Category Archives: By License Type

Indivisible Guide and Toolkit

Indivisible Guide (pdf)

Indivisible Tool Kit (pdf)

Excerpt: “Welcome! You’re receiving this toolkit because you, we, and thousands of groups across the country are ready to stand indivisible. Groups are meeting to plan the resistance against Trump’s agenda, and making plans to visit the offices of their Members of Congress.”

About Indivisible
When we put the Indivisible Guide online as a poorly formatted, typo-filled Google Doc, we never imagined how far and fast it would spread. Since December, the guide has been downloaded over a million times. More than 4,500 local groups have signed up to resist the Trump agenda in nearly every congressional district in the country. What’s more, you all are putting the guide into action—showing up en masse to congressional district offices and events, and flooding the congressional phone lines. You’re resisting—and it’s working.

We are absolutely floored. It may have started as a tweeted Google Doc, but now (and sorry if this sounds corny) we feel an extraordinary sense of responsibility to help this movement as best we can. To do this, the Indivisible Guide team is starting a (nonprofit) organization, and we want to tell you why.

Bottom line, we want to do two big things better:

Demystify congressional advocacy. We get hundreds of questions every day about what Congress is doing, how to organize locally (see the toolkit!), and how to advocate in different situations. We’re going to start sending out timely updates and resources on what’s going on in Congress and how you can best organize, make your voice heard, and influence your members of Congress.

Support the community of local groups putting the Indivisible Guide into action. We want to provide shared tools to help groups organize events, communicate with each other, and share best practices and resources. This also means spotlighting local successes and supporting a sense of a shared purpose. You can see that shared purpose already forming—just look at this beautiful movement on Rachel Maddow.

We are already doing some of this! We now have over seventy (70!) volunteers working early mornings, late nights, weekends, and sick days on everything that you see the Indivisible Guide team do—email responses, congressional updates, the group directory, the website, our social media, and a bunch more. It’s been an amazing labor of love by a stellar group of, yeah we’ll say it, patriots. But we want to do more.

As we form a nonprofit, we want to make something clear: we’re not the leaders of this movement. The last few weeks have made it abundantly clear that local groups are taking ownership of the resistance to Trump’s agenda themselves. You all are the leaders—we’re just here to help.

We’re still developing our long-term strategy, and we want to hear from you about what you need and want. But going forward, you’ll see a lot more from us in those two buckets of work above—we want to demystify the heck out of Congress and build a vibrant community of angelic troublemakers.

In solidarity,

Ezra Levin
President of the Board

Leah Greenberg
Vice President of the Board

Angel Padilla
Secretary of the Board

Sarah Dohl
Board Member

Matt Traldi
Treasurer of the Board

Wilkin, “Human Biology” (2015)

HumanBiologyCK12_humanmusclesNote.  This textbook is the minimum required reading for Yoga School exams.

Textbook: Wilkin, “Human Biology” (2015)
Download the free  PDF (color, 28MB).

Douglas Wilkin, Ph.D.
Jean Brainard, Ph.D.

Please Say Thanks to the Authors for Creating this Open Licensed Textbook.
(No sign in required)

This open licensed textbook is part of full series of anatomy and physiology content provided by  Please support open education resources.

