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Linear Algebra Problem Solver

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ISBN : 9780738668451
Genre : Mathematics
File Size : 44. 12 MB
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The Problem Solvers are an exceptional series of books that are thorough, unusually well-organized, and structured in such a way that they can be used with any text. No other series of study and solution guides has come close to the Problem Solvers in usefulness, quality, and effectiveness. Educators consider the Problem Solvers the most effective series of study aids on the market. Students regard them as most helpful for their school work and studies. With these books, students do not merely memorize the subject matter, they really get to understand it. Each Problem Solver is over 1,000 pages, yet each saves hours of time in studying and finding solutions to problems. These solutions are worked out in step-by-step detail, thoroughly and clearly. Each book is fully indexed for locating specific problems rapidly. For linear algebra courses, as well as for courses in computers, physics, engineering, and sciences which use linear algebra. Concentrations on solutions to applied problems in economics, mechanics, electricity, chemistry, geometry, business, probability, graph theory, and linear programming.

The Algebra Trigonometry Problem Solver

Author : Max Fogiel
ISBN : 0878915087
Genre : Mathematics
File Size : 67. 1 MB
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Provides each kind of problem that might appear on an examination, and includes detailed solutions

Biology Problem Solver

Author : Research & Education Association Editors
ISBN : 0738669539
Genre : Science
File Size : 29. 60 MB
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Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies. Here in this highly useful reference is the finest overview of biology currently available, with hundreds of biology problems that cover everything from the molecular basis of life to plants and invertebrates. Each problem is clearly solved with step-by-step detailed solutions. DETAILS - The PROBLEM SOLVERS are unique - the ultimate in study guides. - They are ideal for helping students cope with the toughest subjects. - They greatly simplify study and learning tasks. - They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding. - They cover material ranging from the elementary to the advanced in each subject. - They work exceptionally well with any text in its field. - PROBLEM SOLVERS are available in 41 subjects. - Each PROBLEM SOLVER is prepared by supremely knowledgeable experts. - Most are over 1000 pages. - PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly. - Educators consider the PROBLEM SOLVERS the most effective and valuable study aids; students describe them as "fantastic" - the best books on the market. TABLE OF CONTENTS Introduction Chapter 1: The Molecular Basis of Life Units and Microscopy Properties of Chemical Reactions Molecular Bonds and Forces Acids and Bases Properties of Cellular Constituents Short Answer Questions for Review Chapter 2: Cells and Tissues Classification of Cells Functions of Cellular Organelles Types of Animal Tissue Types of Plant Tissue Movement of Materials Across Membranes Specialization and Properties of Life Short Answer Questions for Review Chapter 3: Cellular Metabolism Properties of Enzymes Types of Cellular Reactions Energy Production in the Cell Anaerobic and Aerobic Reactions The Krebs Cycle and Glycolysis Electron Transport Reactions of ATP Anabolism and Catabolism Energy Expenditure Short Answer Questions for Review Chapter 4: The Interrelationship of Living Things Taxonomy of Organisms Nutritional Requirements and Procurement Environmental Chains and Cycles Diversification of the Species Short Answer Questions for Review Chapter 5: Bacteria and Viruses Bacterial Morphology and Characteristics Bacterial Nutrition Bacterial Reproduction Bacterial Genetics Pathological and Constructive Effects of Bacteria Viral Morphology and Characteristics Viral Genetics Viral Pathology Short Answer Questions for Review Chapter 6: Algae and Fungi Types of Algae Characteristics of Fungi Differentiation of Algae and Fungi Evolutionary Characteristics of Unicellular and Multicellular Organisms Short Answer Questions for Review Chapter 7: The Bryophytes and Lower Vascular Plants Environmental Adaptations Classification of Lower Vascular Plants Differentiation Between Mosses and Ferns Comparison Between Vascular and Non-Vascular Plants Short Answer Questions for Review Chapter 8: The Seed Plants Classification of Seed Plants Gymnosperms Angiosperms Seeds Monocots and Dicots Reproduction in Seed Plants Short Answer Questions for Review Chapter 9: General Characteristics of Green Plants Reproduction Photosynthetic Pigments Reactions of Photosynthesis Plant Respiration Transport Systems in Plants Tropisms Plant Hormones Regulation of Photoperiodism Short Answer Questions for Review Chapter 10: Nutrition and Transport in Seed Plants Properties of Roots Differentiation Between Roots and Stems Herbaceous and Woody Plants Gas Exchange Transpiration and Guttation Nutrient and Water Transport Environmental Influences