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A Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing
by Niloy J. Mitra Daniel Cohen-Or Chen Greif Tao Ju Olga Sorkine-Hornung Ariel Shamir Hao Richard ZhangA Sampler of Useful Computational Tools for Applied Geometry, Computer Graphics, and Image Processing shows how to use a collection of mathematical techniques to solve important problems in applied mathematics and computer science areas. The book discusses fundamental tools in analytical geometry and linear algebra. It covers a wide range of topics
A Sampling of Remarkable Groups: Thompson's, Self-similar, Lamplighter, and Baumslag-Solitar (Compact Textbooks in Mathematics)
by Marianna C. Bonanome Margaret H. Dean Judith Putnam DeanThis textbook offers students with a basic understanding of group theory a preview of several interesting groups they would not typically encounter until later in their academic careers. By presenting these advanced concepts at this stage, they will gain a deeper understanding of the subject and be motivated to explore more of it.Groups covered include Thompson’s groups, self-similar groups, Lamplighter groups, and Baumslag-Solitar groups. Each chapter focuses on one of these groups, and begins by discussing why they are interesting, how they originated, and why they are important mathematically. A collection of specific references for additional reading, topics for further research, and exercises are included at the end of every chapter to encourage students’ continued education.With its accessible presentation and engaging style, A Sampling of Remarkable Groups is suitable for students in upper-level undergraduate or beginning graduate abstract algebra courses. It will also be of interest to researchers in mathematics, computer science, and related fields.
A Scheme of Heaven: The History Of Astrology And The Search For Our Destiny In Data
by Alexander BoxerAn illuminating look at the surprising history and science of astrology, civilization’s first system of algorithms, from Babylon to the present day. Humans are pattern-matching creatures, and astrology is the universe’s grandest pattern-matching game. In this refreshing work of history and analysis, data scientist Alexander Boxer examines classical texts on astrology to expose its underlying scientific and mathematical framework. Astrology, he argues, was the ancient world’s most ambitious applied mathematics problem, a monumental data-analysis enterprise sustained by some of history’s most brilliant minds, from Ptolemy to al-Kindi to Kepler. Thousands of years ago, astrologers became the first to stumble upon the powerful storytelling possibilities inherent in numerical data. To correlate the configurations of the cosmos with our day-to-day lives, astrologers relied upon a “scheme of heaven,” or horoscope, showing the precise configuration of the planets at a particular instant in time as viewed from a particular place on Earth. Although recognized as pseudoscience today, horoscopes were once considered a cutting-edge scientific tool. Boxer teaches us how to read these esoteric charts—and appreciate the complex astronomical calculations needed to generate them—by diagramming how the heavens appeared at important moments in astrology’s history, from the assassination of Julius Caesar as viewed from Rome to the Apollo 11 lunar landing as seen from the surface of the Moon. He then puts these horoscopes to the test using modern data sets and statistical science, arguing that today’s data scientists do work similar to astrologers of yore. By looking back at the algorithms of ancient astrology, he suggests, we can better recognize the patterns that are timeless characteristics of our own pattern-matching tendencies. At once critical, rigorous, and far ranging, A Scheme of Heaven recontextualizes astrology as a vast, technological project—spanning continents and centuries—that foreshadowed our data-driven world today.
