United States Military Academy
Combined Math and Physics Course
Christopher Lehner and Jon Shupenus
Audience: We will teach the first-semester of physics (mechanics) combined with the second semester of multivariable calculus during the first semester of sophomore year. This year we will have approximately 65 students who have volunteered for honors physics combined with math. It will be a coordinated course with some team teaching.
Goal: Coordination. In the past, cadets at West Point took math and physics without any coordination between the two departments. One result from this was duplication of effort by the departments and confusion among the students over basic items such as notation.
Course Description: The courses will be listed separately but block scheduled in the same rooms. Five instructors (3 math and 2 physics) will be teaching the courses to four sections. The syllabus is coordinated and lessons are scheduled as math or physics. Each instructor team will determine the amount of team teaching and additional integration. Class time consists of 64 lessons of math, 40 lessons of physics and 8 double-period physics labs. Each period is 55 minutes. Two integrated projects will be completed. The courses will be graded separately but projects and some tests will be graded for both physics and math.
Syllabus:
Hour |
16 Aug |
17 Aug |
18 Aug |
19 Aug |
20 Aug |
A or C |
1 |
MA205P Lsn 2: Parametric Equations |
2 |
MA205P Lsn 4: Vector Functions |
3 |
B/H or D/J |
MA205P Lsn 1: Course Intro and Review |
PH251M Lsn 1: 1 Dim. Motion |
MA205P Lsn 3: Vectors |
MA205P Lsn 5: Derivatives and Integrals of Vector Functions |
MA205P Lsn 6: Problem Solving Lab |
23 Aug |
24 Aug |
25 Aug |
26 Aug |
27 Aug |
|
A or C |
MA205P Lsn 7: FSE |
4 |
MA205P Lsn 9: Eqns of Lines & Planes, Dist. in R3 |
5 |
PH251M Lab 1 (Ballistic Motion) |
B/H or D/J |
PH251M Lsn 2: 2 Dim. Motion I |
MA205P Lsn 8: Motion In Space |
PH251M Lsn 3: 2 Dim. Motion II |
MA205P Lsn 10: Problem Solving Lab |
|
30 Aug |
31 Aug |
1 Sep |
2 Sep |
3 Sep |
|
A or C |
6 (Lab 1T) |
PH251M Lsn 4: Newton's Laws I |
7 |
PH251M Lsn 5: Newton's Laws II |
8 (Lab 1U) |
B/H or D/J |
MA205P Lsn 11: Intersections and Collisions |
MA205P Lsn 12: Dot Product |
MA205P Lsn 13: Cross Product |
MA205P Lsn 14: Problem Solving Lab & Review |
MA205P LSN 15: WPR I |
(Tue) 7 Sep |
(Wed) 8 Sep |
(Thu) 9 Sep |
(Fri) 10 Sep |
(Sat) 11 Sep |
|
A or C |
PH251M Lab 2 (Friction & 1 Hour Drop for Lab Tour) |
9 |
PH251M Lsn 7: Newton's Laws IV |
10 (WPR I Drop) |
PH251M Lsn 10: WPR I |
B/H or D/J |
PH251M Lsn 6: Newton's Laws III |
MA205P Lsn 16: Arc Length and Curvature |
MA205P Lsn 17: Functions of Several Variables |
||
R & S Labs |
(C-Section) R: PH251M Lab 2: (Lab Tour) |
(A-Section) S: PH251M Lab 2: (Lab Tour) Make-Ahead WPR |
|||
13 Sep |
14 Sep |
15 Sep |
16 Sep |
17 Sep |
|
A or C |
PH251M Lsn 10: Drop for WPR I |
11 (Lab 2T) |
MA205P Lsn 20/21: Directional Derivative & Gradient |
12 (Lab 2U) |
PH251M Lsn 9: Work & Energy I |
B/H or D/J |
MA205P Lsn 18: Partial Derivatives, Limits, Continuity |
MA205P Lsn 19: Chain rule |
PH251M Lsn 8: Newton's Laws V |
MA205P Lsn 22: Problem Solving Lab |
|
20 Sep |
21 Sep |
22 Sep |
23 Sep |
24 Sep |
|
A or C |
13 |
MA205P Lsn 23/24: Extrema of Functions of 2 Variables |
14 |
MA205P Lsn 25/26: Lagrange Multipliers |
15 |
B/H or D/J |
PH251M Lsn 11: Work & Energy II |
PH251M Lsn 12: Cons. of Energy I |
PH251M Lsn 13: Cons. of Energy II |
||
27 Sep |
28 Sep |
29 Sep |
30 Sep |
1 Oct |
|
A or C |
MA205P Lsn 27/28: Double Integrals Over Rectangles and General Regions |