on Plants Short Answer Questions for Review Chapter 11: Lower Invertebrates The Protozoans Characteristics Flagellates Sarcodines Ciliates Porifera Coelenterata The Acoelomates Platyhelminthes Nemertina The Pseduocoelomates Short Answer Questions for Review Chapter 12: Higher Invertebrates The Protostomia Molluscs Annelids Arthropods Classification External Morphology Musculature The Senses Organ Systems Reproduction and Development Social Orders The Dueterostomia Echinoderms Hemichordata Short Answer Questions for Review Chapter 13: Chordates Classifications Fish Amphibia Reptiles Birds and Mammals Short Answer Questions for Review Chapter 14: Blood and Immunology Properties of Blood and its Components Clotting Gas Transport Erythrocyte Production and Morphology Defense Systems Types of Immunity Antigen-Antibody Interactions Cell Recognition Blood Types Short Answer Questions for Review Chapter 15: Transport Systems Nutrient Exchange Properties of the Heart Factors Affecting Blood Flow The Lymphatic System Diseases of the Circulation Short Answer Questions for Review Chapter 16: Respiration Types of Respiration Human Respiration Respiratory Pathology Evolutionary Adaptations Short Answer Questions for Review Chapter 17: Nutrition Nutrient Metabolism Comparative Nutrient Ingestion and Digestion The Digestive Pathway Secretion and Absorption Enzymatic Regulation of Digestion The Role of the Liver Short Answer Questions for Review Chapter 18: Homeostasis and Excretion Fluid Balance Glomerular Filtration The Interrelationship Between the Kidney and the Circulation Regulation of Sodium and Water Excretion Release of Substances from the Body Short Answer Questions for Review Chapter 19: Protection and Locomotion Skin Muscles: Morphology and Physiology Bone Teeth Types of Skeletal Systems Structural Adaptations for Various Modes of Locomotion Short Answer Questions for Review Chapter 20: Coordination Regulatory Systems Vision Taste The Auditory Sense Anesthetics The Brain The Spinal Cord Spinal and Cranial Nerves The Autonomic Nervous System Neuronal Morphology The Nerve Impulse Short Answer Questions for Review Chapter 21: Hormonal Control Distinguishing Characteristics of Hormones The Pituitary Gland Gastrointestinal Endocrinology The Thyroid Gland Regulation of Metamorphosis and Development The Parathyroid Gland The Pineal Gland The Thymus Gland The Adrenal Gland The Mechanisms of Hormonal Action The Gonadotrophic Hormones Sexual Development The Menstrual Cycle Contraception Pregnancy and Parturition Menopause Short Answer Questions for Review Chapter 22: Reproduction Asexual vs. Sexual Reproduction Gametogenesis Fertilization Parturation and Embryonic Formation and Development Human Reproduction and Contraception Short Answer Questions for Review Chapter 23: Embryonic Development Cleavage Gastrulation Differentiation of the Primary Organ Rudiments Parturation Short Answer Questions for Review Chapter 24: Structure and Function of Genes DNA: The Genetic Material Structure and Properties of DNA The Genetic Code RNA and Protein Synthesis Genetic Regulatory Systems Mutation Short Answer Questions for Review Chapter 25: Principles and Theories of Genetics Genetic Investigations Mitosis and Meiosis Mendelian Genetics Codominance Di- and Trihybrid Crosses Multiple Alleles Sex Linked Traits Extrachromosomal Inheritance The Law of Independent Segregation Genetic Linkage and Mapping Short Answer Questions for Review Chapter 26: Human Inheritance and Population Genetics Expression of Genes Pedigrees Genetic Probabilities The Hardy-Weinberg Law Gene Frequencies Short Answer Questions for Review Chapter 27: Principles and Theories of Evolution Definitions Classical Theories of Evolution Applications of Classical Theory Evolutionary Factors Speciation Short Answer Questions for Review Chapter 28: Evidence for Evolution Definitions Fossils and Dating The Paleozoic Era The Mesozoic Era Biogeographic Realms Types of Evolutionary Evidence Ontogeny Short Answer Questions for Review Chapter 29: Human Evolution Fossils Distinguishing Features The Rise of Early Man Modern Man Overview Short Answer Questions for Review Chapter 30: Principles of Ecology Definitions Competition Interspecific Relationships Characteristics of Population Densities Interrelationships with the Ecosystem Ecological Succession Environmental Characteristics of the Ecosystem Short Answer Questions for Review Chapter 31: Animal Behavior Types of Behavioral Patterns Orientation Communication Hormonal Regulation of Behavior Adaptive Behavior Courtship Learning and Conditioning Circadian Rhythms Societal Behavior Short Answer Questions for Review Index WHAT THIS BOOK IS FOR Students have generally found biology a difficult subject to understand and learn. Despite the publication of hundreds of textbooks in this field, each one intended to provide an improvement over previous textbooks, students of biology continue to remain perplexed as a result of numerous subject areas that must be remembered and correlated when solving problems. Various interpretations of biology terms also contribute to the difficulties of mastering the subject. In a study of biology, REA found the following basic reasons underlying the inherent difficulties of biology: No systematic