A Search for Exotic Higgs Decays: Or: How I Learned to Stop Worrying and Love Long-Lived Particles (Springer Theses)
by Jackson BurzynskiThe absence of new physics at the TeV scale observed thus far at the Large Hadron Collider (LHC) motivates an increasing focus on searches for weakly-coupled new particles and exotic signatures. In particular, particles with macroscopic mean proper lifetimes, known as long-lived particles (LLPs), are of significant interest due to their ability to elude the majority of searches which rely on the assumption that Beyond Standard Model particles decay close to the primary interaction point. Many models which aim to solve various issues with the Standard Model (SM) introduce new particles with lifetimes that are either unconstrained, or even shown to prefer the macroscopic regime. These theories often point to the Higgs boson as a possible portal to new physics, with exotic Higgs decays being the primary phenomenological consequence and means of discovery. It is well motivated both from theory and experimental constraints to consider the scenario in which the particles produced in these exotic decays have macroscopic proper lifetimes and give rise to unique detector signatures.This work describes a search for exotic decays of the Higgs boson to two long-lived, neutral, spin-0 particles which subsequently decay to pairs of b quarks, giving the striking signature of displaced hadronic jets in the ATLAS inner detector. Several other ATLAS searches have probed this decay topology previously, excluding branching ratios of the Higgs boson to LLPs of more than 10% for proper lifetimes greater than 100mm. These searches relied on dedicated triggers designed to select events with LLPs decaying in the ATLAS calorimeter or muon spectrometer. The lack of an equivalent trigger for LLP decays in the ATLAS inner detector has been a limiting factor in probing LLP lifetimes less than 100mm. To circumvent the difficulty of triggering on LLP decays, the search presented in this thesis exploits the ZH associated production mode, relying on leptonic trigger signatures to select interesting events. This is the first search for Higgs boson decays into LLPs to exploit this analysis methodology and additionally makes use of several novel methods for both background rejection and background estimation.No excess over Standard Model predictions is observed, and upper limits are set on the branching ratio of the Higgs boson to LLPs . Depending on the mass of the LLP, branching ratios greater than 10% are excluded for lifetimes as small as 4mm and as large as 100mm, probing an important gap in the ATLAS exotic Higgs decay programme. In comparison to the previous searches for Higgs decays to LLPs, these are among the most stringent limits placed on this scenario, and for LLPs with masses below 40 GeV these results represent the strongest existing constraints on the branching ratio of the Higgs boson to LLPs in this lifetime regime.
A Search for Muon Neutrino to Electron Neutrino Oscillations in the MINOS Experiment (Springer Theses)
by Juan Pedro Ochoa-RicouxThe centerpiece of the thesis is the search for muon neutrino to electron neutrino oscillations which would indicate a non-zero mixing angle between the first and third neutrino generations (θ13), currently the "holy grail" of neutrino physics. The optimal extraction of the electron neutrino oscillation signal is based on the novel "library event matching" (LEM) method which Ochoa developed and implemented together with colleagues at Caltech and at Cambridge, which improves MINOS' (Main Injector Neutrino Oscillator Search) reach for establishing an oscillation signal over any other method. LEM will now be the basis for MINOS' final results, and will likely keep MINOS at the forefront of this field until it completes its data taking in 2011. Ochoa and his colleagues also developed the successful plan to run MINOS with a beam tuned for antineutrinos, to make a sensitive test of CPT symmetry by comparing the inter-generational mass splitting for neutrinos and antineutrinos. Ochoa's in-depth, creative approach to the solution of a variety of complex experimental problems is an outstanding example for graduate students and longtime practitioners of experimental physics alike. Some of the most exciting results in this field to emerge in the near future may find their foundations in this thesis.
A Season to Forget: The Story of the 1988 Baltimore Orioles
by Ron SnyderBetween 1966 and 1983, the Baltimore Orioles were considered the best team in baseball. During that span, the team won three World Series, advanced to three others, and competed for a playoff spot just about every season. The Orioles were a model franchise thanks to its “Orioles Way” approach to building a franchise through a strong farm system. Future Hall of Famers like Brooks Robinson, Jim Palmer, Cal Ripken Jr., and Eddie Murray made their ways through the ranks and helped put consistent winners on the field. But five years after Ripken caught the final out to clinch the Orioles World Series victory over the Philadelphia Phillies, the franchise was in disarray. From not understanding how to utilize free agency to having their once famed farm system dry up of talent, the once-proud franchise was spiraling downward. Heading into the 1988 season, the Orioles expected to struggle after a 95-loss season the year before. Not even the return of famed manager Earl Weaver in 1985 and 1986 was enough to turn the team around. The Orioles attempted to revamp their roster in 1988 with 14 new players on the roster compared to the year before. The team opened that season 0–21, shattering the record for futility to start a season by eight games. They consistently found different ways to lose each night to the point that President Ronald Regan sent a message of support to the lovable losers from Charm City. Religious leaders and mental health professionals even offered to help the team find that elusive first win. In the same vein as Jimmy Breslin’s Can’t Anyone Here Play This Game? on the 1962 New York Mets, author Ron Snyder discusses just how did a once model franchise devolved into a team with the distinction of having the worst start of any team in MLB history. A Season to Forget takes an in-depth look at the lead up to that season, a game-by-game breakdown of the streak, and the toll it took on those who lived through it.