Human Biology Outline

1.1 Organization of the Human Body
1.2 Homeostasis
1.3 Carcinogens and Cancer
1.4 Air Pollution and Illness
1.5 Bioterrorism
1.6 Human Skeletal System
1.7 Structure of Bones
1.8 Growth and Development of Bones
1.9 Skeletal System Joints
1.10 Skeletal System Problems and Diseases
1.11 Smooth, Skeletal, and Cardiac Muscles
1.12 Skeletal Muscles
1.13 Muscle Contraction
1.14 Skin
1.15 Nails and Hair
1.16 Nerve Cells
1.17 Nerve Impulses
1.18 Central Nervous System
1.19 Peripheral Nervous System
1.20 Senses
1.21 Drugs and the Nervous System
1.22 Nervous System Disorders
1.23 Glands
1.24 Hormones
1.25 Hormone Regulation
1.26 Endocrine System Disorders
1.27 Heart
1.28 Blood Vessels
1.29 Circulatory System
1.30 Circulatory System Diseases
1.31 Blood
1.32 Respiration
1.33 Respiratory System Organs
1.34 Processes of Breathing
1.35 Respiratory System Regulation
1.36 Respiratory System Diseases
1.37 Digestive System Organs
1.38 Digestion
1.39 Small Intestine
1.40 Large Intestine
1.41 Digestive System Diseases
1.42 Food and Nutrients
1.43 Balanced Eating
1.44 Excretion
1.45 Urinary System
1.46 Kidneys
1.47 Excretory System Diseases
1.48 Barriers to Pathogens
1.49 Inflammatory Response and Leukocytes
1.50 Lymphatic System
1.51 Humoral Immune Response
1.52 Cell-Mediated Immune Response
1.53 Immunity
1.54 Allergies
1.55 Autoimmune Diseases
1.56 Immunodeficiency
1.57 HIV and AIDS
1.58 Male Reproductive Structures
1.59 Male Reproductive Development
1.60 Human Sperm
1.61 Female Reproductive Structures
1.62 Female Reproductive Development
1.63 Human Egg Cells
1.64 Menstrual Cycle
1.65 Fertilization
1.66 Embryo Growth and Development
1.67 Fetus Growth and Development
1.68 Fetal Development and the Placenta
1.69 Pregnancy and Childbirth
1.70 Development from Birth to Adulthood
1.71 Adulthood and Aging
1.72 Sexually Transmitted Infections
1.73 Bacterial Sexually Transmitted Infections
1.74 Viral Sexually Transmitted Infections
1.75 References

Download the free  PDF (color, 28MB).

Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

Magnus, P.D., "paratodo x: Una Introducción a la Lógica Formal" (2015)

Magnus, P.D., “paratodo x: Una Introducción a la Lógica Formal” (2015).

Philosophy Faculty Books. Book 4.

University at Albany, State University of New York
Scholars Archive
Philosophy Faculty Books Philosophy
Summer 2015
paratodo x: Una Introducción a la Lógica Formal
P.D. Magnus
University at Albany, State University of New York,

►Héroux, Principles of Toxicology (2013)

Dr. Paul Héroux,  PhD

Principles of Toxicology  (2013)

ISBN: 978-1-312-74790-6
License: CC BY-SA-NC

Toxicology studies the injurious effects of chemical and physical agents (including energy) on living organisms, observed as alterations in structure and function. The variety of injurious effects becomes apparent if we examine the major causes of death (Fl .I). Many of these diseases are caused or accelerated by exposure to toxic substances. Toxicity data from various bio-medical sciences document the effects of exposure to natural• or artificial agents.

Purchase Print* Version $49.95  (grayscale,  324 pages)  Compare at  $117  on

Download free PDF* (Print version) (grayscale, 324  pages)

Download original  free color PDF (Full color, 324 pages, 39 MB)

Author’s Toxicology Laboratory Website

*Errata  Page 5-11 contains an incorrect formula, except in the full color pdf.  Replace it with this one (pdf, 154K): 5-11 Replacement Page


Textbook Contents

1. Scope of Toxicology
2. Risk Assessment
3. Targets and Bio-Transformation
4. Toxicokinetics
5. Hemato- and Vascular Toxicity
6. Dermatotoxicity
7. Neurotoxicity
8. Hepatotoxicity
9. Nephrotoxicity
10. Techniques In Vivo & In Vitro
11 . Pulmonary Toxicity
12. Reproductive Toxicity
13. Geno toxicity
14. Carcinogenicity

*Photo Source: (CC BY-SA 2.5

► Seifert, et. al. Educational Psychology (2009)

Seifert and Sutton,  Educational Psychology (2009)

From the authors, “All in all, we hope that you find Educational Psychology a useful and accessible part of your education. If you are preparing to be a teacher, good luck with your studies and your future! If you are an instructor, good luck with helping your students learn about this subject!”

