Posted here are useful links and documents that I composed while teaching or assisting in various math courses.
The documents are review and/or lecture notes, written for particular courses/exams/books.
The corresponding book titles are noted below.
These files may contain outdated information about websites, office hours, etc.,
or contain notes to myself about what to cover in my lectures.
But the math is still good!
These notes may not be comprehensive and may contain errors.
Please email errata information to: dambroise@math.umass.edu
These documents may be reproduced for personal use, but are not to be distributed or sold.
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Topic
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Book
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Errata
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Basic Math
Binary and Other Bases
Roman Numerals
Percents
Interest
Installment Buying
Mortgages
Combinations and Permutations
Probability and Odds
Data and Statistics
Measurements and Conversions
Geometry
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Thinking Mathematically
2nd edition, by Robert Blitzer
(Prentice-Hall)
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Calculus I
Old Exams From Umass Classes
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Calculus: Early Transcendentals
5th Edition, by James Stewart
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Calculus II
Antidifferentiation, Integrals as "Area" and
the Fundamental Theorem of Calculus
6-3 Area Between Curves
6-3 Cumulative Change, Average, Mean Value Theorem, Volume
6-3 Arclength
7-1 Substitution
7-2 Integration By Parts
Review
7-3 Practicing Integration
7-3 Integrating Rational Functions
How To Set Up PFD
7-4 Indefinite Integrals of Type 1 (x goes to infinity)
7-4 Indefinite Integrals of Type 2 (y goes to infinity)
8-1 Differential Equations
8-1 Differential Equations continued
7-6 Tables Of Integrals
Integration Flow Chart & Tables Of Integrals
8-2 Equilibria and Stability
Systems of Differential Equations
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Calculus for Biology and Medicine
2nd Edition, by Claudia Neuhauser
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Calculus II
Overview of Integration, Areas, Volumes and Series
Trig Facts
Step by Step Proof of the Fundamental Theorem of Calculus
Chart of Convergence Tests for Series
Series Convergence Examples
Power, Taylor and Maclaurin Series
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Calculus: Early Transcendentals
5th Edition, by James Stewart
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Calculus III
12-1 Three-Dimensional Coordinate Systems
12-2 Vectors
12-3 The Dot Product
12-4 The Cross Product
12-5-1 Equations of Lines
12-5-2 Equations of Planes
Review Graphing Conic Sections
12-6 Cylinders and Quadric Surfaces
10-1 Curves Defined By Parametric Equations
13-1 Vector Functions and Space Curves
13-2 Derivatives and Integrals of Vector Functions
Review Of Differentiation And Integration
13-3 Arclength and Curvature
13-4 Motion in Space Velocity and Acceleration
Review Part 1a Vectors, Lines, Planes, Surfaces
Review Part 1b Computations with Lines and Planes
14-1 Functions of Several Variables
14-2 Limits and Continuity
14-3 Partial Derivatives
Meaning Of Derivatives Chart
14-4 Tangent Planes and Linear Approximations
14-5 The Chain Rule
14-6 Directional Derivatives and the Gradient Vector
14-7 Maximum and Minimum Values
14-8 Lagrange Multipliers
Review Max/Min Values and Lagrange Multipliers
15-1 Double Integrals over Rectangles
15-2 Iterated Integrals
15-3 Double Integrals over General Regions
Review Part 2
10-3 Polar Coordinates
15-4 Double Integrals in Polar Coordinates
15-5 Applications of Double Integrals
16-1 Vector Fields
16-2 Line Integrals
16-3 Fundamental Theorem For Line Integrals
16-4 Green's Theorem
Summary of Line Integral Methods
Calc III Overview
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Calculus: Early Transcendentals
5th Edition, by James Stewart
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Differential Equations Problems
HW#1
HW#2
HW#3
HW#4
HW#5
HW#6
HW#7
Course-Wide Review (very computational)
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Elementary Differential Equations
8th Edition, by Boyce & DiPrima
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Differential Equations
Review Part I (both qualitative and computational)
3-7 Trace-Determinant Plane
(classifies all possible phase plane behaviours
of constant-coeff second order homogeneous eqns)
3-6 2nd Order Linear Constant Coeff Equations
Some Problems 3-7, 4-1
(4-1: NonHomog 2nd Order Linear Eqns,
i.e. forced harmonic oscillators)
6-1 Definition of Laplace Transforms
List Of Laplace Transforms
Some Laplace Transform Problems
6-5 Convolutions
6-6 Poles of Laplace Transform (qualitative results)
Review Problems
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Differential Equations
8th Edition, by Blanchard, Devaney and Hall
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