A Season to Remember
by The Toronto StarWhat started as a baseball season like any other became the most thrilling sports story of 2015Canada's team began the season with as many losses as wins, but things changed rapidly. With inspired moves by management at the trade deadline, and a bullpen rally not seen since the back-to-back championships of 1992 and 1993, they were back on top. The boys in blue went on to score 891 runs--127 runs more than the next best team--and finished with a superb record from the trade deadline onward. When they clinched a play-off spot, Toronto was ecstatic. When they took the division title, beating their long-time AL East rivals in New York, fans everywhere cheered with excitement and support. And, in their first post-season appearance in 22 years, the entire country erupted in celebration. Here, in this special commemorative book, relive the entire spectacular 2015 run--from the outlook at training camp and the struggle of the early season, to the brilliant trades, to the stellar run to the post-season. And, yes, the game five drama against Texas. Beautifully illustrated with action and candid photographs, and with exclusive content from the Toronto Star, this is the must-have book for every fan. Content previously published by the Toronto Star.
A Second Course In Statistics: Regression Analysis
by Terry Sincich William MendenhallA Second Course in Statistics: Regression Analysis, Seventh Edition, focuses on building linear statistical models and developing skills for implementing regression analysis in real situations. This text offers applications for engineering, sociology, psychology, science, and business. The authors use real data and scenarios extracted from news articles, journals, and actual consulting problems to show how to apply the concepts. In addition, seven case studies, now located throughout the text after applicable chapters, invite readers to focus on specific problems.
A Second Course in Analysis (HBA Lecture Notes in Mathematics)
by M. Ram MurtyThis book discusses major topics in measure theory, Fourier transforms, complex analysis and algebraic topology. It presents material from a mature mathematical perspective. The text is suitable for a two-semester graduate course in analysis and will help students prepare for a research career in mathematics. After a short survey of undergraduate analysis and measure theory, the book highlights the essential theorems that have now become ubiquitous in mathematics. It studies Fourier transforms, derives the inversion theorem and gives diverse applications ranging from probability theory to mathematical physics. It reviews topics in complex analysis and gives a synthetic, rigorous development of the calculus of residues as well as applications to a wide array of problems. It also introduces algebraic topology and shows the symbiosis between algebra and analysis. Indeed, algebraic archetypes were providing foundational support from the start. Multivariable calculus is comprehended in a single glance through the algebra of differential forms. Advanced complex analysis inevitably leads one to the study of Riemann surfaces, and so the final chapter gives the student a hint of these motifs and underlying algebraic patterns.
A Second Course in Complex Analysis
by William A. VeechA clear, self-contained treatment of important areas in complex analysis, this text is geared toward upper-level undergraduates and graduate students. The material is largely classical, with particular emphasis on the geometry of complex mappings.Author William A. Veech, the Edgar Odell Lovett Professor of Mathematics at Rice University, presents the Riemann mapping theorem as a special case of an existence theorem for universal covering surfaces. His focus on the geometry of complex mappings makes frequent use of Schwarz's lemma. He constructs the universal covering surface of an arbitrary planar region and employs the modular function to develop the theorems of Landau, Schottky, Montel, and Picard as consequences of the existence of certain coverings. Concluding chapters explore Hadamard product theorem and prime number theorem.
A Second Course in Linear Algebra (Cambridge Mathematical Textbooks)
by Roger A. Horn Stephan Ramon GarciaLinear algebra is a fundamental tool in many fields, including mathematics and statistics, computer science, economics, and the physical and biological sciences. This undergraduate textbook offers a complete second course in linear algebra, tailored to help students transition from basic theory to advanced topics and applications. Concise chapters promote a focused progression through essential ideas, and contain many examples and illustrative graphics. In addition, each chapter contains a bullet list summarising important concepts, and the book includes over 600 exercises to aid the reader's understanding. Topics are derived and discussed in detail, including the singular value decomposition, the Jordan canonical form, the spectral theorem, the QR factorization, normal matrices, Hermitian matrices (of interest to physics students), and positive definite matrices (of interest to statistics students).
