Physics 234
Classical Mechanics with Professor Charlie Duke
Spring 2002
Weekly Assignments
General Course Schedule
Exam Schedule
Course Grading
Problem Set Solutions
General Comments
Mathematical Techniques
email Prof. DukeClassical Mechanics provides the core foundation for physics. Thus, a thorough knowledge of the methods and concepts of mechanics is essential for understanding of all areas of physics. This course will combine physical concepts with various mathematical techniques from calculus, linear algebra and differential equations. Thus, in this course, you will use mathematics more rigorously than in your introductory or modern physics courses. As a self-contained discipline (there are no loose ends!), I expect that you enjoy and appreciate the power of mathematical reasoning applied to everyday (well, almost everyday) phenomena.
A major goal of this course is to develop and hone your problem-solving skills. For this reason, I will often give daily assignments, usually several short problems that you will return to me the following class period. Sometimes, you will present these problems on the blackboard in class. At other times, I will pass out problems for you or your group to work in class on the blackboard. Also, we will have the usual weekly problem sets composed of both short and longer problems. I encourage you to work in small groups on these problem sets; however, each of you must do your own work in preparing your presentation of the solution to give to me.
We will loosely follow the text and our class activities will not precisely mirror material in the text. Thus, class attendance becomes especially important as is keeping up to date with the problem assignments. As you can see in the following, I have scheduled three hour exams plus a final.
Text: "Newtonian Dynamics," Ralph Baierlein (McGraw-Hill, 1983)
Week of January 21 Review Mechanics from Physics 131 Week of January 28 Chapter 1: A Review of Some Basics Week of February 4 Chapter 2: The Harmonic Oscillator Week of February 11 Chapter 2: The Harmonic Oscillator
Friday, February 15: First ExamWeek of February 18 Chapter 4: Lagrangian Formulation Week of February 25 Chapter 4: Lagrangian Formulation Week of March 4 Chapter 5: Two-Body Problem Week of March 11 Chapter 5: Two-Body Problem
Friday, March 15: Second ExamWeek of April 1 Chapter 6: Rotating Frames of Reference Week of April 8 Chapter 6: Rotating Frames of Reference Week of April 15 Chapter 7: Extended Bodies in Rotation Week of April 22 Monday, Aprill 22: Third Exam
Chapter 7: Extended Bodies in RotationWeek of April 29 Chapter 8: Cross-Sections Week of May 6 Chapter 8: Cross-Sections [top]
We will have three hour-exams and a comprehensive final exam. One problem on each exam will come directly from the problem sets. The hour-exams will be scheduled as follows:
1. February 15, Friday
2. March 15, Friday
3. April 22, MondayFinal Exam: May 15, Monday 9:00 AM
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Hour-exams: 50%
Problem sets: 20%
Final exam: 30%[top]
You should prepare your problems-set solutions as presentations. That is, each completed problem should present a logical solution that includes a diagram, prose comments and explanations, and appropriate mathematics beginning with first principles as much as possible. I will return your problem sets as quickly as possible and will post solutions. I will place problem assignments on the course webpage.
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1. Keeping up with the problem assignments is crucial.
2. Start working on the problem sets as soon as they are assigned.
3. Raise questions in class about the assigned problems or come see me.
4. Use math handouts and textbook references.
5. I hope a number of you will become interested in working on several interesting
computer solutions -- more about this later.[top]
Here is a partial list of various techniques you should know (or learn as the semester progresses). I will provide handouts or references so don't worry if you haven't seen these techniques yet.
1. Basic vector algebra (unit vectors, scalar and cross products)
2. Basic vector calculus (gradient and curl, tangent and normal vectors)
3. Kinematics in polar, cylindrical, and spherical coordinates
4. Binomial expansion and Taylor series expansion
5. Expressions in both Cartesian and polar coordinates for an ellipse, parabola, and hyperbola
6. Solutions to second-order, non-homogeneous differential equations with constant coefficients
7. Determination of eigenvalues and eigenvectors of symmetric, square matrices
8. Rotation of coordinate systems and properties of orthogonal matrices[top]
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