rules of analysis were ever developed to follow in a step-by-step manner to solve typically encountered problems. This results from numerous different conditions and principles involved in a problem that leads to many possible different solution methods. To prescribe a set of rules for each of the possible variations would involve an enormous number of additional steps, making this task more burdensome than solving the problem directly due to the expectation of much trial and error. Current textbooks normally explain a given principle in a few pages written by a biologist who has insight into the subject matter not shared by others. These explanations are often written in an abstract manner that causes confusion as to the principle's use and application. Explanations then are often not sufficiently detailed or extensive enough to make the reader aware of the wide range of applications and different aspects of the principle being studied. The numerous possible variations of principles and their applications are usually not discussed, and it is left to the reader to discover this while doing exercises. Accordingly, the average student is expected to rediscover that which has long been established and practiced, but not always published or adequately explained. The examples typically following the explanation of a topic are too few in number and too simple to enable the student to obtain a thorough grasp of the involved principles. The explanations do not provide sufficient basis to solve problems that may be assigned for homework or given on examinations. Poorly solved examples such as these can be presented in abbreviated form which leaves out much explanatory material between steps, and as a result requires the reader to figure out the missing information. This leaves the reader with an impression that the problems and even the subject are hard to learn - completely the opposite of what an example is supposed to do. Poor examples are often worded in a confusing or obscure way. They might not state the nature of the problem or they present a solution, which appears to have no direct relation to the problem. These problems usually offer an overly general discussion - never revealing how or what is to be solved. Many examples do not include accompanying diagrams or graphs, denying the reader the exposure necessary for drawing good diagrams and graphs. Such practice only strengthens understanding by simplifying and organizing biology processes. Students can learn the subject only by doing the exercises themselves and reviewing them in class, obtaining experience in applying the principles with their different ramifications. In doing the exercises by themselves, students find that they are required to devote considerable more time to biology than to other subjects, because they are uncertain with regard to the selection and application of the theorems and principles involved. It is also often necessary for students to discover those "tricks" not revealed in their texts (or review books) that make it possible to solve problems easily. Students must usually resort to methods of trial and error to discover these "tricks," therefore finding out that they may sometimes spend several hours to solve a single problem. When reviewing the exercises in classrooms, instructors usually request students to take turns in writing solutions on the boards and explaining them to the class. Students often find it difficult to explain in a manner that holds the interest of the class, and enables the remaining students to follow the material written on the boards. The remaining students in the class are thus too occupied with copying the material off the boards to follow the professor's explanations. This book is intended to aid students in biology overcome the difficulties described by supplying detailed illustrations of the solution methods that are usually not apparent to students. Solution methods are illustrated by problems that have been selected from those most often assigned for class work and given on examinations. The problems are arranged in order of complexity to enable students to learn and understand a particular topic by reviewing the problems in sequence. The problems are illustrated with detailed, step-by-step explanations, to save the students large amounts of time that is often needed to fill in the gaps that are usually found between steps of illustrations in textbooks or review/outline books. The staff of REA considers biology a subject that is best learned by allowing students to view the methods of analysis and solution techniques. This learning approach is similar to that practiced in various scientific laboratories, particularly in the medical fields. In using this book, students may review and study the illustrated problems at their own pace; students are not limited to the time such problems receive in the classroom. When students want to look up a particular type of problem and solution, they can readily locate it in the book by referring to the index that has been extensively prepared. It is also possible to locate a particular type of problem by glancing at just the material within the boxed portions. Each problem is numbered and surrounded by a heavy black border for speedy identification.

