Math 0100 Topics

Note: two of these sections run on a MWF schedule
and one of the sections runs on a TuTh schedule.
For this reason, there might not be an exact day-to-day
match between the listed topics and the lectures.
However, the syllabus should be very accurate on a
week by week basis.

Week 1 Chapter 5 -- the integral (mostly review)

• review of differentiation
• 5.1-5.2: review of integration (5.1-5.2)
• 5.3-5.4: fundamental theorem of calculus
• 5.5: u-substitition

Week 2 Chapter 6 -- applications of the integral

• 6.1: area under a curve
• 6.2-6.3 : volumes
• 6.5: average value of a function
• 8.1: arc length

Week 3 Chapter 7 -- techniques of integration

• 7.1: integration by parts
• 7.2: trigonometric integrals

Week 4 Chapter 7 -- techniques of integration

• 7.3: trig substitution
• 7.4: partial fractions

First Midterm (Covers up to Sect. 7.3)

Week 5 Chapter 7 -- techniques of integration

• 7.4: partial fractions
• 7.7: approximation
• 7.8: indefinite integrals

Week 6 Chapter 9 -- differential equations

• modelling
• direction fields; Euler's method
• separable equations

Week 7 Chapter 9 -- differential equations

• linear equations
• science applications

Week 8 Chapter 9,11 -- differential equations, series

• 2nd order linear differential equations
• introduction to sequences

Week 9 Chapter 11 -- series

• properties of sequences
• elementary properties of series

Second Midterm

Week 10 Chapter 11 -- series

• the integral test
• comparison tests

Week 11 Chapter 11 -- series

• alternating series
• root and ratio tests; radius of convergence

Week 12 Chapter 11 -- series

• power series
• Taylor series
  

Week 13 Chapter 11 -- series

• Taylor/MacLauren Theorem
• applications to differential equations

Week 14 Chapter 10

• paramatric equations
• polar coordinates

Any time left over before the final
will be dedicated to rewiew.

Final