MATH 1271   Calculus I
INSTRUCTOR: SCOT ADAMS
(look ahead)

Some material from the course will be covered two, or even three, times.

I'll discuss it, in lecture, *before* the it's covered in the videos. Then I'll discuss it, again, at the time that it's covered in the videos.

The first time through, we are "looking ahead", and, typically, the look-ahead material focuses on simple skills (e.g., differentiation and integration). The second time through, we'll go into more depth, and try to understand how the skills are to be used.

Finally, as time permits, we may "look back" at material already covered in the videos, for review.

The following is the plan for looking ahead:

• WEEK 01:
  • W: start practicing differentiation of polynomials and trig functions
  • F: start practicing the product rule, from f(g(x)) to f and g(x), (d/dx)(f(x))=f'(x)
• WEEK 02:
  • M: practice quotient rule, power series of e^x, sin x and cos x, triple product rule, derivative of constant
  • W: practice chain rule, Newton's method, linear approximation
  • F: derivative of e^x, practice chain rule
• WEEK 03:
  • M: practice differentiation, from gph of f to domain of f', derivative of \ln(x) and \ln|x|
  • W: practice differentiation; logarithmic differentiation; derivative of x^a, a^x, log_a(x), where a is constant
  • F: practice differentiation, chain rule: (d/dx)(expression of u), (d/dt)(expression of v), etc.
• WEEK 04:
  • M: practice differentiation, start differentiation of inverse trig functions
  • W: practice differentiation
  • F: practice differentiation, derivatives of inverse functions
• WEEK 05:
  • M: antidifferentiation / indefinite integration of x^n, for positive integers n
  • W: antidifferentiation / indefinite integration of x^n, for positive integers n
  • F: antidifferentiation / linearity of antidifferentiation and indefinite integration / indefinite integration of polynomials
• WEEK 06:
  • M: no look ahead, prepare for Midterm 1
  • W: no look ahead, prepare for Midterm 1
  • F: antidifferentiation / indefinite integration of \sin and \cos
• WEEK 07:
  • M: antidifferentiation / indefinite integration of 1/x
  • W: integration by substitution
  • F: practice antidifferentiation / indefinite integration
• WEEK 08:
  • M: lengths (length of arc of circle, circumference of circle),
  • M: areas (rectangle, parallelogram, triangle, sector, cylinder, cone, disk, hemisphere, sphere),
  • M: volumes (cylinder/prism, cone/pyramid, solid sector, ball)
  • W: integration of reciprocals of quadratics (x^2 + 1, then x^2 - 1, then 1 - x^2, then ax^2 + bx + c)
  • F: distance = area under velocity (for constant velocity, then linear velocity, then continuous velocity)
  • F: area under t^2 from 0 to 2 (the hard way, the easy way)
  • F: the Fundamental Theorem of Calculus
• WEEK 09:
  • M: compare [Fundamental Theorem of Calculus] to [Fundamental Theorem of Precalculus]
  • W: integration of sin^2, cos^2, sqrt{1-x^2}, wait until 1272 for general sqrt{quadratic}
  • F: definite integration by substitution
• WEEK 10:
  • M: Taylor polynomials
  • W: area between two curves
  • F: volume of sphere by disk method
• WEEK 11:
  • M: no look ahead, prepare for Midterm 2
  • W: no look ahead, prepare for Midterm 2
  • F: volume of sphere by shell method