The Genetics Problem Solver

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ISBN : 0738670618
Genre : Genetics
File Size : 65. 55 MB
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Machine Design Problem Solver

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ISBN : 0738670820
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File Size : 70. 70 MB
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Business Accounting Finance Problem Solver

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ISBN : 0738671339
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File Size : 35. 27 MB
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Fluid Mechanics Dynamics Problem Solver

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ISBN : 0738671185
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File Size : 82. 91 MB
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Differential Equations Problem Solver

Author : David R. Arterburn
ISBN : 9780738668307
Genre : Mathematics
File Size : 68. 36 MB
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Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies. Here in this highly useful reference is the finest overview of differential equations currently available, with hundreds of differential equations problems that cover everything from integrating factors and Bernoulli's equation to variation of parameters and undetermined coefficients. Each problem is clearly solved with step-by-step detailed solutions. DETAILS - The PROBLEM SOLVERS are unique - the ultimate in study guides. - They are ideal for helping students cope with the toughest subjects. - They greatly simplify study and learning tasks. - They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding. - They cover material ranging from the elementary to the advanced in each subject. - They work exceptionally well with any text in its field. - PROBLEM SOLVERS are available in 41 subjects. - Each PROBLEM SOLVER is prepared by supremely knowledgeable experts. - Most are over 1000 pages. - PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly. TABLE OF CONTENTS Introduction Units Conversion Factors Chapter 1: Classification of Differential Equations Chapter 2: Separable Differential Equations Variable Transformation u = ax + by Variable Transformation y = vx Chapter 3: Exact Differential Equations Definitions and Examples Solving Exact Differential Equations Making a Non-exact Differential Equation Exact Chapter 4: Homogenous Differential Equations Identifying Homogenous Differential Equations Solving Homogenous Differential Equations by Substitution and Separation Chapter 5: Integrating Factors General Theory of Integrating Factors Equations of Form dy/dx + p(x)y = q(x) Grouping to Simplify Solutions Solution Directly From M(x, y)dx + N(x, y)dy = 0 Chapter 6: Method of Grouping Chapter 7: Linear Differential Equations Integrating Factors Bernoulli's Equation Chapter 8: Riccati's Equation Chapter 9: Clairaut's Equation Geometrical Construction Problems Chapter 10: Orthogonal Trajectories Elimination of Constants Orthogonal Trajectories Differential Equations Derived from Considerations of Analytical Geometry Chapter 11: First Order Differential Equations: Applications I Gravity and Projectile Hooke's Law, Springs Angular Motion Over-hanging Chain Chapter 12: First Order Differential Equations: Applications II Absorption of Radiation Population Dynamics Radioactive Decay Temperature Flow from an Orifice Mixing Solutions Chemical Reactions Economics One-Dimensional Neutron Transport Suspended Cable Chapter 13: The Wronskian and Linear Independence Determining Linear Independence of a Set of Functions Using the Wronskian in Solving Differential Equations Chapter 14: Second Order Homogenous Differential Equations with Constant Coefficients Roots of Auxiliary Equations: Real Roots of Auxiliary: Complex Initial Value Higher Order Differential Equations Chapter 15: Method of Undetermined Coefficients First Order Differential Equations Second Order Differential Equations Higher