1. Course Introduction and Newtonian Mechanics

Professor Ramamurti Shankar introduces the year-long physics course, covering major ideas from Galileo and Newton to the revolutions in relativity and quantum mechanics. He emphasizes the broad appeal of the subject and the potential relevance to various fields, including medicine. The professor also outlines the course organization, including the taped lectures as part of a pilot program funded by the Hewlett Foundation, and provides details about the course's logistics, such as meeting times, homework submission, and grading policy.

The professor discusses the course's grading structure, which includes homework, a midterm, and a final exam. He introduces the 'Amnesty Plan,' which allows the final exam grade to override the midterm grade in calculating the final course grade, providing an incentive for students to improve their understanding throughout the semester. The professor also covers the importance of attending lectures and doing homework, as well as the resources available, such as TAs and office hours, to support student learning.

Professor Shankar encourages students to collaborate on homework problems, emphasizing that physics is often a collaborative endeavor. He highlights the importance of each group member contributing to the understanding of the problem and stresses the value of utilizing TA support and the undergraduate lounge as resources for problem-solving and collaboration.

The professor sets expectations for classroom behavior, including not talking during lectures, the acceptable use of sleeping in class, and the importance of active participation through asking questions. He also addresses the logistics of the taped lectures, assuring students that the camera's presence will not affect them and encourages them to focus on the content rather than the recording.

Professor Shankar clarifies the mathematical prerequisites for the course, including knowledge of differential calculus, and reassures students that the course will focus on understanding physics concepts rather than extensive mathematical computations. He encourages students to ask questions at any time to clarify understanding and to engage with the material, rather than memorizing formulas.

The professor provides information about the midterm exam, including the expected date and the coverage of topics. He also discusses the importance of taking a concurrent lab course to reinforce the principles of physics through practical experiments and provides guidance on choosing the appropriate lab section.

Professor Shankar begins the physics content by explaining the two-part program of Newtonian mechanics: kinematics, which describes the present state of an object, and dynamics, which predicts future states based on present conditions. He uses the example of a thrown piece of candy to illustrate the principles of kinematics and dynamics, emphasizing the importance of initial conditions and the predictability of motion in physics.

The professor delves into the mathematical representation of motion, explaining how graphs of position versus time can be used to determine an object's average velocity and acceleration. He introduces the concept of instantaneous velocity as the derivative of position with respect to time and discusses the importance of understanding calculus to follow the logic behind physics problems.

Professor Shankar explains the process of integration in physics, starting with simple examples of constant acceleration and deriving the general position formula for a particle. He discusses the importance of understanding the physical meaning behind mathematical constants and the limitations of using formulas outside their valid contexts.

The professor presents a practical problem of a falling object to demonstrate how physics formulas can predict future states based on initial conditions. He walks through the steps of solving for the object's position, maximum height, and final velocity, emphasizing the importance of understanding the assumptions behind each formula and the need to critically engage with the material.

Professor Shankar discusses the importance of considering all solutions provided by physics equations, even those that may seem unintended or unexpected. He uses the example of the falling object problem to illustrate how additional solutions can provide new insights and understanding, drawing parallels to significant discoveries in physics, such as the prediction of antiparticles.

The professor concludes the lecture by discussing the application of calculus in physics, specifically the use of derivatives and integrals to relate velocity, position, and acceleration. He provides an alternative derivation of the final velocity formula using calculus techniques and emphasizes the importance of understanding when certain mathematical manipulations are valid in the context of physics problems.