her acting career and how she feels stuck. Amy tries to encourage her, but Penny is feeling particularly down about her lack of success. The conversation shifts to their respective relationships, and Amy reveals that she is feeling neglected by Sheldon, who is more focused on his past than their present.

The scene transitions to Howard and Bernadette, who are at their home. They are preparing for a visit from Howard's mother, which makes Howard anxious. Bernadette tries to reassure him, but Howard is clearly nervous about the impending visit. The tension builds as they discuss how Howard's mother can be overbearing and critical.

Back at the apartment, Sheldon is still fixated on his memories of 2003. He decides to recreate a moment from that year by inviting Leonard to join him in a nostalgic activity. Leonard reluctantly agrees, but he is clearly not as invested in the idea as Sheldon is. They begin to reminisce about their lives back then, and Sheldon becomes increasingly animated, while Leonard remains more grounded.

As the episode progresses, Penny and Amy decide to take matters into their own hands regarding their relationships. They come up with a plan to confront Sheldon and Leonard about their behavior. They want to encourage Sheldon to be more present in his relationship with Amy and for Leonard to be more supportive of Penny's acting career.

The scene shifts back to Howard and Bernadette, who are now dealing with Howard's mother. She arrives, and the tension in the room is palpable. Howard's mother immediately begins to criticize him, which leads to a series of comedic exchanges. Howard tries to stand up for himself, but his mother's comments continue to undermine his confidence.

In a pivotal moment, Penny and Amy confront Sheldon and Leonard about their behavior. They express their frustrations and urge them to be more attentive to their partners. Sheldon, initially resistant to the idea, begins to reflect on his actions and how they may be affecting Amy. Leonard, on the other hand, is more receptive to Penny's concerns and vows to be more supportive.

The episode culminates in a series of realizations for the characters. Sheldon decides to make a conscious effort to be more present in his relationship with Amy, while Leonard takes steps to support Penny in her acting career. The final scenes show the couples coming together, with Sheldon and Amy sharing a heartfelt moment, and Leonard encouraging Penny to pursue her dreams.

The episode ends on a light note, with the group coming together to celebrate their friendships and relationships, highlighting the importance of being present and supportive in their lives.

In the ending of "The 2003 Approximation," Sheldon and Leonard confront their pasts as they navigate their friendship and the impact of their choices. Meanwhile, Howard and Bernadette deal with the challenges of impending parenthood, and Raj finds himself in a moment of self-reflection regarding his romantic life.

As the episode unfolds, Sheldon and Leonard's conversation leads to a deeper understanding of their friendship, while Howard and Bernadette's discussions about parenting reveal their excitement and anxiety about the future. Raj, feeling left out, contemplates his own relationship status, ultimately realizing the importance of self-acceptance.

The episode begins with Sheldon and Leonard in their apartment, where they are discussing a recent event that has stirred up memories from their past. Sheldon is particularly fixated on a moment from 2003, which he believes has shaped their current friendship. Leonard, while initially dismissive, begins to engage with Sheldon's nostalgia, leading to a deeper conversation about their growth over the years.

As they reminisce, the scene shifts to Howard and Bernadette, who are preparing for the arrival of their baby. They are both excited yet anxious, discussing their plans and fears about becoming parents. Howard expresses his worries about being a good father, while Bernadette reassures him, emphasizing their partnership and love. This scene highlights their evolving relationship and the new challenges they are about to face together.

Meanwhile, Raj is seen in a coffee shop, feeling somewhat isolated as he watches couples around him. He reflects on his own romantic life, feeling the weight of his single status. His friends' discussions about their relationships and impending parenthood only amplify his feelings of loneliness. Raj's internal struggle is palpable as he grapples with his desire for companionship and the reality of his situation.

Back in the apartment, Sheldon and Leonard's conversation deepens as they explore the significance of their friendship. Sheldon reveals how much he values Leonard's presence in his life, despite their differences. Leonard, in turn, acknowledges the quirks that make Sheldon who he is, reinforcing the bond they share. This moment serves as a turning point for both characters, as they come to appreciate the complexities of their friendship.

The episode culminates with a scene that brings all the characters together. Howard and Bernadette share their excitement about becoming parents, while Raj, feeling inspired by his friends' happiness, decides to embrace his single life and focus on self-improvement. Sheldon and Leonard, having resolved their past grievances, reaffirm their commitment to each other as friends.

In the final moments, the characters reflect on their journeys, with each one finding a sense of peace in their current situations. Sheldon and Leonard's friendship is stronger than ever, Howard and Bernadette are ready to face parenthood together, and Raj is on a path of self-discovery. The episode closes with a sense of hope and camaraderie, showcasing the importance of friendship and personal growth in the face of life's challenges.

In "The 2003 Approximation," there is no post-credit scene. The episode concludes without any additional scenes after the credits roll. The focus remains on the main storyline and character interactions throughout the episode, which centers around Howard and Bernadette's relationship dynamics, as well as Sheldon and Amy's attempts to navigate their own relationship challenges. The episode wraps up with the main plot points addressed, leaving no further content after the credits.

In this episode, Leonard and Penny's relationship is tested when Leonard feels insecure about their marriage. He worries that Penny is not as committed as he is, especially when she expresses a desire to go out and have fun, reminiscent of her single days. This leads to a deeper conversation about their relationship dynamics.

In 'The 2003 Approximation', Sheldon becomes nostalgic about 2003 after he and Leonard discover that they have been living in the same apartment for over a decade. This realization prompts Sheldon to reflect on the past, particularly the time when he was more carefree and had a different social life.

Howard plays a significant role in Sheldon's nostalgia as he reminisces about their past adventures together. He encourages Sheldon to embrace the memories and even suggests that they recreate some of their past experiences, which highlights the bond they share and the changes in their lives since then.

Raj's storyline intersects with Sheldon's reflections as he grapples with his own feelings of loneliness and the changes in his life. While Sheldon is looking back at the past, Raj is trying to navigate his current romantic struggles, which adds a layer of complexity to the theme of nostalgia and the passage of time.

Sheldon wants to recreate a specific event from 2003, which is a time when he and his friends attended a comic book convention together. This event is significant for Sheldon as it represents a time of friendship and fun before the complexities of adult life set in, highlighting his desire to return to a simpler, more enjoyable time.

"The Big Bang Theory" Season 9, Episode 4, titled "The 2003 Approximation," contains some elements that may be considered objectionable or upsetting for children or sensitive viewers. Here are a few aspects to consider:

1. Mature Themes: The episode explores themes of relationships and dating, which may include discussions about romantic feelings and breakups that could be complex for younger viewers to understand.

2. Humor Style: The show's humor often includes sarcasm and adult-oriented jokes that may not be suitable for children. Some jokes may touch on topics like intimacy and personal relationships.

3. Social Situations: Characters experience awkward social interactions and emotional distress related to their personal lives, which could be uncomfortable for sensitive viewers.

4. Language: While the language is generally mild, there may be occasional use of terms or phrases that some parents might find inappropriate for younger audiences.

Overall, while the episode is not overtly explicit, it does contain elements that may require parental guidance for younger viewers.