Order Differential Equations Chapter 16: Variation of Parameters Solution of Second Order Constant Coefficient Differential Equations Solution of Higher Order Constant Coefficient Differential Equations Solution of Variable Coefficient Differential Equations Chapter 17: Reduction of Order Chapter 18: Differential Operators Algebra of Differential Operators Properties of Differential Operators Simple Solutions Solutions Using Exponential Shift Solutions by Inverse Method Solution of a System of Differential Equations Chapter 19: Change of Variables Equation of Type (ax + by + c)dx + (dx + ey + f)dy = 0 Substitutions for Euler Type Differential Equations Trigonometric Substitutions Other Useful Substitutions Chapter 20: Adjoint of a Differential Equation Chapter 21: Applications of Second Order Differential Equations Harmonic Oscillator Simple Pendulum Coupled Oscillator and Pendulum Motion Beam and Cantilever Hanging Cable Rotational Motion Chemistry Population Dynamics Curve of Pursuit Chapter 22: Electrical Circuits Simple Circuits RL Circuits RC Circuits LC Circuits Complex Networks Chapter 23: Power Series Some Simple Power Series Solutions May Be Expanded Finding Power Series Solutions Power Series Solutions for Initial Value Problems Chapter 24: Power Series about an Ordinary Point Initial Value Problems Special Equations Taylor Series Solution to Initial Value Problem Chapter 25: Power Series about a Singular Point Singular Points and Indicial Equations Frobenius Method Modified Frobenius Method Indicial Roots: Equal Special Equations Chapter 26: Laplace Transforms Exponential Order Simple Functions Combination of Simple Functions Definite Integral Step Functions Periodic Functions Chapter 27: Inverse Laplace Transforms Partial Fractions Completing the Square Infinite Series Convolution Chapter 28: Solving Initial Value Problems by Laplace Transforms Solutions of First Order Initial Value Problems Solutions of Second Order Initial Value Problems Solutions of Initial Value Problems Involving Step Functions Solutions of Third Order Initial Value Problems Solutions of Systems of Simultaneous Equations Chapter 29: Second Order Boundary Value Problems Eigenfunctions and Eigenvalues of Boundary Value Problem Chapter 30: Sturm-Liouville Problems Definitions Some Simple Solutions Properties of Sturm-Liouville Equations Orthonormal Sets of Functions Properties of the Eigenvalues Properties of the Eigenfunctions Eigenfunction Expansion of Functions Chapter 31: Fourier Series Properties of the Fourier Series Fourier Series Exppansions Sine and Cosine Expansions Chapter 32: Bessel and Gamma Functions Properties of the Gamma Function Solutions to Bessel's Equation Chapter 33: Systems of Ordinary Differential Equations Converting Systems of Ordinary Differential Equations Solutions of Ordinary Differential Equation Systems Matrix Mathematics Finding Eigenvalues of a Matrix Converting Systems of Ordinary Differential Equations into Matrix Form Calculating the Exponential of a Matrix Solving Systems by Matrix Methods Chapter 34: Simultaneous Linear Differential Equations Definitions Solutions of 2 x 2 Systems Checking Solution and Linear Independence in Matrix Form Solution of 3 x 3 Homogenous System Solution of Non-homogenous System Chapter 35: Method of Perturbation Chapter 36: Non-Linear Differential Equations Reduction of Order Dependent Variable Missing Independent Variable Missing Dependent and Independent Variable Missing Factorization Critical Points Linear Systems Non-Linear Systems Liapunov Function Analysis Second Order Equation Perturbation Series Chapter 37: Approximation Techniques Graphical Methods Successive Approximation Euler's Method Modified Euler's Method Chapter 38: Partial Differential Equations Solutions of General Partial Differential Equations Heat Equation Laplace's Equation One-Dimensional Wave Equation Chapter 39: Calculus of Variations Index WHAT THIS BOOK IS FOR Students have generally found differential equations a difficult subject to understand and learn. Despite the pub.