Purchase print copy $49.95 (365 pages, 12 chapters, see table of contents below)

Download Free PDF (color, 4 Mb, 365 pages).

Original Source:  Global Text Project


Table of Contents

1. The changing teaching profession and you.

  • The joys of teaching
  • Are there also challenges to teaching?
  • Teaching is different from in the past
  • How educational psychology can help

2. The learning process

  • Teachers’ perspectives on learning
  • Major theories and models of learning

3. Student development.

  • Why development matters.
  • Physical development during the school years
  • Cognitive development: the theory of Jean Piaget
  • Social development: relationships,personal motives, and morality
  • Moral development: forming a sense of rights and responsibilities
  • Understanding “the typical student” versus understanding students.

4. Student diversity

  • Individual styles of learning and thinking.
  • Multiple intelligences.
  • Gifted and talented students
  • Gender differences in the classroom
  • Differences in cultural expectations and styles
  • Oppositional cultural identity.
  • Accommodating cultural diversity in practice.

5. Students with special educational needs

  • Look at these three people from the past. All were assigned marginal status in society because of beliefs about disabilities:.
  • Growing support for people with disabilities: legislation and its effects
  • Responsibilities of teachers for students with disabilities.
  • Categories of disabilities—and their ambiguities
  • Learning disabilities.
  • Attention deficit hyperactivity disorder.
  • Intellectual disabilities.
  • Behavioral disorders.
  • Physical disabilities and sensory impairments
  • The value of including students with special needs

6. Student motivation

  • Motives as behavior
  • Motives as goals.
  • Motives as interests.
  • Motives related to attributions
  • Motivation as self-efficacy.
  • Motivation as self-determination
  • Expectancy x value: effects on students’ motivation
  • TARGET: a model for integrating ideas about motivation.

7. Classroom management and the learning environment

  • Why classroom management matters
  • Preventing management problems by focusing students on learning.
  • Responding to student misbehavior.
  • Keeping management issues in perspective.

8. The nature of classroom communication

  • Communication in classrooms vs communication elsewhere.
  • Effective verbal communication.
  • Effective nonverbal communication.
  • Structures of participation: effects on communication
  • Communication styles in the classroom.
  • Using classroom talk to stimulate students’ thinking
  • The bottom line: messages sent, messages reconstructed

9. Facilitating complex thinking

  • Forms of thinking associated with classroom learning
  • Critical thinking
  • Creative thinking
  • Problem-solving
  • Broad instructional strategies that stimulate complex thinking
  • Teacher-directed instruction
  • Student-centered models of learning.
  • Inquiry learning
  • Cooperative learning.
  • Examples of cooperative and collaborative learning
  • Instructional strategies: an abundance of choices.

10. Planning instruction

  • Selecting general learning goals.
  • Formulating learning objectives
  • Differentiated instruction and response to intervention.
  • Students as a source of instructional goals.
  • Enhancing student learning through a variety of resources.
  • Creating bridges among curriculum goals and students’ prior experiences.
  • Planning for instruction as well as for learning.

11. Teacher-made assessment strategies.

  • Basic concepts.
  • Assessment for learning: an overview of the process
  • Selecting appropriate assessment techniques I: high quality assessments
  • Reliability
  • Absence of bias
  • Selecting appropriate assessment techniques II: types of teacher-made assessmentsSelected response items
  • Constructed response items
  • Portfolios.
  • Assessment that enhances motivation and student confidence
  • Teachers’ purposes and beliefs
  • Choosing assessments
  • Providing feedback
  • Self and peer assessment
  • Adjusting instruction based on assessment.
  • Communication with parents and guardians.
  • Action research: studying yourself and your students.
  • Grading and reporting

12. Standardized and other formal assessments

  • Basic concepts.
  • High-stakes testing by states
  • International testing.
  • International comparisons
  • Understanding test results.
  • Issues with standardized tests

