The lecture begins with a review of the loop-the-loop problem. Professor Shankar then reviews basic terminology in relation to work, kinetic energy and potential energy. He then goes on to define the Work-Energy Theorem. Finally, the Law of Conservation of Energy is discussed and demonstrated with specific examples.
The lecture begins with the application of Newton’s three laws, with the warning that they are not valid for objects that move at speeds comparable to the speed of light or objects that are incredibly small and of the atomic scale. Friction and static friction are discussed. The dreaded inclined plane is dealt with head on. Finally, Professor Shankar explains the motion of objects using Newton’s laws in specific problems related to objects in circular motion, such as roller coasters and a planet orbiting the Sun.
This lecture introduces Newton’s Laws of Motion. The First Law on inertia states that every object will remain in a state of rest or uniform motion in a straight line unless acted upon by an external force. The Second Law (F = ma) relates the cause (the force F) to the acceleration. Several different forces are discussed in the context of this law. The lecture ends with the Third Law which states that action and reaction are equal and opposite.
In this lecture, Professor Shankar discusses motion in more than one dimension. Vectors are introduced and discussed in multiple dimensions. Vector magnitude and direction are also explained. Null vectors, minus vectors, unit and velocity vectors are discussed along with their properties. Finally, several specific problems are solved to demonstrate how vectors can be added, and problems of projectile motion are expounded.
Professor Shankar introduces the course and answers student questions about the material and the requirements. He gives an overview of Newtonian mechanics and explains its two components: kinematics and dynamics. He then reviews basic concepts in calculus through two key equations: x = x0 + v0t + ½ at2 and v2 = v02+ 2 a (x-x0), tracing the fate of a particle in one dimension along the x-axis.
Final Exam covers the second half of the course.
The last class of the semester consists of a brief recapitulation of topics in the Divine Comedy addressed throughout the course, followed by an extensive question and answer session with the students. The questions posed allow Professor Mazzotta to elaborate on issues raised over the course of the semester, from Dante’s place within the medieval love tradition to the relationship between his roles as poet and theologian.
Professor Mazzotta lectures on the final cantos of Paradise (XXX-XXXIII). The pilgrim’s journey through the physical world comes to an end with his ascent into the Empyrean, a heaven of pure light beyond time and space. Beatrice welcomes Dante into the Heavenly Jerusalem, where the elect are assembled in a celestial rose. By describing the Empyrean as both a garden and a city, Dante recalls the poles of his own pilgrimage while dissolving the classical divide between urbs and rus, between civic life and pastoral retreat.
This lecture focuses on Paradise XXVII-XXIX. St. Peter’s invective against the papacy from the Heaven of the Fixed Stars is juxtaposed with Dante’s portrayal of its contemporary incumbent, Boniface VIII, in the corresponding canto of Inferno. Recalls of infernal characters proliferate as the pilgrim ascends with Beatrice into the primum mobile. Bid to look back on the world below, Dante perceives the mad track of his uneasy archetype, Ulysses.
This lecture covers Paradise XXIV-XXVI. In the Heaven of the Fixed Stars, Dante is examined on the three theological virtues by the apostles associated with each: St. Peter with faith (Paradise XXIV), St. James with hope (Paradise XXV), and St. John with love (Paradise XXVI). While mastering these virtues is irrelevant to the elect, it is crucial to the message of reform the pilgrim-turned-poet will relay on his return home. Dante’s scholastic profession of faith before St.
