This book was written for an experimental freshman course at the University of Colorado. The course is now an elective that the majority of our electrical and computer engineering students take in the second semester of their freshman year, just before their first circuits course. Our department decided to offer this course for several reasons:

we wanted to pique student' interest in engineering by acquainting them with engineering teachers early in their university careers and by providing with exposure to the types of problems that electrical and computer engineers are asked to solve;
we wanted students entering the electrical and computer engineering programs to be prepared in complex analysis, phasors, and linear algebra, topics that are of fundamental importance in our discipline;
we wanted students to have an introduction to a software application tool, such as MATLAB, to complete their preparation for practical and efficient computing in their subsequent courses and in their professional careers;
we wanted students to make early contact with advanced topics like vector graphics, filtering, and binary coding so that they would gain a more rounded picture of modern electrical and computer engineering.
In order to introduce this course, we had to sacrifice a second semester of Pascal programming. We concluded that the sacrifice was worth making because we found that most of our students were prepared for high-level language computing after just one semester of programming.

We believe engineering educators elsewhere are reaching similar conclusions about their own students and curriculums. We hope this book helps create a much needed dialogue about curriculum revision and that it leads to the development of similar introductory courses that encourage students to enter and practice our craft.Students electing to take this course have completed one semester of calculus, computer programming, chemistry, and humanities.

Concurrently with this course, students take physics and a second semester of calculus, as well as a second semester in the humanities. By omitting the advanced topics marked by asterisks, we are able to cover Complex Numbers through Linear Algebra, plus two of the three remaining chapters. The book is organized so that the instructor can select any two of the three. If every chapter of this book is covered, including the advanced topics, then enough material exists for a two-semester course.

The first three chapters of this book provide a fairly complete coverage of complex numbers, the functions e^x and e^jand phasors. Our department philosophy is that these topics must be understood if a student is to succeed in electrical and computer engineering. These three chapters may also be used as a supplement to a circuits course. A measured pace of presentation, taking between sixteen and eighteen lectures, is sufficient to cover all but the advanced sections in Complex Numbers through Phasors.

The chapter on "linear algebra" is prerequisite for all subsequent chapters. We use eight to ten lectures to cover it. We devote twelve to sixteen lectures to cover topics from Vector Graphics through Binary Codes. (We assume a semester consisting of 42 lectures and three exams.) The chapter on vector graphics applies the linear algebra learned in the previous chapter to the problem of translating, scaling, and rotating images. "Filtering" introduces the student to basic ideas in averaging and filtering. The chapter on "Binary Codes" covers the rudiments of binary coding, including Huffman codes and Hamming codes.

If the users of this book find "Vector Graphics" through "Binary Codes" too confining, we encourage them to supplement the essential material in "Complex Numbers" through "Linear Algebra" with their own course notes on additional topics. Within electrical and computer engineering there are endless possibilities. Practically any set of topics that can be taught with conviction and enthusiasm will whet the student's appetite. We encourage you to write to us or to our editor, Tom Robbins, about your ideas for additional topics. We would like to think that our book and its subsequent editions will have an open architecture that enables us to accommodate a wide range of student and faculty interests.

Throughout this book we have used MATLAB programs to illustrate key ideas. MATLAB is an interactive, matrix-oriented language that is ideally suited to circuit analysis, linear systems, control theory, communications, linear algebra, and numerical analysis. MATLAB is rapidly becoming a standard software tool in universities and engineering companies. (For more information about MATLAB, return the attached card in the back of this book to The MathWorks, Inc.) MATLAB programs are designed to develop the student's ability to solve meaningful problems, compute, and plot in a high-level applications language. Our students get started in MATLAB by working through “An Introduction to MATLAB,” while seated at an IBM PC (or look-alike) or an Apple Macintosh. We also have them run through the demonstration programs in "Complex Numbers". Each week we give three classroom lectures and conduct a one-hour computer lab session. Students use this lab session to hone MATLAB skills, to write programs, or to conduct the numerical experiments that are given at the end of each chapter. We require that these experiments be carried out and then reported in a short lab report that contains (i) introduction, (ii) analytical computations, (iii) computer code, (iv) experimental results, and (v) conclusions. The quality of the numerical results and the computer graphics astonishes students. Solutions to the chapter problems are available from the publisher for instructors who adopt this text for classroom use.

We wish to acknowledge our late colleague Richard Roberts, who encouraged us to publish this book, and Michael Lightner and Ruth Ravenel, who taught "Linear Algebra" and "Vector Graphics" and offered helpful suggestions on the manuscript. We thank C. T. Mullis for allowing us to use his notes on binary codes to guide our writing of "Binary Codes". We thank Cédric Demeure and Peter Massey for their contributions to the writing of "An Introduction to MATLAB" and "The Edix Editor". We thank Tom Robbins, our editor at Addison-Wesley, for his encouragement, patience, and many suggestions. We are especially grateful to Julie Fredlund, who composed this text through many drafts and improved it in many ways. We thank her for preparing an excellent manuscript for production.