Appendices and Resources

  • Appendix A: Preparing for licensure.
  • Appendix B: Deciding for yourself about the research
  • Appendix C: The reflective practitioner.
  • Resources for professional development and learning
  • Reading and understanding professional articles
  • Action research: hearing from teachers about improving practice.
  • The challenges of action research.
  • Benefiting from all kinds of research

► Nievergelt,"Algorithms and Data Structures – With Applications to Graphics and Geometry" (2011)

Nievergelt, Algorithms and Data Structures – With Applications to Graphics and Geometry” (2011)product_thumbnail.php

An Open Textbook by Jurg Nievergelt and Klaus Hinrichs

An introductory coverage of algorithms and data structures with application to graphics and geometry.”

This textbook, released under a Creative Commons Share Alike (CC BY SA) license, is presented in its original format with the academic content unchanged. It was authored by Jurg Nievergelt (ETH Zurich) and Klaus Hinrichs (Institut für Informatik) and provided by the University of Georgia’s Global Textbook Project.

Photo Credit: Renato Keshet (GFDL)

Buy Print Copy $39.99 (371 pages, paperback, B&W)

Free PDF Download  (5.5 Mb)

Table of Contents

Part I: Programming environments for motion, graphics, and geometry

Reducing a task to given primitives: programming motion
A robot car, its capabilities, and the task to be performed
Wall-following algorithm described informally
Algorithm specified in a high-level language
Algorithm programmed in the robot’s language
The robot’s program optimized
Graphics primitives and environments
Turtle graphics: a basic environment
QuickDraw: a graphics toolbox
A graphics frame program
Algorithm animation
Computer-driven visualization: characteristics and techniques
A gallery of algorithm snapshots

Part II: Programming concepts: beyond notation

Algorithms and programs as literature: substance and form
Programming in the large versus programming in the small
Documentation versus literature: is it meant to be read?
Pascal and its dialects: lingua franca of computer science
Divide-and-conquer and recursion
An algorithmic principle
Divide-and-conquer expressed as a diagram: merge sort
Recursively defined trees
Recursive tree traversal
Recursion versus iteration: the Tower of Hanoi
The flag of Alfanumerica: an algorithmic novel on iteration and recursion
Syntax and semantics
Grammars and their representation: syntax diagrams and EBNF
An overly simple syntax for simple expressions
Parenthesis-free notation for arithmetic expressions
Syntax analysis
The role of syntax analysis
Syntax analysis of parenthesis-free expressions by counting
Analysis by recursive descent
Turning syntax diagrams into a parser

Part III: Objects, algorithms, programs

Truth values, the data type ‘set’, and bit acrobatics
Bits and boolean functions
Swapping and crossovers: the versatile exclusive-or
The bit sum or “population count”
Ordered sets
Sequential search
Binary search
In-place permutation
Recognizing a pattern consisting of a single string
Paths in a graph
Boolean matrix multiplication
Warshall’s algorithm
Minimum spanning tree in a graph
Operations on integers
The Euclidean algorithm
The prime number sieve of Eratosthenes
Large integers
Modular number systems: the poor man’s large integers
Random numbers
Floating-point numbers
Some dangers
Horner’s method
Newton’s method for computing the square root
Straight lines and circles
Drawing digitized lines
The riddle of the braiding straight lines
Digitized circles

Part IV: Complexity of problems and algorithms

Computability and complexity
Models of computation: the ultimate RISC
Almost nothing is computable
The halting problem is undecidable
Computable, yet unknown
Multiplication of complex numbers
Complexity of matrix multiplication
The mathematics of algorithm analysis
Growth rates and orders of magnitude
Summation formulas
Recurrence relations
Asymptotic performance of divide-and-conquer algorithms
Sorting and its complexity
What is sorting? How difficult is it?
Types of sorting algorithms
Simple sorting algorithms that work in time T(n)
A lower bound O(n · log n)
Analysis for three cases: best, “typical”, and worst
Is it possible to sort in linear time?
Sorting networks

