IMP112 Course Outline
1. Introduction to 3-D:
coordinates, vectors, dot product, equations of lines, describing motion using parametric equations and vector-valued functions
2. Differentials, integrals, derivatives:
the relationship between the Riemann sum approach and the differential approach to integrals
3. Work, line integrals. and kinetic energy:
straight line motion, constant force parallel to line - multiply;
straight line motion, constant force not parallel to line - dot product;
straight line motion, non-constant force - 1-D integral;
motion along curve, non-constant force - vector field and line integral;
kinetic energy and the work-energy theorem
4. Potential energy and conservation of energy
5. More on 3-D:
cross product, equations of planes, functions of several variables, surfaces
6. Momentum 1:
discrete mass distributions, conservation of momentum, impulse
7. Additional applications of integration, double and triple integrals:
volume, density and mass, center of mass, polar coordinates, cylindrical coordinates
8. Momentum 2:
continuous mass distributions, conservation of momentum
9. Relativity
kinematics, energy, momentum
10. Rigid body rotation:
angular acceleration, torque, moment of inertia for discrete system of particles and for continuous distributions by integration
11. Waves