The First Note music curriculum is made up of 30 complete multi-cultural lessons broken down into 4-5 separate videos for each lesson. The program incorporates proven methods of music instruction developed by Carl Orff (Orff Schulwerk), Emile Jacques Dalcroze, Zoltan Kodaly and others. Video teaching tips are also included.

The program is a standards-based music program for use in Kindergarten and 1st Grade classrooms. Best of all, it's designed to be facilitated by all K-1 school teachers, and as an aid to all music instructors.

Word Count: 27595

(Note: This resource's metadata has been created automatically by reformatting and/or combining the information that the author initially provided as part of a bulk import process.)

Inflation, unemployment, recession, economic growth—these economic concepts affect people in very real ways. In two thought-provoking, interactive lessons, this course teaches students about fiscal policy, the avenue by which Congress and the president attempt to influence the economy. Graphs compliments of FRED.

The goal of this five-day exemplar is to explicitly model the process of searching for and interpreting intra-textual connections. In this lesson sequence, the teacher poses an analytic focusing question and then guides students in gathering and interpreting evidence from the text in order to come to a deeper understanding of the story. Simple word play and art activities give students practice in closely attending to language and word choice, and in visualizing and recording their interpretations. Discussion and a short writing exercise help students to synthesize what they have learned.

Students will work in collaborative groups to analyze and interpret research information from their previous reading assignment on the social, political, and economic impact of the Great Depression on the lives of Alabamians. Next, students will use a graphic organizer to collect information needed to develop and write a five paragraph expository essay on the social, political, and economic impact of the Great Depression on the lives of Alabamians. Finally, students will present their expository essay to the class. This unit was created as part of the ALEX Interdisciplinary Resource Development Summit.

This is a streamlined lesson for students to prepare for a Community Resilience Expo, focusing on flood.

Explore pressure in the atmosphere and underwater. Reshape a pipe to see how it changes fluid flow speed. Experiment with a leaky water tower to see how the height and water level determine the water trajectory.

Explore the forces at work when you try to push a filing cabinet. Create an applied force and see the resulting friction force and total force acting on the cabinet. Charts show the forces, position, velocity, and acceleration vs. time. View a Free Body Diagram of all the forces (including gravitational and normal forces).

Explore the forces at work when you try to push a filing cabinet. Create an applied force and see the resulting friction force and total force acting on the cabinet. Charts show the forces, position, velocity, and acceleration vs. time. View a Free Body Diagram of all the forces (including gravitational and normal forces).

Explore the forces at work in a tug of war or pushing a refrigerator, crate, or person. Create an applied force and see how it makes objects move. Change friction and see how it affects the motion of objects.

Explore the forces at work when you try to push a filing cabinet. Create an applied force and see the resulting friction force and total force acting on the cabinet. Charts show the forces, position, velocity, and acceleration vs. time. View a Free Body Diagram of all the forces (including gravitational and normal forces).

In this course, you will cover some of the most basic math applications, like decimals, percents, and even fractions. You will not only learn the theory behind these topics, but also how to apply these concepts to your life. You will learn some basic mathematical properties, such as the reflexive property, associative property, and others. The best part is that you most likely already know them, even if you did not know the proper mathematical terminology.

This lesson requires two class periods. In the first class period, students are asked to think of a way to decide who gets 100 pennies and how many each person gets. They learn about the concept of allocation and about different resource allocation methods. They evaluate the different methods using a graphic organizer. Next they listen to different scenarios and try to determine which allocation method was used. Then, after listening to the story Four Feet, Two Sandals about two girls who face some resource allocation issues, they identify the methods used in the story. In the second class period, the students are placed into groups to act out skits illustrating a resource allocation method that their classmates then try to guess. Finally, they read a news article about a resource and write letters to a city council outlining the ways the city could allocate the resource.

Learn how to make waves of all different shapes by adding up sines or cosines. Make waves in space and time and measure their wavelengths and periods. See how changing the amplitudes of different harmonics changes the waves. Compare different mathematical expressions for your waves.

Learn how to make waves of all different shapes by adding up sines or cosines. Make waves in space and time and measure their wavelengths and periods. See how changing the amplitudes of different harmonics changes the waves. Compare different mathematical expressions for your waves.

Match shapes and numbers to earn stars in this fractions game. Challenge yourself on any level you like. Try to collect lots of stars! The main topics of this interactive simulation include fractions, equivalent fractions, and mixed numbers.

Match shapes and numbers to earn stars in this fractions game. Challenge yourself on any level you like. Try to collect lots of stars! The main topics of this interactive simulation include fractions, equivalent fractions, and mixed numbers.