Part V: Data structures

What is a data structure?
Data structures old and new
The range of data structures studied
Performance criteria and measures
Abstract data types
Concepts: What and why?
First-in-first-out queue
Priority queue
Implicit data structures
What is an implicit data structure?
Array storage
Implementation of the fixed-length fifo queue as a circular buffer
Implementation of the fixed-length priority queue as a heap
List structures
Lists, memory management, pointer variables
The fifo queue implemented as a one-way list
Tree traversal
Binary search trees
Height-balanced trees
Address computation
Concepts and terminology
The special case of small key domains
The special case of perfect hashing: table contents known a priori
Conventional hash tables: collision resolution
Choice of hash function: randomization
Performance analysis
Extendible hashing
A virtual radix tree: order-preserving extendible hashing
Metric data structures
Organizing the embedding space versus organizing its contents
Radix trees, tries
Quadtrees and octtrees
Spatial data structures: objectives and constraints
The grid file
Simple geometric objects and their parameter spaces
Region queries of arbitrary shape
Evaluating region queries with a grid file
Interaction between query processing and data access

Part VI: Interaction between algorithms and data structures: case studies in geometric computation

Sample problems and algorithms
Geometry and geometric computation
Convex hull: a multitude of algorithms
The uses of convexity: basic operations on polygons
Visibility in the plane: a simple algorithm whose analysis is not
Plane-sweep: a general-purpose algorithm for two-dimensional problems illustrated using line segment intersection
The line segment intersection test
The skeleton: Turning a space dimension into a time dimension
Data structures
Updating the y-table and detecting an intersection
Sweeping across intersections
Degenerate configurations, numerical errors, robustness
The closest pair
The problem
Plane-sweep applied to the closest pair problem
Sweeping in three or more dimensions

►Feher,"Introduction to Digital Logic" with Laboratory Exercises (2010)

James Feher,”Introduction to Digital Logic” with Laboratory Exercises (2010)

This lab manual provides an introduction to digital logic, starting with simple gates and building up to state machines. Students should have a solid understanding of algebra as well as a rudimentary understanding of basic electricity including voltage, current, resistance, capacitance, inductance and how they relate to direct current circuits.

Buy Print Format $23.49 (99 pages, B&W)

ISBN 978-1-312-50167-6

Download Free PDF (100 pages, color, 3.2 Mb)

Extra Features

  • Peer Reviewed
    Exercises & Solutions

Table of Contents

1. Introduction

2. The transistor and inverter

The transistor
The breadboard
The inverter

3. Logic gates

History of logic chips
Logic symbols
Logical functions

4. Logic simplification

De Morgan’s laws
Karnaugh maps
Circuit design, construction and debugging

5. More logic simplification

Additional K-map groupings
Input placement on K-map
Don’t care conditions

6. Multiplexer

Background on the “mux”
Using a multiplexer to implement logical functions

7. Timers and clocks

Timing in digital circuits
555 timer
Timing diagrams

8. Memory

SR latch

9. State machines

What is a state machine?
State transition diagrams
State machine design
Debounced switches

10. More state machines

How many bits of memory does a state machine need?
What are unused states?

11. What’s next?


Appendix A: Chip pinouts
Appendix B: Resistors and capacitors
Appendix C: Lab notebook
Appendix F: Solutions
Chapter 1 review exercises
Chapter 2 review exercises
Chapter 3 review exercises
Chapter 4 review exercises
Chapter 5 review exercises
Chapter 6 review exercises
Chapter 7 review exercises
Chapter 8 review exercises
Chapter 9 review exercises

►Schmidt-Jones, The Basic Elements of Music (2013)

By Evdokiya [CC-BY-SA-3.0 (], via Wikimedia Commons
The Basic Elements of Music
By Catherine Schmidt-Jones
Explanations (suitable for any age) of the basic elements of music, with suggested activities for introducing the each concept to children at early elementary school level. The course may be used by instructors not trained in music; all necessary definitions and explanations are included. – From the book

Textbook Equity Edition
ISBN: 978-1-312-48694-2
License CC BY-SA

Buy Print  $19.95 + s&h, tax

Download Free PDF (107 pages, 2.7 MB) (registration not required)

Explanations (suitable for any age) of the basic elements of music, with suggested activities for introducing the each concept to children at early elementary school level. The course may be used by instructors not trained in music; all necessary definitions and explanations are included. – From the book

This music textbook, authored by Catherine Schmidt-Jones, is released under a Creative Commons Attribution Share-Alike license, published by Textbook Equity without changes to the academic content.