16 (Lab 3T) |
PH251M Lab 3 (Cause and Effect) |
17 (Lab 3U) |
PH251M Lsn 15 & 16: Cons. of Linear Momentum I & II |
B/H or D/J |
PH251M Lsn 14: Systems of Particles |
MA205P Lsn 29: Applications of Double Integrals |
|||
4 Oct |
5 Oct |
6 Oct |
7 Oct |
No class 8 – 11 Oct Columbus Day |
|
A or C |
18 (WPR II Drop for Sat. 18 Oct.) |
PH251M Lab 4 (Cons. of Energy) |
19 |
Combined MID-TERM EXAM |
|
B/H or D/J |
MA205P Lsn 30: Applications of Double Integrals |
MA205P Lsn 31: Problem Solving Lab & Review |
|||
(Tue) 12 Oct |
(Wed) 13 Oct |
(Thu) 14 Oct |
(Fri) 15 Oct |
(Sat) 16 Oct |
|
A or C |
20 (Lab 4T) |
PH251M Lsn 17: TBD |
21 (Lab 4U) |
PH251M Lsn 20: TBD |
22 |
B/H or D/J |
MA205P Lsn 33: Polar & Spherical Coordinates |
MA205P Lsn 34: Double Integrals Polar Coordinates |
PH251M Lsn 19: TBD |
MA205P Lsn 35: Problem Solving Lab |
MA205P Lsn 36: Applications of Double Integrals in Polar Coordinates |
18 Oct |
19 Oct |
20 Oct |
21 Oct |
22 Oct |
|
A or C |
PH251M Lsn 21: Rotational Motion I |
23 |
PH251M Lsn 22: Rotational Motion II |
24 |
PH251M Lsn 24: Rotation of Rigid Bodies |
B/H or D/J |
MA205P Lsn 37: Triple Integrals |
MA205P Lsn 38: Triple Integrals in Cylindrical/Spherical Coordinates |
MA205P Lsn 39: Project Drop |
PH251M Lsn 23: Torque |
MA205P Lsn 40: Problem Solving Lab |
25 Oct |
26 Oct |
27 Oct |
28 Oct |
29 Oct |
|
A or C |
PH251M Lsn 26: Rigid Body Equilibrium |
PH251M Lab 5 (Cons. of Angular Moment.) |
27 |
||
B/H or D/J |
PH251M Lsn 25: Cons. of Angular Momentum |
MA205P Lsn 41: Sequences |
MA205P Lsn 42: Series |
MA205P Lsn 43: Other Convergence Tests |
|
1 Nov |
2 Nov |
3 Nov |
4 Nov |
5 Nov |
|
A or C |
MA205P Lsn 44: Math of Gravitation |
28 |
PH251M Lsn 28: Kepler's Laws |
29 (Lab 6T) |
PH251M Lsn 29: Orbital Mechanics |
B/H or D/J |
PH251M Lsn 27: Gravitation |
MA205P Lsn 45: Problem Solving Lab |
MA205P Lsn 46: Motion in Space (Mathematics of Kepler’s Laws) |
MA205P Lsn 47: Power Series |
MA205P Lsn 48: Taylor & Maclaurin Series |
8 Nov |
9 Nov |
10 Nov |
(Fri) 12 Nov |
(Sat) 13 Nov |
|
A or C |
30 (Lab 6U) |
PH251M Lsn 30: Simple Harmonic Motion |
31 |
PH251M Lsn 32: (Drop for WPR III) |
PH251M Lsn 32:WPR III |
B/H or D/J |
MA205P Lsn 49: Taylor & Maclaurin Series |
MA205P Lsn 50: Problem Solving Lab |
MA205P Lsn 51: Using Series to Solve ODEs |
MA205P Lsn 52: Problem Solving Lab |
|
15 Nov |
16 Nov |
17 Nov |
18 Nov |
19 Nov |
|
A or C |
32 (WPR III Drop) |
PH251M Lsn 31: Energy & Pendula |
33 (Lab 7T) |
PH251M Lab 6 (Pendulum) |
34 (Lab 7U) |
B/H or D/J |
MA205P Lsn 53: WPR Review |
MA205P Lsn 54: WPR III |
MA205P Lsn 55: Math Applications |
PH251M Lsn 33: Damped & Forced Oscillations |
|
R & S Labs |
Make-Up WPR III |
||||
22 Nov |
23 Nov |
24 Nov |
25 Nov |
26 Nov |
|
A or C |
PH251M Lsn 34: Wave Motion |
35 |
PH251M Lsn 35: Standing Waves |
Thanksgiving leave |
|
B/H or D/J |
MA205P Lsn 56: Math Applications |
MA205P Lsn 57: Math Applications |
MA205P Lsn 58: Math Applications |
||
29 Nov |
30 Nov |
1 Dec |
2 Dec |
3 Dec |
|
A or C |
PH251M Lsn 36: Wave Effects |
36 |
PH251M Lab 7 (Design I) |
37 |
PH251M Lab 8 (Design II) |
B/H or D/J |
MA205P Lsn 59: Math Applications |
MA205P Lsn 60: Math Applications |
MA205P Lsn 61: Project Drop |
||
6 Dec |
7 Dec |
8 Dec |
9 Dec |
10 Dec |
|
A or C |
38 (Lab 8T) |
PH251M Lsn 38: TBD |
39 (Lab 8U) |
PH251M Lsn 39: TBD |
40 |
B/H or D/J |
PH251M Lsn 37: TBD |
MA205P Lsn 62: Math Applications |
MA205P Lsn 63: Math Applications |
MA205P Lsn 64: Math Applications |
PH251M Lsn 40: TBD |
Next syllabus