See the course Blackboard Site for detailed information and assignments.


Advanced Mechanics is the second in a two-semester sequence of courses in undergraduate classical mechanics. It is the expectation of the instructor that each student is comfortable with Physics I and II and has a passing understanding of the core elements and techniques of Modern Physics (PH 401) and Mechanics (PH 439) as taught in the Fall semester of 2003. The purpose of Advanced Mechanics is that you master these core elements at a high undergraduate level.



To pass the course, all students will master the following Level 1 (introductory) and Level 2 (intermediate) tasks.

Level 1 Tasks:

All students completing Advanced Mechanics will be able to perform the following Level 1 tasks by midterm.

• Successfully work and orally explain any “standard” mechanics problems from the introductory Physics I text in a timely manner without texts or formulas.
• Integrate using u and basic trigonometric substitutions without integration tables.
• Perform surface and volume integrals on basic geometric shapes.
• Sketch the graph of any function f(x) – identifying features such as singularities, local extrema, and asymptotic behavior.
• Take the dot or cross product of any two vectors.
• Take the gradient of a function, and the divergence and curl of any vector field.
• Solve 1st order ODEs by separation of variables.
• Solve linear, 2nd order homogeneous ODEs.

Level 2 Tasks:

All students completing Advanced Mechanics will be able to perform the following Level 2 tasks by the end of the course.

• Successfully work and orally explain “complex” mechanics problems from the introductory Physics I text in a timely manner without texts or formulas.
• Perform “complex” integrals using an integration table.
• Apply solutions to differential equations to physics by evaluating initial conditions.
• Write a Lagrangian for a given system and obtain equations of motion. Simplify these equations of motion using conserved quantities.
• Write a Hamiltonian for a given system and obtain equations of motion.
• Obtain the gravitational field and gravitational potential for “standard” mass distributions using multi-dimensional integrals.
• Explain and work problems in central force motion at the level of Thornton and Marion.
• Explain and work problems in the dynamics of systems of particles at the level of Thornton and Marion.

Students will use the following texts and sources liberally throughout this course:

1. Classical Dynamics of Particles and Systems by Thornton and Marion,
2. any standard introductory Physics textbook,
3. the GRE Physics book published by the Research and Education Association,
4. the Schaum’s Outline Series book on Advanced Mathematics for Engineers and Scientists, and
5. the University of Pittsburgh Preliminary Examination Packet.


1. Students will demonstrate mastery of Level 1 tasks in a 30-minute oral examination by the Physics faculty at midterm.

2. Students will demonstrate mastery of Level 2 tasks in a comprehensive, two-hour final exam at the end of the term. The problems on this final exam will be on the level of Physics GRE and University of Pittsburgh Preliminary Examination.

Students must pass both the oral exam and final exam to pass the course. A final course grade will be determined by averaging the two exams.

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