A Second Course in Topos Quantum Theory
by Cecilia FloriThis advanced course, a sequel to the first volume of this lecture series on topos quantum theory, delves deeper into the theory, addressing further technical aspects and recent advances. These include, but are not limited to, the development of physical quantities and self-adjoint operators; insights into the quantization process; the description of an alternative, covariant version of topos quantum theory; and last but not least, the development of a new concept of spacetime. The book builds on the concepts introduced in the first volume (published as Lect. Notes Phys. 868), which presents the main building blocks of the theory and how it could provide solutions to interpretational problems in quantum theory, such as: What are the main conceptual issues in quantum theory? And how can these issues be solved within a new theoretical framework of quantum theory? These two volumes together provide a complete, basic course on topos quantum theory, offering a set of mathematical tools to readers interested in tackling fundamental issues in quantum theory in general, and in quantum gravity in particular. From the reviews of the first volume: The book is self-contained and can be used as a textbook or self-study manual teaching the usage of category theory and topos theory, in particular in theoretical physics or in investigating the foundations of quantum theory in mathematically rigorous terms. [The] book is a very welcome contribution. Frank Antonsen, Mathematical Reviews, December, 2013
A Semidiscrete Version of the Citti-Petitot-Sarti Model as a Plausible Model for Anthropomorphic Image Reconstruction and Pattern Recognition (SpringerBriefs in Mathematics)
by Jean-Paul Gauthier Dario PrandiThis book proposes a semi-discrete version of the theory of Petitot and Citti-Sarti, leading to a left-invariant structure over the group SE(2,N), restricted to a finite number of rotations. This apparently very simple group is in fact quite atypical: it is maximally almost periodic, which leads to much simpler harmonic analysis compared to SE(2). Based upon this semi-discrete model, the authors improve on previous image-reconstruction algorithms and develop a pattern-recognition theory that also leads to very efficient algorithms in practice.
A Seminar on Graph Theory (Dover Books on Mathematics)
by Frank HararyPresented in 1962–63 by experts at University College, London, these lectures offer a variety of perspectives on graph theory. Although the opening chapters form a coherent body of graph theoretic concepts, this volume is not a text on the subject but rather an introduction to the extensive literature of graph theory. The seminar's topics are geared toward advanced undergraduate students of mathematics.Lectures by this volume's editor, Frank Harary, include "Some Theorems and Concepts of Graph Theory," "Topological Concepts in Graph Theory," "Graphical Reconstruction," and other introductory talks. A series of invited lectures follows, featuring presentations by other authorities on the faculty of University College as well as visiting scholars. These include "Extremal Problems in Graph Theory" by Paul Erdös, "Complete Bipartite Graphs: Decomposition into Planar Subgraphs," by Lowell W. Beineke, "Graphs and Composite Games," by Cedric A. B. Smith, and several others.
A Sensory Approach to STEAM Teaching and Learning: Materials-Based Units for Students K-6
by Kerry P. Holmes Jerilou J. Moore Stacy V. HolmesDid you know you have the power and the materials at your fingertips to facilitate the actual brain growth of students? This book is a practical resource to engage K-6 students with STEAM content through their five senses: seeing, listening, touch/movement, smell and taste. It combines historical research, practical suggestions, and current practices on the stages of cognitive development and the brain’s physical response to emotion and novelty; to help you learn ways to transform ordinary lesson plans into novel and exciting opportunities for students to learn through instruction, exploration, inquiry, and discovery. In addition to providing examples of sensory-rich unit plans, the authors take you through the step-by-step process on how to plan a thematic unit and break it down into daily seamless lesson plans that integrate science, technology, engineering, arts, and mathematics. With 25 themed STEAM unit plans and activities based on national standards, up-to-date research on brain science, and real classroom experience, this book shows multiple ways to develop and deliver active multisensory activities and wow your students with sights and sounds as soon as they come through the door of your classroom.
A Sensory Approach to STEAM Teaching and Learning: Materials-Based Units for Students K-6
by Kerry P. Holmes Jerilou J. Moore Stacy V. HolmesDid you know you have the power and the materials at your fingertips to facilitate the actual brain growth of students?This book is a practical resource to engage K-6 students with STEAM content through their five senses: seeing, listening, touch/movement, smell and taste. It combines historical research, practical suggestions, and current practices on the stages of cognitive development and the brain’s physical response to emotion and novelty; to help you learn ways to transform ordinary lesson plans into novel and exciting opportunities for students to learn through instruction, exploration, inquiry, and discovery.In addition to providing examples of sensory-rich unit plans, the authors take you through the step-by-step process on how to plan a thematic unit and break it down into daily seamless lesson plans that integrate science, technology, engineering, arts, and mathematics.With 25 themed STEAM unit plans and activities based on national standards, up-to-date research on brain science, and real classroom experience, this book shows multiple ways to develop and deliver active multisensory activities and wow your students with sights and sounds as soon as they come through the door of your classroom.
