Study smarter and stay on top of your differential equations course with the bestselling Schaum's Outline--now with the NEW Schaum's app and website!

Schaum's Outline of Differential Equations, Fifth Edition is the go-to study guide for all students of science who need to learn or refresh their knowledge of differential equations. With an outline format that facilitates quick and easy review and mirrors the course in scope and sequence, this book helps you understand basic concepts and get the extra practice you need to excel in the course. It supports the all major differential equations textbooks and is useful for study in Calculus (I, II, and III), Mathematical Modeling, Introductory Differential Equations and Differential Equations.

Chapters include an Introduction to Modeling and Qualitative Methods, Classifications of First-Order Differential Equations, Linear Differential Equations, Variation of Parameters, Initial-Value Problems for Linear Differential Equations, Graphical and Numerical Methods for Solving First-Order Differential Equations, Solutions of Linear Differential Equations with Constant Coefficients by Laplace Transforms, and more.

Features:

• NEW to this edition: the new Schaum's app and website!
• NEW CHAPTERS include Autonomous Differential Equations and Qualitative Methods; Eigenvalues and Eigenvectors; three chapters dealing with Solutions of Systems of Autonomous Equations via Eigenvalues and Eigenvectors (real and distinct, real and equal, and complex conjugate Eigenvalues)
• 20 problem-solving videos online
• 563 solved problems
• Outline format provides a quick and easy review of differential equations
• Clear, concise explanations of differential equations concepts
• Hundreds of examples with explanations of key concepts
• Supports all major textbooks for differential equations courses
• Appropriate for the following courses: Calculus (I, II, and III), Mathematical Modeling, Introductory Differential Equations, and Differential Equations

The ideal review for your matrix operations course

More than 40 million students have trusted Schaum's Outlines for their expert knowledge and helpful solved problems. Written by renowned experts in their respective fields, Schaum's Outlines cover everything from math to science, nursing to language. The main feature for all these books is the solved problems. Step-by-step, authors walk readers through coming up with solutions to exercises in their topic of choice.

• 363 detailed problems with step-by-step solutions
• Clear, concise explanations of matrix operations
• Help with Eigenvalues and the QR Algorithm
• A solved-problem approach that teaches you with hands-on help
• Exercises for improving your problem-solving skills

Confusing Textbooks? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's Outlines. More than 40 million students have trusted Schaum's to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. You also get hundreds of examples, solved problems, and practice exercises to test your skills.

This Schaum's Outline gives you

• Practice problems with full explanations that reinforce knowledge
• Coverage of the most up-to-date developments in your course field
• In-depth review of practices and applications

Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores!

Schaum's Outlines-Problem Solved.

If you are looking for a quick nuts-and-bolts overview, turn to Schaum's Easy Outlines!

Schaum's Easy Outline of Differential Equations is a pared-down, simplified, and tightly focused review of the topic. With an emphasis on clarity and brevity, it features a streamlined and updated format and the absolute essence of the subject, presented in a concise and readily understandable form. Graphic elements such as sidebars, reader-alert icons, and boxed highlights stress selected points from the text, illuminate keys to learning, and give you quick pointers to the essentials.

• Expert tips for mastering differential equations
• Last-minute essentials to pass the course
• Easy-to-follow review of differential equations
• Supports all the major textbooks for differential equations courses
• Appropriate for the following courses: Calculus I, II, and III; Mathematical Modeling; Introductory Differential Equations; Differential Equations

Confusing Textbooks? Missed Lectures? Not Enough Time?

Fortunately for you, there's Schaum's.

More than 40 million students have trusted Schaum's Outlines to help them succeed in the classroom and on exams. Schaum's is the key to faster learning and higher grades in every subject. Each Outline presents all the essential course information in an easy-to-follow, topic-by-topic format. In Schaum's foreign language outlines, you'll get hundreds of examples, helpful usage explanations, and practice exercises to test your skills.

Fully compatible with your classroom text, Schaum's highlights all the important facts you need to know. Use Schaum's to shorten your study time-and get your best test scores

Schaum's Outlines-Problem Solved.

Linear Algebra: Algorithms, Applications, and Techniques, Fourth Edition offers a modern and algorithmic approach to computation while providing clear and straightforward theoretical background information. The book guides readers through the major applications, with chapters on properties of real numbers, proof techniques, matrices, vector spaces, linear transformations, eigen values, and Euclidean inner products. Appendices on Jordan canonical forms and Markov chains are included for further study. This useful textbook presents broad and balanced views of theory, with key material highlighted and summarized in each chapter. To further support student practice, the book also includes ample exercises with answers and hints.

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Novel topics compiled in this one-of-a-kind volume provide tantalizing hints for clinical application through future translational research. Only recently have we come to ask what role the male might play in pregnancy loss and embryo implantation failure, beyond contributing an abnormal set of paternal chromosomes at fertilization. This volume explores the recent evidence that these conditions might also be related to the transmission of previously unrecognized chromosomal micro-deletions and duplications, or via the epigenetic dysregulation of early embryonic gene function by spermatozoal microRNAs or alterations in sperm DNA methylation patterning, or by DNA damage secondary to either reactive oxygen species or environmental toxicants. In addition, the composition of seminal plasma has been found to be highly complex, containing many factors that play important roles in altering the uterine environment and the female immune system permissive of embryo implantation and trophectoderm outgrowth leading to successful pregnancy. Coverage includes an examination of both spermatozoa and seminal fluid component factors.