Recommended Material For The Pre-Calculus and Calculus Course Sequence

The Pre-Calculus Sequence

Our present text for Pre-Calculus I and II (Math 163.1 and 163.2, respectively) is Functions Modeling Change (2nd Edition) by Connally, Hughes-Hallett, Gleason, et al.

Pre-Calculus I:

Chapter 1: Cover sections 1.1-1.5. Section 1.6 is optional.
Chapter 2: Cover sections 2.1-2.6.
Chapter 3: Cover sections 3.1-3.4.
Chapter 4: Cover sections 4.1-4.3. Section 4.4 is optional.
Chapter 5: Cover sections 5.1-5.5.

Remarks: If the above material is finished, jump to Chapter 9. Don't go into Chapter 6, as the material on Trigonometry is the main unit for Pre-Calc II

Pre-Calculus II:

Chapter 6: Cover sections 6.1-6.7.
Chapter 7: Cover sections 7.1-7.6.
Chapter 8: Cover sections 8.1-8.3.
Chapter 9: Cover sections 9.1-9.6.
Chapter 10: Cover sections 10.1-10.4.

Remarks: Chapters 1, 2, 3, 5, 6, and 9 have sections at the end called Tools. These sections review material from elementary algebra which is needed in the chapter. It is recommended that some work be assigned from these sections to reinforce these skills which, as we are only too aware, are often lacking. These sections should probably not be covered in class since they are about material the students should already know, but rather, used as review.

The Calculus Sequence

Our current Calculus text continues the program begun in Pre-Calculus. The Calculus text, Calculus, Single and Multivariable (3nd Edition) by Hughes-Hallett, Gleason, McCallum, et al, is written by the same Calculus Consortium that wrote the Pre-Calculus text, and the spirit and philosophy behind the two texts should be very similar, resulting in a more unified sequence of courses.

Calculus I:

Chapter 1: This chapter contains material already covered in Pre-Calculus. It should be viewed as reference material and not actually covered in class.
Chapter 2: Cover sections 2.2-2.7.
Chapter 3: Cover sections 3.1-3.10.
Chapter 4: Cover sections 4.1-4.7. Sections 4.4 and 4.6 are optional.

Calculus II:

Chapter 5: Cover sections 5.1-5.4.
Chapter 6: Cover sections 6.1-6.5.
Chapter 7: Cover sections 7.1-7.8. Section 7.8 is optional. Don’t spend much time on sections 7.5 and 7.6.
Chapter 8: Cover sections 8.1-8.4. Additional topics from sections 8.5-8.7 may be included if time permits. Alternatively…
Chapter 11: If time permits, the first few sections here could be included.

Calculus III:

Chapter 9: Cover sections 9.1-9.4.
Chapter 10: Cover sections 10.1-10.3. Section 10.4 is optional.
Chapter 12: Cover sections 12.1-12.6.
Chapter 13: Cover sections 13.1-13.4. Students should have already seen 2D-vectors in Pre-Calc II. The extension to 3D should be fairly smooth.
Chapter 14: Cover sections 14.1-14.7. Section 14.8 is optional
Chapter 15: Cover sections 15.1-15.2. Section 15.3 is optional.

Calculus IV:

Chapter 16: Cover sections 16.1-16.5. Sections 16.6, 16.7 are optional.
Chapter 17: Cover sections 17.1-17.5.
Chapter 18: Cover sections 18.1-18.4.
Chapter 19: Cover sections 19.1-19.3.
Chapter 20: Cover sections 20.1-20.5.