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This book covers the standard material for a one-semester course in multivariable calculus. The topics include curves, differentiability and partial derivatives, multiple integrals, vector fields, line and surface integrals, and the theorems of Green, Stokes, and Gauss. Roughly speaking the book is organized into three main parts corresponding to the type of function being studied: vector-valued functions of one variable, real-valued functions of many variables, and finally the general case of vector-valued functions of many variables. As is always the case, the most productive way for students to learn is by doing problems, and the book is written to get to the exercises as quickly as possible. The presentation is geared towards students who enjoy learning mathematics for its own sake. As a result, there is a priority placed on understanding why things are true and a recognition that, when details are sketched or omitted, that should be acknowledged. Otherwise the level of rigor is fairly normal. Matrices are introduced and used freely. Prior experience with linear algebra is helpful, but not required.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Vector valued functions Calculus Textbooks
- Resource Type:
- e-book
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e-book
Mathematical Reasoning: Writing and Proofis designed to be a text for the ?rst course in the college mathematics curriculum that introduces students to the processes of constructing and writing proofs and focuses on the formal development of mathematics. The primary goals of the text are to help students: Develop logical thinking skills and to develop the ability to think more abstractly in a proof oriented setting. Develop the ability to construct and write mathematical proofs using standard methods of mathematical proof including direct proofs, proof by contradiction, mathematical induction, case analysis, and counterexamples. Develop the ability to read and understand written mathematical proofs. Develop talents for creative thinking and problem solving. Improve their quality of communication in mathematics. This includes improving writing techniques, reading comprehension, and oral communication in mathematics. Better understand the nature of mathematics and its language. This text also provides students with material that will be needed for their further study of mathematics.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
- Resource Type:
- e-book
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e-book
This award-winning text carefully leads the student through the basic topics of Real Analysis. Topics include metric spaces, open and closed sets, convergent sequences, function limits and continuity, compact sets, sequences and series of functions, power series, differentiation and integration, Taylor's theorem, total variation, rectifiable arcs, and sufficient conditions of integrability. Well over 500 exercises (many with extensive hints) assist students through the material. For students who need a review of basic mathematical concepts before beginning "epsilon-delta"-style proofs, the text begins with material on set theory (sets, quantifiers, relations and mappings, countable sets), the real numbers (axioms, natural numbers, induction, consequences of the completeness axiom), and Euclidean and vector spaces; this material is condensed from the author's Basic Concepts of Mathematics, the complete version of which can be used as supplementary background material for the present text.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematical analysis Textbooks
- Resource Type:
- e-book
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e-book
Math in Society is a free, open textbook. This book is a survey of contemporary mathematical topics, most non-algebraic, appropriate for a college-level topics course for liberal arts majors. The text is designed so that most chapters are independent, allowing the instructor to choose a selection of topics to be covered. Emphasis is placed on the applicability of the mathematics. Core material for each topic is covered in the main text, with additional depth available through exploration exercises appropriate for in-class, group, or individual investigation. This book is appropriate for Math 107 (Washington State Community Colleges common course number).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Mathematics Textbooks
- Resource Type:
- e-book
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e-book
Linear Regression Using R: An Introduction to Data Modeling presents one of the fundamental data modeling techniques in an informal tutorial style. Learn how to predict system outputs from measured data using a detailed step-by-step process to develop, train, and test reliable regression models. Key modeling and programming concepts are intuitively described using the R programming language. All of the necessary resources are freely available online.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Linguistics -- Statistical methods R (Computer program language) Mathematical linguistics
- Resource Type:
- e-book
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e-book
This is a book on linear algebra and matrix theory. While it is self contained, it will work best for those who have already had some exposure to linear algebra. It is also assumed that the reader has had calculus. Some optional topics require more analysis than this, however. This book features an ugly, elementary, and complete treatment of determinants early in the book. Thus it might be considered as Linear algebra done wrong. I have done this because of the usefulness of determinants. However, all major topics are also presented in an alternative manner which is independent of determinants. The book has an introduction to various numerical methods used in linear algebra. This is done because of the interesting nature of these methods. The presentation here emphasizes the reasons why they work. It does not discuss many important numerical considerations necessary to use the methods effectively. These considerations are found in numerical analysis texts.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
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e-book
After being traditionally published for many years, this formidable text by W. Keith Nicholson is now being released as an open educational resource and part of Lyryx with Open Texts! Supporting today's students and instructors requires much more than a textbook, which is why Dr. Nicholson opted to work with Lyryx Learning. Overall, the aim of the text is to achieve a balance among computational skills, theory, and applications of linear algebra. It is a relatively advanced introduction to the ideas and techniques of linear algebra targeted for science and engineering students who need to understand not only how to use these methods but also gain insight into why they work. The contents have enough flexibility to present a traditional introduction to the subject, or to allow for a more applied course. Chapters 1–4 contain a one-semester course for beginners whereas Chapters 5–9 contain a second semester course. The text is primarily about real linear algebra with complex numbers being mentioned when appropriate (reviewed in Appendix A).
