| Date | Notes | |
| Monday 8/23 | Reading material: sections 1.1, 1.2, 1.9, 1.10, 1.11. Scalars and vectors: some examples. Elementary scalar and vector operations. Scalar (dot) product of vectors. Magnitude of a vector. Unit vectors. Position vectors. | |
| Wednesday 8/25 | Reading material: section 1.12. Vector product of two vectors, properties. Right-hand rule. Epsilon permutation symbols (Levi-Civita density). Einstein convention for summing repeated dummy indices. | |
| Friday 8/27 | Reading material: section 1.12. Triple product of three vectors ABC=A.(BxC). Proving vector identities. | |
| Monday 8/30 | Introductions, course policies. Syllabus. Review of the first week. Scalars, vectors, dot product. Einstein convention. Vector product. Problem 1-24. | |
| Wednesday 9/1 | Reading material: sections 1.13, 1.14, 1.15. Differentiation of vectors. Position, velocity and acceleration in Cartesian and cylindrical coordinates. Angular velocity. | |
| Friday 9/3 | Reading material: section 1.16. Gradient operator. Gradient of a scalar function. Geometrical interpretation. Divergence and curl of a vector function. Laplacian. | |
| Monday 9/6 | Labor Day - no class. | |
| Wednesday 9/8 | Reading material: section 1.17. Integration of vectors: volume, surface and contour integrals. Gauss's theorem and Stokes's theorem. | |
| Friday 9/10 | Reading material: sections 2.1, 2.2, 2.3, see also 2.7. Physics models. Physics laws versus definitions. Newton's Laws. Inertial vs gravitational mass. Inertial reference frames. | |
| Monday 9/13 | Reading material: section 2.4. Example 2.1: Block sliding on a smooth inclined plane (no friction). | |
| Wednesday 9/15 | Examples 2.2 and 2.3: Block sliding on an inclined plane with friction. Static and kinetic friction. Solving Newton's law as a differential equation: the special cases of F(t) and F(x). | |
| Friday 9/17 | Problem 2.38. Solving Newton's law as a differential equation: the special case of F(v). Retarding forces. Example 2.4: Horizontal particle motion with friction. Example 2.5: Vertical particle motion with friction. | |
| Monday 9/20 | Example 2.6: Projectile motion in two dimensions without friction. Example 2.7: Projectile motion in two dimensions with friction. Example 2.9: Atwood's machine. Example 2.10: Particle motion in a constant magnetic field. | |
| Wednesday 9/22 | Reading material: section 2.5. Conservation laws: linear momentum, angular momentum, energy. Conservative forces. Potential energy. | |
| Friday 9/24 | Example: Problems 2-53. Reading material: section 2.6. Turning points and equilibrium. Bounded and unbounded motion. Final examples from Chapter 2. Problem 2-47. Problem 2-28. | |
| Monday 9/27 | Review for the exam. Due to the power outage, class was dismissed early and the notes for problems 2-12 and 2-26 are here. Sample exams from previous years are linked to the exams web page. | |
| Wednesday 9/29 | First Midterm Exam: Chapter 2. | |
| Friday 10/1 | Review of second-order linear inhomogeneous ordinary differential equations with constant coefficients. | |
| Monday 10/4 | Reading material: sections 3.1 and 3.2. Simple harmonic oscillator: solution x(t), amplitude and phase angle, angular frequency, period, kinetic, potential and total energy. Example 3.1: Spherical pendulum. | |
| Wednesday 10/6 | Reading material: section 3.5. Damped oscillations: general solution. Damped oscillations: underdamped, critically damped and overdamped motion. Logarithmic decrement of motion. | |
| Friday 10/8 | Reading material: section 3.3. Harmonic oscillations in two dimensions. Lissajous patterns. Problem 3.6. | |
| Monday 10/11 | Reading material: section 3.4. Phase diagrams. The phase diagram of a) simple, b) underdamped and c) critically damped oscillator. Problem 3-21. Problem 3-7: a floating pendulum. Example 3.3. | |
| Wednesday 10/13 | Reading material: section 3.6. Driven oscillators. Derivation of the particular solution. | |
| Friday 10/15 | Homecoming - no class. | |
| Monday 10/18 | Resonance phenomena. Resonance frequency. Quality factor. | |
| Wednesday 10/20 | Reading material: section 3.7. Equivalent electrical circuits. Example 3.5. Problem 3-26. | |
| Friday 10/22 | Solving problems with dimensional analysis. You can read these notes, in particular see examples 3.1, 3.2 and 3.3. | |
| Monday 10/25 | Review for the test. Energy of a driven oscillator. Kinetic energy resonance. (subsection "Resonance phenomena" in Section 3.6). Simple pendulum (problem 3-12 and example 3.3). Grandfather clock (problem 3-45). Exams from previous years are now linked to the exams web page. | |
| Wednesday 10/27 | Second Midterm Exam. | |
| Friday 10/29 | Reading material: section 3.8 Principle of superposition - Fourier series. Oscillators driven by arbitrary periodic functions. Fourier representation of periodic functions. Example 3.6: sawtooth function. | |
| Monday 11/1 | Fourier series: examples. Problem 3-29. | |
| Wednesday 11/3 | Section 3.9. Response to a step function. | |
| Friday 11/5 | Response to an impulse function. Green's function and Green's method. | |
| Monday 11/8 | Review of response to forced oscillations. Example 3-7. | |
| Wednesday 11/10 | Discussion of EC Homework 11. Section 4.7 Mapping. Logistic map. | |
| Friday 11/12 | Chapter 5: Gravitation. Newton's law of gravity. Force and gravitational field vector. Potential energy and gravitational potential. | |
| Monday 11/15 | Finding the gravitational field of a continuous mass distribution. Example 5-1. | |
| Wednesday 11/17 | Section 5.3 Lines of force and equipotential surfaces. Analogy between mechanics and electrostatics. Applications of Gauss' law for finding the gravitational field. Example 5-1. Examples: spherically symmetric distribution; infinite thin wire. | |
| Friday 11/19 | Section 5.5. Ocean tides. | |
| Monday 11/22 | Applications of Gauss' law: Problem 5-2. The gravitational field of an infinite wire. Problem 5-16. | |
| Wednesday 11/24 | Bonus lecture: dark matter and modified Newtonian dynamics. | |
| Friday 11/26 | Thanksgiving holiday - no class. | |
| Monday 11/29 | Work done on a body in gravitational field. Problem 5-14. Problem 5-5. | |
| Wednesday 12/1 | Third Midterm Exam. The exam covers sections 3.8, 3.9, 5.1, 5.2, 5.3 and 5.4. Section 5.5 "Ocean tides" will not be covered. | |
| Friday 12/3 | Motion of objects with variable mass. Read Section 9.11 "Rocket motion" and the two examples in it: rocket motion in free space and vertical ascent under gravity. | |
| Monday 12/6 | Review: Finding the gravitational field of extended objects. Problem 5-21. Problem 5-7. | |
| Wednesday 12/8 | (This material will not be on the final exam). Section 1.3 Coordinate transformations. Section 1.4. Properties of rotation matrices. Section 1.5. Matrix operations. Section 1.6. Further definitions. Section 1.7. Geometrical significance. Section 1.8. Definition of a scalar and a vector in terms of transformation matrices. Invariance of the dot product under rotations. | |
| Tuesday 12/14 | Final Exam: 12:30 pm - 2:30 pm |