An implementation of TAMU Coalition freshman math

As an example (not a prescription) of how the FC freshman calculus curriculum can be implemented, we present here a daily record of the classes taught by S. A. Fulling during Fall 1997 and Spring 1998. In some instances these "diary entries" were written in advance and served as lecture notes; in others they were reconstructed after the fact. Added remarks in ALL CAPS label plans that were not executed because of shortage of time, or attempt to evaluate the success or failure of various pedagogical strategies. (Frequently, pidgin TeX syntax is used for mathematical expressions.) The paper version includes photocopies of some overhead transparencies used or written in the course of the classes.

For a variety of reasons, the day-to-day content of the classes does not correspond exactly to the syllabi in Part One. This is especially so for the fall semester, which matched only approximately the Spring 1998 version taught by D. L. Barrow; in particular, he reversed the order of topics 4 and 5 to improve the coordination with the physics syllabus.

List of teaming, active learning, and assessment activities

1. Maple, Functions and Graphs, Calculus Preview
   • Objectives: Week 1; Week 2
   • Text material on the Web: Introduction and Maple; Functions
   • Classes: 1.1; 1.2; 2.1.
2. Tangents and Velocities, Limits, Continuity
   • Objectives: Week 2; Week 3.
   • Classes: 2.2; 3.1 and 3.2.

   Review and Test 1a (Day 3.3)

3. Derivatives and Antiderivatives
   • Objectives
   • Classes: 3.3; 4.1; 4.2
4. Differentiation Rules and Applications
   • Objectives: Week 5; Week 6
   • Classes: 4.3; 5.1; 5.2

   Review and Test 1b (Day 5.3)

5. Vectors
   • Objectives
   • Text material on the Web
   • Classes: 6.1; 6.2; 6.3
6. Parametric Curves; Polar Coordinates
   • Objectives
   • Text material on the Web: Parametric Curves ; Polar Coordinates
   • Classes: 6.2; 6.3
7. Chain Rule, Implicit Differentiation, Related Rates
   • Objectives
   • Classes: 7.1; 7.2; 7.3; 8.1
   • Associated material on the Web (DVI landscape) (PDF portrait); cf. later days 10.1; 10.2; 10.3
8. Definite Integral; Numerical Integration
   • Objectives: Week 8; Week 9
   • Classes: 8.1; 8.2; 9.1; 9.2

   Review and Test 2 (Day 8.3)

9. Integration: Fundamental Theorem, Substitution, Area
   • Objectives: Week 9; Week 10
   • Classes: 9.3; 10.1; 10.2
10. Line Integrals, Vector Fields, Double Integrals
    • Objectives: Week 10; Week 11; Week 12; Week 13
    • Text material on the Web [not yet available]
    • Classes: 10.3; 11.1; 11.2 and 11.3; 12.1; 12.2; 13.1; 13.2

    Review and Test 3 (Day 12.3)

11. Properties of Functions and Graphs (Extrema, Concavity, Asymptotes, etc.)
    • Objectives: Week 13; Week 14
    • Classes: 14.1; 14.2; 14.3; 15.1

    Review and Midterm Exam

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12. Vectors in Three Dimensions
    • Objectives
    • Classes: 16.T; 16.R
13. Applied Max/Min Problems
    • Objectives
    • Classes: 16.T; 16.R; 17.T; 17.R
    • Associated material on the Web
14. Differentials; Newton's Method
    • Objectives
    • Text material on the Web
    • Classes: 17.T; 17.R
15. Transcendental Functions (exp, ln, Inverse Trig)
    • Objectives: Week 17; Week 18
    • Classes: 17.R; 18.T; 18.R; 19.T
    • Associated material on the Web
16. L'Hospital's Rules
    • Objectives
    • Text material on the Web
    • Classes: 19.T

    Review and Test 4 (Day 19.R)

17. Integration by Parts
    • Objectives
    • Classes: 20.T
18. Volumes
    • Objectives: Week 20; Week 21
    • Classes: 20.T; 20.R; 21.T
19. Centers of Mass and Moments of Inertia
    • Objectives: Week 21; Week 22
    • Text material on the Web
    • Classes: 21.T; 21.R; 22.T; 22.R
20. First-Order Differential Equations
    • Objectives: Week 22; Week 23
    • Classes: 22.R; 23.T

    Review and Test 5 (Day 23.R)

21. Second-Order Differential Equations
    • Objectives
    • Classes: 24.T; 24.R; 25.T
22. Taylor Expansions
    • Objectives
    • Text material on the Web
    • Classes: 25.T; 25.R; 26.T; 27.T
23. Logic and Limits
    • Objectives
    • Text material on the Web (DVI ) (PDF )
    • Classes: 26.T; 26.R; 27.T
24. Limits Involving Infinity; Improper Integrals
    • Objectives
    • Classes: 27.T; 28.T; 28.R

    Review and Test 6 (Day 27.R)

25. Sequences and Series
    • Objectives: Week 28; Week 29
    • Text material on the Web (DVI landscape) (PDF portrait)
    • Classes: 28.R; 29.T; 29.R
26. Historical Perspective
    • Objectives
    • Classes: 30.T

    Review and Final Exam