United States Military Academy
Combined Math and Physics Course
Christopher Lehner and Jon Shupenus
Audience: We will teach the firstsemester 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 doubleperiod 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 R^{3} 
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 
(CSection) R: PH251M Lab 2: (Lab Tour) 
(ASection) S: PH251M Lab 2: (Lab Tour) MakeAhead 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 MIDTERM 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 
MakeUp 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
Syllabi index
Introduction