Math 9 Course Syllabus

Calculus of One and Several Variables

Syllabus

The following is a tentative syllabus for the course. This page will be updated irregularly. On the other hand, the weekly syllabus contained in the Homework Assigments page will always be accurate. You may notice that the syllabus is similar with that of Math 8. This is no coincidence - while the topics in Math 9 are virtually the same as those in Math 8, the treatment of these topics will differ.

Lectures Sections in Text Brief Description

Day 1:  9/25 10.1, 10.2 General DEs, models, direction fields (skip Euler's method)

Day 2:  9/27 10.3, 10.4 Separable equations (skip orthogonal trajectories), exponential growth

Day 3:  9/30 8.1, 10.6 Integration by Parts (quickly), First Order Linear Differential Equations

Day 4:  10/2 10.6, Appendix G First Order Linear DE applications, Complex Numbers

Day 5:  10/4 Appendix G, 18.1 Complex Numbers, Second order linear DEs

Day 6:  10/7 18.1, 18.3 Second order linear DEs (continued); Applications

Day 7:  10/9 12.1, 12.2 Basics about sequences and series; geometric series

Day 8:  10/11 12.3, 12.4, 12.5 Comparison test; Alternating series; Absolute convergence (quickly)

Day 9:  10/14 12.6, 12.8, Ratio test; Power Series

Day 10:  10/16 12.9, 12.10 Representing functions as power series; Taylor Series

Day 11:  10/18 12.10 Taylor Series

Day 12:  10/21 12.12 Error Estimates on Talyor polynomials

Day 12: 10/21 First Hour Exam 6 - 8 pm

Day 13:  10/23 13.1, 13.2 Three dimensional coordinate systems, vectors

Day 14:  10/25 13.3, 13.4 Dot products, Cross products

Day 15:  10/28 13.5 Equations of lines

Day 16:  10/30 13.5 Equations of planes

Day 17:  11/1* 14.1, 14.2 Vector functions and space curves, derivatives of vector functions (Classes meet in x-hour instead of Friday)

Day 18:  11/4 14.3, 14.4 Arc length, velocity and acceleration (motion problems)),

Day 19:  11/6 15.1, 15.2 Functions of several variables, limits, continuity

Day 20:  11/8 15.3 Partial derivatives (skip Cobb-Douglas function)

Day 21:  11/11 15.4 Tangent planes and approximation

Day 21: 11/11 Second Hour Exam 6 - 8 pm

Day 22:  11/13 15.5 Chain rule

Day 23:  11/15 15.5, 15.6 Chain rule (cont.), Directional derivative and gradient

Day 24:  11/18 15.6 Directional derivative and gradient (cont.)

Day 25:  11/20 15.7 Maxima and minima

Day 26:  11/22 15.7 Maxima and minima (cont.)

Day 27:  11/25 15.8 Lagrange multipliers

Thanksgiving break 11/27 and 12/1

Day 28:  12/2 15.8 Lagrange multipliers (cont.), Loose ends, questions, etc.

Day 29:  12/4 -- Review etc.

Lectures	Sections in Text	Brief Description
Day 1: 9/25	10.1, 10.2	General DEs, models, direction fields (skip Euler's method)
Day 2: 9/27	10.3, 10.4	Separable equations (skip orthogonal trajectories), exponential growth
Day 3: 9/30	8.1, 10.6	Integration by Parts (quickly), First Order Linear Differential Equations
Day 4: 10/2	10.6, Appendix G	First Order Linear DE applications, Complex Numbers
Day 5: 10/4	Appendix G, 18.1	Complex Numbers, Second order linear DEs
Day 6: 10/7	18.1, 18.3	Second order linear DEs (continued); Applications
Day 7: 10/9	12.1, 12.2	Basics about sequences and series; geometric series
Day 8: 10/11	12.3, 12.4, 12.5	Comparison test; Alternating series; Absolute convergence (quickly)
Day 9: 10/14	12.6, 12.8,	Ratio test; Power Series
Day 10: 10/16	12.9, 12.10	Representing functions as power series; Taylor Series
Day 11: 10/18	12.10	Taylor Series
Day 12: 10/21	12.12	Error Estimates on Talyor polynomials
Day 12: 10/21		First Hour Exam 6 - 8 pm
Day 13: 10/23	13.1, 13.2	Three dimensional coordinate systems, vectors
Day 14: 10/25	13.3, 13.4	Dot products, Cross products
Day 15: 10/28	13.5	Equations of lines
Day 16: 10/30	13.5	Equations of planes
Day 17: 11/1*	14.1, 14.2	Vector functions and space curves, derivatives of vector functions (Classes meet in x-hour instead of Friday)
Day 18: 11/4	14.3, 14.4	Arc length, velocity and acceleration (motion problems)),
Day 19: 11/6	15.1, 15.2	Functions of several variables, limits, continuity
Day 20: 11/8	15.3	Partial derivatives (skip Cobb-Douglas function)
Day 21: 11/11	15.4	Tangent planes and approximation
Day 21: 11/11		Second Hour Exam 6 - 8 pm
Day 22: 11/13	15.5	Chain rule
Day 23: 11/15	15.5, 15.6	Chain rule (cont.), Directional derivative and gradient
Day 24: 11/18	15.6	Directional derivative and gradient (cont.)
Day 25: 11/20	15.7	Maxima and minima
Day 26: 11/22	15.7	Maxima and minima (cont.)
Day 27: 11/25	15.8	Lagrange multipliers
		Thanksgiving break 11/27 and 12/1
Day 28: 12/2	15.8	Lagrange multipliers (cont.), Loose ends, questions, etc.
Day 29: 12/4	--	Review etc.