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
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e-book
We believe the entire book can be taught in twenty five 50-minute lectures to a sophomore audience that has been exposed to a one year calculus course. Vector calculus is useful, but not necessary preparation for this book, which attempts to be self-contained. Key concepts are presented multiple times, throughout the book, often first in a more intuitive setting, and then again in a definition, theorem, proof style later on. We do not aim for students to become agile mathematical proof writers, but we do expect them to be able to show and explain why key results hold. We also often use the review exercises to let students discover key results for themselves; before they are presented again in detail later in the book. The book has been written such that instructors can reorder the chapters (using the La- TeX source) in any (reasonable) order and still have a consistent text. We hammer the notions of abstract vectors and linear transformations hard and early, while at the same time giving students the basic matrix skills necessary to perform computations. Gaussian elimination is followed directly by an “exploration chapter” on the simplex algorithm to open students minds to problems beyond standard linear systems ones. Vectors in Rn and general vector spaces are presented back to back so that students are not stranded with the idea that vectors are just ordered lists of numbers. To this end, we also labor the notion of all functions from a set to the real numbers. In the same vein linear transformations and matrices are presented hand in hand. Once students see that a linear map is specified by its action on a limited set of inputs, they can already understand what a basis is. All the while students are studying linear systems and their solution sets, so after matrices determinants are introduced. This material can proceed rapidly since elementary matrices were already introduced with Gaussian elimination. Only then is a careful discussion of spans, linear independence and dimension given to ready students for a thorough treatment of eigenvectors and diagonalization. The dimension formula therefore appears quite late, since we prefer not to elevate rote computations of column and row spaces to a pedestal. The book ends with applications–least squares and singular values. These are a fun way to end any lecture course. It would also be quite easy to spend any extra time on systems of differential equations and simple Fourier transform problems.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
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e-book
This text covers the standard material for a US undergraduate first course: linear systems and Gauss's Method, vector spaces, linear maps and matrices, determinants, and eigenvectors and eigenvalues, as well as additional topics such as introductions to various applications. It has extensive exercise sets with worked answers to all exercises, including proofs, beamer slides for classroom use, and a lab manual for computer work. The approach is developmental. Although everything is proved, it introduces the material with a great deal of motivation, many computational examples, and exercises that range from routine verifications to a few challenges. Ancillary materials are available at the publisher link.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Textbooks Algebras Linear
- Resource Type:
- e-book
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e-book
This is a first draft of a free (as in speech, not as in beer, [Sta02]) (although it is free as in beer as well) textbook for a one-semester, undergraduate statistics course. It was used for Math 156 at Colorado State University–Pueblo in the spring semester of 2017.
- Subjects:
- Mathematics and Statistics
- Keywords:
- Statistics Textbooks
- Resource Type:
- e-book