A Sequence of Events: The Math Kids (Book 2) (The Math Kids)
by David ColeThe Math Kids Club is back! After solving the case of the prime-time burglars, the Math Kids—Jordan, Justin, and Stephanie—are ready to return to the original purpose of their club: solving math problems. And the district Math Olympics is the perfect opportunity to do just that. But before they can enter the competition, they need a fourth teammate. The Math Kids set their sights on Catherine Duchesne. Even though Catherine has been quiet in class, she knows some really cool math tricks that are sure to help the Math Kids win the competition. But when Catherine doesn&’t show up for school and Jordan, Justin, and Stephanie find out her father&’s been kidnapped, the group springs into action to help their new friend. The Math Kids: A Sequence of Events is the second book in the Math Kids series.
A Shock-Fitting Primer (Chapman & Hall/CRC Applied Mathematics & Nonlinear Science)
by Manuel D. SalasA defining feature of nonlinear hyperbolic equations is the occurrence of shock waves. While the popular shock-capturing methods are easy to implement, shock-fitting techniques provide the most accurate results. A Shock-Fitting Primer presents the proper numerical treatment of shock waves and other discontinuities. The book begins by recounting the events that lead to our understanding of the theory of shock waves and the early developments related to their computation. After presenting the main shock-fitting ideas in the context of a simple scalar equation, the author applies Colombeau’s theory of generalized functions to the Euler equations to demonstrate how the theory recovers well-known results and to provide an in-depth understanding of the nature of jump conditions. He then extends the shock-fitting concepts previously discussed to the one-dimensional and quasi-one-dimensional Euler equations as well as two-dimensional flows. The final chapter explores existing and future developments in shock-fitting methods within the framework of unstructured grid methods.Throughout the text, the techniques developed are illustrated with numerous examples of varying complexity. On the accompanying downloadable resources, MATLAB® codes serve as concrete examples of how to implement the ideas discussed in the book.
A Short Account of the History of Mathematics (Dover Books on Mathematics)
by W. W. BallThis is a new printing, the first inexpensive one, of one of the most honored histories of mathematics of all time. When the last revised edition appeared in 1908, it was hailed by mathematicians and laymen alike, and it remains one of the clearest, most authoritative, and most accurate works in the field. Mathematicians welcomed it as a lucid overview of the development of mathematics down through the centuries. Laymen welcomed it as a work which gave them an opportunity to understand the development of one of the most recondite and difficult of all intellectual endeavors, and the individual contributions of its great men.In this standard work, Dr. Ball treats hundreds of figures and schools that have been instrumental in the development of mathematics from the Egyptians and Phoenicians to such giants of the 19th century as Grassman, Hermite, Galois, Lie, Riemann, and many others who established modern mathematics as we know it today. This semi-biographical approach gives you a real sense of mathematics as a living science, but where Dr. Ball has found that the biographical approach is not sufficient or suited to presenting a mathematical discovery or development, he does not hesitate to depart from his major scheme and treat the mathematics in detail by itself. Thus, while the book is virtually a pocket encyclopedia of the major figures of mathematics and their discoveries, it is also one of the best possible sources for material on such topics as the problems faced by Greek mathematicians, the contributions of the Arab mathematicians, the development of mathematical symbolism, and the invention of the calculus.While some background in mathematics is desirable to follow the reference in some of the later sections, most of the book can be read without any more preparation than high school algebra. As a history of mathematics to browse through, or as a convenient reference work, it has never been excelled.
A Short Book on Long Sums: Infinite Series for Calculus Students (Undergraduate Texts in Mathematics)
by Fernando Q. GouvêaThis concise textbook introduces calculus students to power series through an informal and captivating narrative that avoids formal proofs but emphasizes understanding the fundamental ideas. Power series—and infinite series in general—are a fundamental tool of pure and applied mathematics. The problems focus on ideas, applications, and creative thinking instead of being repetitive and procedural. Calculus is about functions, so the book turns on two fundamental ideas: using polynomials to approximate a function and representing a function in terms of simpler functions. The derivative is reinterpreted in terms of linear approximations, which then leads to Taylor polynomials and the question of convergence. Enough of the theory of convergence is developed to allow a more complete understanding of power series and their applications. A final chapter looks at the distant horizon and discusses other kinds of series representations. SageMath, a free open-source mathematics software system, is used throughout to do computations, provide examples, and create many graphs. While most problems do not require SageMath, students are encouraged to use it where appropriate. An instructor’s guide with solutions to all the problems is available. The book is intended as a supplementary textbook for calculus courses; lecturers and instructors will find innovative and engaging ways to teach this topic. The informal and conversational tone make the book useful to any student seeking to understand this essential aspect of analysis.
