|Week start||Topics this week||Reading and Assignments|
5.1 Sequences, convergence and limits of sequences.
|Watch 0: Introduction, 1:Sequences, 2:Limits of sequences, and 3: Monotone sequences.
Read section 5.1 in the text.
Homework HW1 on Lumen OHM, due Wed. Feb 10
|2/8||finish 5.1 limits of sequences, monotone convergence.
5.2 Infinite sums: the harmonic series, geometric series, telescoping series
|Watch All previous videos (01-03), 4: comparing sequences , 5: Infinite series, 6: The harmonic series and 7: Geometric series. See also this this Numberphile video about series.
Read section 5.2 and the first half of section 5.6 in the text.
Homework HW2 on Lumen OHM, due Wed. Feb 17
|2/15||5.6.1 The Ratio test and absolute convergence
6.1 Power series and functions, radius of convergence
|Watch 8: telescoping series , 9: the divergence test, 10: The ratio test, 11: power series (intro), and 12: power series (radius of convergence).
Read last week's reading, and also section 6.1 in the text.
Homework HW3 on Lumen OHM, due Wed. Feb 24
|2/22||6.2 Manipulating power series: adding, subtracting, substitution, multiplication, differentiation, integration.||Watch 11: power series (intro), and 12: power series (radius of convergence).
Read last week's reading, and also section 6.2 and 6.3 in the text.
Homework HW4 on Lumen OHM, due Wed. March 3
|3/1||6.3 Taylor and Maclaurin series, Taylor series with remainder, approximating with Taylor series
6.4 The binomial series
|Watch all the previous videos you haven't watched yet, as well as 13: new power series from old, 14: multiplication of power series, 15: definition of Taylor series; see also these from 2011: Maclaurin and Taylor series, Manipulating Taylor series and the binomial series.
Read last week's reading, and also section 6.3 and 6.4 in the text.
Homework HW5 on Lumen OHM, due Wed. March 10
|3/8||6.4 Using Taylor series: Taylor series for common functions, limits with Taylor series, evaluating integrals.
5.3.2 The integral test
|Watch all the previous videos you haven't watched yet, as well as 16: Shortcuts for Taylor series, 17: Computing limits with Taylor series, 18: The binomial series, and 19: Estimating the error of approximation by Taylor polynomials and 20: Integrals with Taylor series.
Read sections 6.4 and 5.3 in the text.
Homework HW6 on Lumen OHM, due Wed. March 17 Sunday March 21
|3/15||5.4.2 comparison test and limit comparison test
5.5 absolute convergence and alternating series
6.1.2 interval of convergence
4pm on March 19: Last day to move down to MAT132/MAT126.
|Watch 21: Interval of convergence, 22: review of improper integrals (optional), 23: The integral test, 24: p-series, 25: The comparison test, 26: The limit comparison test, 27: Absolute convergence, and 28: alternating series.
Read all of chapters 5 and 6.
Homework There is no HW7; we included this material on HW6. Study for the midterm instead, by reviewing old homeworks and quizzes.
Midterm on 3/24 or 3/25. See details here.
|Watch all the videos you need to prepare for the midterm.
Read all of chapters 5 and 6.
Homework not this week, but don't worry, we will have more.
|3/29||4.1 Differential equations: general and particular solutions, initial value problems.
4.2 Direction fields, Euler's method
It is the Stony Brook staycation week, so no quiz this week and also no homework due.
|Watch 29: Introduction to differential equations, 30: Basics of differential equations, 31: Slope (direction) fields, 32: Tutorial about slope-field plotting software, and 33: Euler's method.
Read section 4.1 and 4.2 in the text.
Homework HW8 on Lumen OHM, due Wed. April 7
|4/5||4.2 Euler's method
4.3 Separable equations. Mixing problems, Newton's law of cooling.
|Watch 33: Euler's method, 34: Separation of Variables, 35: Newton's law of cooling.
Read section 4.2 and 4.3 in the text.
Homework HW9 on Lumen OHM, due Wed. April 14
|4/12||4.4 The Logistic equation and population dynamics.
6.4 Power series solutions
|Watch 36: Models (mostly separable), 37: Population growth- the Logistic model, and 38: Series solutions to differential equations.
Read Section 4.4 in the text and examples 6.20 and 6.21 (in section 6.4). See also Using series to solve ODEs.
Homework HW10 on Lumen OHM, due Wed. April 21
start second order linear ODEs
|Watch 39: Complex number review, and 40: The complex exponential and Euler's Formula.
Read A review of algebra and arithmetic for complex numbers, and Euler's formula and the polar form of complex numbers.
Homework HW11 on Lumen OHM, due Wed. April 28
|4/26||Second order linear homogeneous equations with constant coefficients.||Watch 41: Second order linear equations, part 1 and 42: Second order linear equations with complex roots.
Read Notes on second order linear homogeneous differential equations. See also 2nd order linear ODEs and applications.
Homework HW12 on Lumen OHM, due Wed. May 6
|5/3||Review||Watch any or all the videos
Read Chapters 4, 5, and 6 in the text.
Homework that would just be mean.
Wednesday, May 12, 11:15am-1:45pm