Algebra And Trigonometry Problem Solver

Author : Jerry R. Shipman
ISBN : 9780738665412
Genre : Mathematics
File Size : 50. 86 MB
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Each Problem Solver is an insightful and essential study and solution guide chock-full of clear, concise problem-solving gems. All your questions can be found in one convenient source from one of the most trusted names in reference solution guides. More useful, more practical, and more informative, these study aids are the best review books and textbook companions available. Nothing remotely as comprehensive or as helpful exists in their subject anywhere. Perfect for undergraduate and graduate studies. Here in this highly useful reference is the finest overview of algebra and trigonometry currently available, with hundreds of algebra and trigonometry problems that cover everything from algebraic laws and absolute values to quadratic equations and analytic geometry. Each problem is clearly solved with step-by-step detailed solutions. DETAILS - The PROBLEM SOLVERS are unique - the ultimate in study guides. - They are ideal for helping students cope with the toughest subjects. - They greatly simplify study and learning tasks. - They enable students to come to grips with difficult problems by showing them the way, step-by-step, toward solving problems. As a result, they save hours of frustration and time spent on groping for answers and understanding. - They cover material ranging from the elementary to the advanced in each subject. - They work exceptionally well with any text in its field. - PROBLEM SOLVERS are available in 41 subjects. - Each PROBLEM SOLVER is prepared by supremely knowledgeable experts. - Most are over 1000 pages. - PROBLEM SOLVERS are not meant to be read cover to cover. They offer whatever may be needed at a given time. An excellent index helps to locate specific problems rapidly. - Educators consider the PROBLEM SOLVERS the most effective and valuable study aids; students describe them as "fantastic" - the best books on the market. TABLE OF CONTENTS Introduction Chapter 1: Fundamental Algebraic Laws and Operations Chapter 2: Least Common Multiple / Greatest Common Divisor Chapter 3: Sets and Subsets Chapter 4: Absolute Values Chapter 5: Operations with Fractions Chapter 6: Base, Exponent, Power Chapter 7: Roots and Radicals Simplification and Evaluation of Roots Rationalizing the Denominator Operations with Radicals Chapter 8: Algebraic Addition, Subtraction, Multiplication, Division Chapter 9: Functions and Relations Chapter 10: Solving Linear Equations Unknown in Numerator Unknown in Numerator and/or Denominator Unknown Under Radical Sign Chapter 11: Properties of Straight Lines Slopes, Intercepts, and Points of Given Lines Finding Equations of Lines Graphing Techniques Chapter 12: Linear Inequalities Solving Inequalities and Graphing Inequalities with Two Variables Inequalities Combined with Absolute Values Chapter 13: Systems of Linear Equations and Inequalities Solving Equations in Two Variables and Graphing Solving Equations in Three Variables Solving Systems of Inequalities and Graphing Chapter 14: Determinants and Matrices Determinants of the Second Order Determinants and Matrices of Third and Higher Order Applications Chapter 15: Factoring Expressions and Functions Nonfractional Fractional Chapter 16: Solving Quadratic Equations by Factoring Equations without Radicals Equations with Radicals Solving by Completing the Square Chapter 17: Solutions by Quadratic Formula Coefficients with Integers, Fractions, Radicals, and Variables Imaginary Roots Interrelationships of Roots: Sums; Products Determining the Character of Roots Chapter 18: Solving Quadratic Inequalities Chapter 19: Graphing Quadratic Equations / Conics and Inequalities Parabolas Circles, Ellipses, and Hyberbolas Inequalities Chapter 20: Systems of Quadratic Equations Quadratic/Linear Combinations Quadratic/Quadratic (Conic) Combinations Multivariable Combinations Chapter 21: Equations and Inequalities of Degree Greater than Two Degree 3 Degree 4 Chapter 22: Progressions and Sequences Arithmetic Geometric Harmonic Chapter 23: Mathematical Induction Chapter 24: Factorial Notation Chapter 25: Binomial Theorem / Expansion Chapter 26: Logarithms and Exponentials Expressions Interpolations Functions and Equations Chapter 27: Trigonometry Angles and Trigonometric Functions Trigonometric Interpolations Trigonometric Identities Solving Triangles Chapter 28: Inverse Trigonometric Functions Chapter 29: Trigonometric Equations Finding Solutions to Equations Proving Trigonometric Identities Chapter 30: Polar Coordinates Chapter 31: Vectors and Complex Numbers Vectors Rectangular and Polar/Trigonometric Forms of Complex Numbers Operations with Complex Numbers Chapter 32: Analytic Geometry Points of Line Segments Distances Between Points and in Geometrical Configurations Circles, Arcs, and Sectors Space-Related Problems Chapter 33: Permutations Chapter 34: Combinations Chapter 35: Probability Chapter 36: Series Chapter 37: Decimal / Factional Conversions / Scientific Notation Chapter 38: Areas and Perimeters Chapter 39: Angles of Elevation, Depression and Azimuth Chapter 40: Motion Chapter 41: Mixtures / Fluid Flow Chapter 42: Numbers, Digits, Coins, and Consecutive Integers Chapter 43: Age and Work Chapter 44: Ratio, Proportions, and Variations Ratios and Proportions Direct Variation Inverse Variation Joint and Combined Direct-Inverse Variation Chapter 45: Costs Chapter 46: Interest and Investments Chapter 47: Problems in Space Index WHAT THIS BOOK IS FOR Students have generally found algebra and trigonometry difficult subjects to understand and learn. Despite the publication of hundreds of textbooks in this field, each one intended to provide an improvement over previous textbooks, students of algebra and trigonometry continue to remain perplexed