Table of Contents

1 Time Elements
1.1 Rhythm
1.2 Simple Rhythm Activities
1.3 Meter in Music
1.4 Musical Meter Activities
1.7 Dynamics and Accents in Music
1.8 A Musical Dynamics Activity
1.9 A Musical Accent Activity
2 Pitch Elements
2.1 Timbre
2.2 Melody
2.3 Harmony
3 Combining Time and Pitch
3.1 The Textures of Music
3.2 A Musical Textures Activity
3.3 An Introduction to Counterpoint
3.4 Counterpoint Activities: Listening and Discussion
3.6 Music Form Activities
3.7 Form in Music


arpeggiated chords
bass line
block chords
borrowed division
chord progression
chords chorus
conjunct motion
disjunct motion
functional harmony
harmonic rhythm
implied harmony
inner parts
inner voices
language arts
lesson plan
Measure or bar
melodic contour
melodic line
melodic phrase
melodic shape
movie music
movie score
musical instruments
national art standard
national dance standard
national English standard
national music standard
on the beat
on the downbeat
parallel harmony
polyphonic texture
rhythm section
sentence shape
time signature
tone quality
vivace voices

►TBQ Editors,"College Biology – Chapter Summaries, Learning Exercises & Answers" (2014)

[Paged Updated 10/06/2015]

College Biology -Chapter Summaries, Learning Exercises & Answers” (2014)

This useful publication contains the learning exercises, answers, and glossary of “College Biology” Volumes 1 – 3.


Buy Printed Version  $19.99 USD (Black & White, 263 pages)
ISBN: 978-1-312-45149-0

Download PDF (free, color, 263 pages, 22 Mb)


  • Chapter Summaries
  • Art Connection Questions
  • Review Questions
  • Critical Thinking Exercises
  • Answers by Chapter
  • Complete Glossary/Key Terms

This textbook is designed as a quick reference for “College Biology” volumes one through three. It contains the “Chapter Summary”, “Art Connection”, “Review”, and “Critical Thinking” Exercises found in each of the three volumes. It also contains the COMPLETE alphabetical listing of the key terms. “College Biology”, intended for capable college students, is adapted from OpenStax College’s open (CC BY) textbook “Biology”. It is Textbook Equity’s derivative to ensure continued free and open access, and to provide low cost print formats. For manageability and economy, Textbook Equity created three volumes from the original that closely match typical semester or quarter biology curriculum. No academic content was changed from the original. See This supplement covers all 47 chapters.

►TBQ Editors, Mathematical Analysis Vol 1 (2011)

2product_thumbnail.phpMathematical Analysis Vol 1 (2011)

A top quality open textbook for advanced undergraduates and graduate students.

A complementary textbook to Saylor Academy’s Free Online Math 241 course.

Purchase Print $28.92, 365 pages.  Softcover, black and white.

Download free pdf, 4mb, 385 pages.

  • Peer Reviewed
  • Widely Adopted
  • Plenty of practice problems


Mathematical Analysis Vol 1, (2011)

* “Starred” sections may be omitted by beginners.