A Short Course in Automorphic Functions (Dover Books on Mathematics)
by Joseph LehnerThis concise three-part treatment introduces undergraduate and graduate students to the theory of automorphic functions and discontinuous groups. Author Joseph Lehner begins by elaborating on the theory of discontinuous groups by the classical method of Poincaré, employing the model of the hyperbolic plane. The necessary hyperbolic geometry is developed in the text. Chapter two develops automorphic functions and forms via the Poincaré series. Formulas for divisors of a function and form are proved and their consequences analyzed. The final chapter is devoted to the connection between automorphic function theory and Riemann surface theory, concluding with some applications of Riemann-Roch theorem. <p> The book presupposes only the usual first courses in complex analysis, topology, and algebra. Exercises range from routine verifications to significant theorems. Notes at the end of each chapter describe further results and extensions, and a glossary offers definitions of terms.
A Short Course in Computational Geometry and Topology (SpringerBriefs in Applied Sciences and Technology)
by Herbert EdelsbrunnerThis monograph presents a short course in computational geometry and topology. In the first part the book covers Voronoi diagrams and Delaunay triangulations, then it presents the theory of alpha complexes which play a crucial role in biology. The central part of the book is the homology theory and their computation, including the theory of persistence which is indispensable for applications, e. g. shape reconstruction. The target audience comprises researchers and practitioners in mathematics, biology, neuroscience and computer science, but the book may also be beneficial to graduate students of these fields.
A Short Course in Differential Topology (Cambridge Mathematical Textbooks)
by Bjørn Ian DundasManifolds are abound in mathematics and physics, and increasingly in cybernetics and visualization where they often reflect properties of complex systems and their configurations. Differential topology gives us the tools to study these spaces and extract information about the underlying systems. This book offers a concise and modern introduction to the core topics of differential topology for advanced undergraduates and beginning graduate students. It covers the basics on smooth manifolds and their tangent spaces before moving on to regular values and transversality, smooth flows and differential equations on manifolds, and the theory of vector bundles and locally trivial fibrations. The final chapter gives examples of local-to-global properties, a short introduction to Morse theory and a proof of Ehresmann's fibration theorem. The treatment is hands-on, including many concrete examples and exercises woven into the text, with hints provided to guide the student.
A Short Course in Discrete Mathematics (Dover Books on Computer Science)
by Edward A. Bender S. Gill WilliamsonWhat sort of mathematics do I need for computer science? In response to this frequently asked question, a pair of professors at the University of California at San Diego created this text. Its sources are two of the university's most basic courses: Discrete Mathematics, and Mathematics for Algorithm and System Analysis. Intended for use by sophomores in the first of a two-quarter sequence, the text assumes some familiarity with calculus. Topics include Boolean functions and computer arithmetic; logic; number theory and cryptography; sets and functions; equivalence and order; and induction, sequences, and series. Multiple choice questions for review appear throughout the text. Original 2005 edition. Notation Index. Subject Index.
A Short Course in Ordinary Differential Equations (Universitext)
by Qingkai KongThis text is a rigorous treatment of the basic qualitative theory of ordinary differential equations, at the beginning graduate level. Designed as a flexible one-semester course but offering enough material for two semesters, A Short Course covers core topics such as initial value problems, linear differential equations, Lyapunov stability, dynamical systems and the Poincaré--Bendixson theorem, and bifurcation theory, and second-order topics including oscillation theory, boundary value problems, and Sturm--Liouville problems. The presentation is clear and easy-to-understand, with figures and copious examples illustrating the meaning of and motivation behind definitions, hypotheses, and general theorems. A thoughtfully conceived selection of exercises together with answers and hints reinforce the reader's understanding of the material. Prerequisites are limited to advanced calculus and the elementary theory of differential equations and linear algebra, making the text suitable for senior undergraduates as well.