as a result of numerous subject areas that must be remembered and correlated when solving problems. Various interpretations of algebra and trigonometry terms also contribute to the difficulties of mastering the subject. In a study of algebra and trigonometry, REA found the following basic reasons underlying the inherent difficulties of both math subjects: No systematic rules of analysis were ever developed to follow in a step-by-step manner to solve typically encountered problems. This results from numerous different conditions and principles involved in a problem that leads to many possible different solution methods. To prescribe a set of rules for each of the possible variations would involve an enormous number of additional steps, making this task more burdensome than solving the problem directly due to the expectation of much trial and error. Current textbooks normally explain a given principle in a few pages written by a mathematics professional who has insight into the subject matter not shared by others. These explanations are often written in an abstract manner that causes confusion as to the principle's use and application. Explanations then are often not sufficiently detailed or extensive enough to make the reader aware of the wide range of applications and different aspects of the principle being studied. The numerous possible variations of principles and their applications are usually not discussed, and it is left to the reader to discover this while doing exercises. Accordingly, the average student is expected to rediscover that which has long been established and practiced, but not always published or adequately explained. The examples typically following the explanation of a topic are too few in number and too simple to enable the student to obtain a thorough grasp of the involved principles. The explanations do not provide sufficient basis to solve problems that may be assigned for homework or given on examinations. Poorly solved examples such as these can be presented in abbreviated form which leaves out much explanatory material between steps, and as a result requires the reader to figure out the missing information. This leaves the reader with an impression that the problems and even the subject are hard to learn - completely the opposite of what an example is supposed to do. Poor examples are often worded in a confusing or obscure way. They might not state the nature of the problem or they present a solution, which appears to have no direct relation to the problem. These problems usually offer an overly general discussion - never revealing how or what is to be solved. Many examples do not include accompanying diagrams or graphs, denying the reader the exposure necessary for drawing good diagrams and graphs. Such practice only strengthens understanding by simplifying and organizing algebra and trigonometry processes. Students can learn the subject only by doing the exercises themselves and reviewing them in class, obtaining experience in applying the principles with their different ramifications. In doing the exercises by themselves, students find that they are required to devote considerable more time to algebra and trigonometry than to other subjects, because they are uncertain with regard to the selection and application of the theorems and principles involved. It is also often necessary for students to discover those "tricks" not revealed in their texts (or review books) that make it possible to solve problems easily. Students must usually resort to methods of trial and error to discover these "tricks," therefore finding out that they may sometimes spend several hours to solve a single problem. When reviewing the exercises in classrooms, instructors usually request students to take turns in writing solutions on the boards and explaining them to the class. Students often find it difficult to explain in a manner that holds the interest of the class, and enables the remaining students to follow the material written on the boards. The remaining students in the class are thus too occupied with copying the material off the boards to follow the professor's explanations. This book is intended to aid students in algebra and trigonometry overcome the difficulties described by supplying detailed illustrations of the solution methods that are usually not apparent to students. Solution methods are illustrated by problems that have been selected from those most often assigned for class work and given on examinations. The problems are arranged in order of complexity to enable students to learn and understand a particular topic by reviewing the problems in sequence. The problems are illustrated with detailed, step-by-step explanations, to save the students large amounts of time that is often needed to fill in the gaps that are usually found between steps of illustrations in textbooks or review/outline books. The staff of REA considers algebra and trigonometry subjects that are best learned by allowing students to view the methods of analysis and solution techniques. This learning approach is similar to that practiced in various scientific laboratories, particularly in the medical fields. In using this book, students may review and study the illustrated problems at their own pace; students are not limited to the time such problems receive in the classroom. When students want to look up a particular type of problem and solution, they can readily locate it in the book by referring to the index that has been extensively prepared. It is also possible to locate a particular type of problem by glancing at just the material within the boxed portions. Each problem is numbered and surrounded by a heavy black border for speedy identification.

Mathematics For Engineers Problem Solver

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ISBN : 0738670766
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