Essential Calculus with Applications (eBook)

Richard A. Silverman (Autor)

eBook Download: EPUB

2013
320 Seiten
Dover Publications (Verlag)
9780486318592 (ISBN)

Infos

Calculus is an extremely powerful tool for solving a host of practical problems in fields as diverse as physics, biology, and economics, to mention just a few. In this rigorous but accessible text, a noted mathematician introduces undergraduate-level students to the problem-solving techniques that make a working knowledge of calculus indispensable for any mathematician.The author first applies the necessary mathematical background, including sets, inequalities, absolute value, mathematical induction, and other "e;precalculus"e; material. Chapter Two begins the actual study of differential calculus with a discussion of the key concept of function, and a thorough treatment of derivatives and limits. In Chapter Three differentiation is used as a tool; among the topics covered here are velocity, continuous and differentiable functions, the indefinite integral, local extrema, and concrete optimization problems. Chapter Four treats integral calculus, employing the standard definition of the Riemann integral, and deals with the mean value theorem for integrals, the main techniques of integration, and improper integrals. Chapter Five offers a brief introduction to differential equations and their applications, including problems of growth, decay, and motion. The final chapter is devoted to the differential calculus of functions of several variables.Numerous problems and answers, and a newly added section of "e;Supplementary Hints and Answers,"e; enable the student to test his grasp of the material before going on. Concise and well written, this text is ideal as a primary text or as a refresher for anyone wishing to review the fundamentals of this crucial discipline.

Inhalt

To the Instructor; To the StudentChapter 1. Mathematical Background1.1 Introductory Remarks1.2 Sets1.3 Numbers1.4 Inequalities1.5 The Absolute Value1.6 Intervals and Neighborhoods1.7 Rectangular Coordinates1.8 Straight Lines1.9 More about Straight LinesChapter 2. Differential Calculus2.1 Functions2.2 More about Functions2.3 Graphs2.4 Derivatives and Limits2.5 More about Derivatives2.6 More about Limits2.7 Differentiation Technique2.8 Further Differentiation Technique2.9 Other Kinds of LimitsChapter 3. Differentiation as a Tool3.1 Velocity and Acceleration3.2 Related Rates and Business Applications3.3 Properties of Continuous Functions3.4 Properties of Differentiable Functions3.5 Applications of the Mean Value Theorem3.6 Local Extrema3.7 Concavity and Inflection Points3.8 Optimization ProblemsChapter 4. Integral Calculus4.1 The Definite Integral4.2 Properties of Definite Integrals4.3 The Logarithm4.4 The Exponential4.5 More about the Logarithm and Exponential4.6 Integration Technique4.7 Improper IntegralsChapter 5. Integration as a Tool5.1 Elementary Differential Equations5.2 Problems of Growth and Decay5.3 Problems of MotionChapter 6. Functions of Several Variables6.1 From Two to n Dimensions6.2 Limits and Differentiation6.3 The Chain Rule6.4 Extrema in n DimensionsTables; Selected Hints and Answers; Supplementary Hints and Answers; Index

Produkt-Details

• Erscheint lt. Verlag: 22.4.2013
• Reihe/Serie: Dover Books on Mathematics
• Reihe/Serie: Dover Books on Mathematics
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik
• Schlagworte: Advanced Calculus • Advanced Topics • Algebraic • analytic geometry • answer key • apostol • Applications • applied math • assigned textbook • axler • Berge • books on analytic geometries • books on functional analysis • books on graph theories • books on mathematical analysis • books on math textbooks • Boyce • browder • Buck • Calc • calculus class • calculus courses • calculus text • calculus textbook • Cambridge • chapra • chartrand • classic text • college calculus • College Students • complaints • Complex Analysis • deeper understanding • determinants • dieudonne • DIFF • Differential Calculus • Differential Equations • Differentiation • discrete • Edwards • Exercises • Fourier • Functional Analysis • Functions • grad school • Graduate level • Graphs • graph theory • hamiltonian • Hamming • Hardy • instructor • Integral calculus • integrals • Introductory Calculus • intuitive approach • intuitive understanding • Kline • Laplace • learn calculus • linear algebra • Linear equations • Mathematical Analysis • mathematical background • mathematical proofs • mathematical rigor • mathematical thinking • math major • math textbooks • math texts • Matrix • measure theory • modern texts • Notation • Numerical Methods • odes • ordinary differential • partial differential • physical approach • pollard • Prior knowledge • Projective Geometry • purely mathematical • pure math • Pure Mathematics • Rigorous • school students • self study • Self-study • Solutions Manual • solved problems • Spivak • statics • Stewart • stochastic • strang • tenenbaum • Theorems • theoretical physics • Topology • trig • Trudeau • understand calculus • upper level • Vector analysis • Wilson • Zill
• ISBN-13: 9780486318592 / 9780486318592