Chapter 1. Set Theory

1–3. Sets and Operations on Sets. Quantifiers 1
Problems in Set Theory 6
4–7. Relations. Mappings 8
Problems on Relations and Mappings 14
8. Sequences 15
9. Some Theorems on Countable Sets 18
Problems on Countable and Uncountable Sets 21

Chapter 2. Real Numbers. Fields 23

1–4. Axioms and Basic Definitions 23
5–6. Natural Numbers. Induction 27
Problems on Natural Numbers and Induction 32
7. Integers and Rationals 34
8–9. Upper and Lower Bounds. Completeness 36
Problems on Upper and Lower Bounds 40
10. Some Consequences of the Completeness Axiom 43
11–12. Powers With Arbitrary Real Exponents. Irrationals 46
Problems on Roots, Powers, and Irrationals 50
13. The Infinities. Upper and Lower Limits of Sequences 53
Problems on Upper and Lower Limits of Sequences in E* 60

Chapter 3. Vector Spaces. Metric Spaces 63

1–3. The Euclidean n-space, En 63
Problems on Vectors in En 69
4–6. Lines and Planes in En 71
Problems on Lines and Planes in En 75
7. Intervals in En 76
Problems on Intervals in En 79
8. Complex Numbers 80
Problems on Complex Numbers 83
*9. Vector Spaces. The Space Cn. Euclidean Spaces 85
Problems on Linear Spaces 89
*10. Normed Linear Spaces 90
Problems on Normed Linear Spaces 93
11. Metric Spaces 95
Problems on Metric Spaces 98
12. Open and Closed Sets. Neighborhoods 101
Problems on Neighborhoods, Open and Closed Sets 106
13. Bounded Sets. Diameters 108
Problems on Boundedness and Diameters 112
14. Cluster Points. Convergent Sequences 114
Problems on Cluster Points and Convergence 118
15. Operations on Convergent Sequences 120
Problems on Limits of Sequences 123
16. More on Cluster Points and Closed Sets. Density 135
Problems on Cluster Points, Closed Sets, and Density 139
17. Cauchy Sequences. Completeness 141
Problems on Cauchy Sequences 144

Chapter 4. Function Limits and Continuity 149

1. Basic Definitions 149
Problems on Limits and Continuity 157
2. Some General Theorems on Limits and Continuity 161
More Problems on Limits and Continuity 166
3. Operations on Limits. Rational Functions 170
Problems on Continuity of Vector-Valued Functions 174
4. Infinite Limits. Operations in E* 177
Problems on Limits and Operations in E* 180
5. Monotone Functions 181
Problems on Monotone Functions 185
6. Compact Sets 186
Problems on Compact Sets 189
*7. More on Compactness 192
8. Continuity on Compact Sets. Uniform Continuity 194
Problems on Uniform Continuity; Continuity on Compact Sets. 200
9. The Intermediate Value Property 203
Problems on the Darboux Property and Related Topics 209
10. Arcs and Curves. Connected Sets 211
Problems on Arcs, Curves, and Connected Sets 215
*11. Product Spaces. Double and Iterated Limits 218
*Problems on Double Limits and Product Spaces 224
12. Sequences and Series of Functions 227
Problems on Sequences and Series of Functions 233
13. Absolutely Convergent Series. Power Series 237
More Problems on Series of Functions 245

Chapter 5. Differentiation and Antidifferentiation 251

1. Derivatives of Functions of One Real Variable 251
Problems on Derived Functions in One Variable 257
2. Derivatives of Extended-Real Functions 259
Problems on Derivatives of Extended-Real Functions 265
3. L’Hˆopital’s Rule 266
Problems on L’Hˆopital’s Rule 269
4. Complex and Vector-Valued Functions on E1 271
Problems on Complex and Vector-Valued Functions on E1 275
5. Antiderivatives (Primitives, Integrals) 278
Problems on Antiderivatives 285
6. Differentials. Taylor’s Theorem and Taylor’s Series 288
Problems on Taylor’s Theorem 296
7. The Total Variation (Length) of a Function f : E1 ? E 300
Problems on Total Variation and Graph Length 306
8. Rectifiable Arcs. Absolute Continuity 308
Problems on Absolute Continuity and Rectifiable Arcs 314
9. Convergence Theorems in Differentiation and Integration 314
Problems on Convergence in Differentiation and Integration 321
10. Sufficient Condition of Integrability. Regulated Functions 322
Problems on Regulated Functions 329
11. Integral Definitions of Some Functions 331
Problems on Exponential and Trigonometric Functions 338