Lecture 1: Kinematics-1
Introduction to Kinematics. Introduces velocity and acceleration. Definition of vectors, scalars and dot products. The definition of basis vectors.
Lecture 2: Vectors
Introduces vectors and vector transformations. Defining Orthogonal transformations. Discusses about pseudo scalars, vector products and triple products.
Lecture 3: Kinematics-2
The motion in higher dimensions are discussed. As an example, it covers projectile and circular motion. The horizontal and vertical motions of the projectile are worked out. The trajectory of the projectile body is shown to be parabolic in nature. The launch angle is crucial in determining the height and the range of the projectile motion for a given initial velocity. Derivation of the centripetal acceleration is provided and the comparison to mass-spring system is outlined. Plane Polar coordinates are introduced, and they are used for studying circular motion. The general circular motion is also analyzed.
Lecture 4: Cylindrical and Spherical Coordinates
This lecture covers the cylindrical and spherical polar coordinates. The cylindrical coordinates can be seen as a simple extension of plane polar coordinates. The velocity and acceleration vectors in both coordinate systems are discussed.
Lecture 5: Vector Calculus
In this lecture, the vector calculus is introduced such as Gradient, Divergence and Curl. In addition we also discussed Kepler's laws and Newton's Laws of motion.
Lecture 6: Gravitation
A very short introduction to gravitation. Gravitational force between two point masses is discussed. The gravitational force inside and outside of a solid sphere is studied. Newton's shell theorem is briefed. Implications of Keplers' laws, the gravitational potential energy, work done by gravitational force are analyzed. Mechanical energy of a satelite orbiting a planet is obtained.
Lecture 6: Special Theory of Relativity
A very short introduction to special theory of relativity. The basic elements for STR are defined, including the standard configuration. Other discussions include Lorentz transformations, spacetime diagrams, and time dilation.
Comentarios