Atnaujinkite slapukų nuostatas

El. knyga: Calculus for Scientists and Engineers

, ,
Kitos knygos pagal šią temą:
Calculus for Scientists and EngineersDidesnis paveikslėlis
Kitos knygos pagal šią temą:

DRM apribojimai

  • Kopijuoti:

    neleidžiama

  • Spausdinti:

    neleidžiama

  • El. knygos naudojimas:

    Skaitmeninių teisių valdymas (DRM)
    Leidykla pateikė šią knygą šifruota forma, o tai reiškia, kad norint ją atrakinti ir perskaityti reikia įdiegti nemokamą programinę įrangą. Norint skaityti šią el. knygą, turite susikurti Adobe ID . Daugiau informacijos  čia. El. knygą galima atsisiųsti į 6 įrenginius (vienas vartotojas su tuo pačiu Adobe ID).

    Reikalinga programinė įranga
    Norint skaityti šią el. knygą mobiliajame įrenginyje (telefone ar planšetiniame kompiuteryje), turite įdiegti šią nemokamą programėlę: PocketBook Reader (iOS / Android)

    Norint skaityti šią el. knygą asmeniniame arba „Mac“ kompiuteryje, Jums reikalinga  Adobe Digital Editions “ (tai nemokama programa, specialiai sukurta el. knygoms. Tai nėra tas pats, kas „Adobe Reader“, kurią tikriausiai jau turite savo kompiuteryje.)

    Negalite skaityti šios el. knygos naudodami „Amazon Kindle“.

This book presents the basic concepts of calculus and its relevance to real-world problems, covering the standard topics in their conventional order. By focusing on applications, it allows readers to view mathematics in a practical and relevant setting. Organized into 12 chapters, this book includes numerous interesting, relevant and up-to date applications that are drawn from the fields of business, economics, social and behavioural sciences, life sciences, physical sciences, and other fields of general interest. It also features MATLAB, which is used to solve a number of problems. The book is ideal as a first course in calculus for mathematics and engineering students. It is also useful for students of other sciences who are interested in learning calculus.
1 Functions and Models
1(38)
1.1 Function, Domain, and Range
1(7)
1.2 Various Types of Functions
8(7)
1.3 Important Examples of Functions
15(8)
1.4 Functions as Models
23(6)
1.5 Algebra of Functions
29(1)
1.6 Proofs, Mathematical Induction
30(2)
1.7 Geometric Transformation of Functions
32(1)
1.8 Exercises
33(6)
2 Limit and Continuity
39(16)
2.1 Idea and Definition of the Limit
39(5)
2.2 Evaluating Limits
44(4)
2.3 Continuous Functions
48(3)
2.4 Improper Limits
51(1)
2.5 Exercises
52(3)
3 Derivatives
55(48)
3.1 Definition of the Derivative
55(4)
3.2 Derivative of Elementary Functions
59(5)
3.3 Some Differentiation Formulas
64(13)
3.4 Derivatives of Higher Order
77(1)
3.5 A Basic Differential Equation
78(5)
3.6 Differentials, Newton-Raphson Approximation
83(7)
3.7 Indeterminate Forms and l'Hopital's Rule
90(7)
3.8 Sensitivity Analysis
97(2)
3.9 Exercises
99(4)
4 Optimization
103(26)
4.1 Extremum Values of Functions
103(3)
4.2 Monotonicity
106(2)
4.3 Further Properties of Extremum Values
108(2)
4.4 Convexity and Concavity
110(3)
4.5 Applications of Optimization
113(13)
4.6 Exercises
126(3)
5 Sequences and Series
129(24)
5.1 Sequences and Their Limits
129(5)
5.2 Infinite Series
134(7)
5.3 Alternating Series, Absolute and Conditional Convergence
141(1)
5.4 Power Series
142(6)
5.5 Exercises
148(5)
6 Integration
153(40)
6.1 Introduction
153(1)
6.2 Integral and Area
154(2)
6.3 Antiderivatives and Rules of Integration
156(4)
6.4 Integration by Substitution
160(3)
6.5 Integration by Parts
163(6)
6.6 The Fundamental Theorem of Calculus
169(4)
6.7 Trigonometric Integrals
173(6)
6.8 Partial Fractions and Integration
179(2)
6.9 Improper Integrals
181(5)
6.10 Additional Tables of Integrals
186(4)
6.11 Exercises
190(3)
7 Applications of Integration
193(46)
7.1 Areas Under Curves
193(9)
7.2 Determination of Length, Area, and Volume
202(10)
7.3 Definite Integral as Average
212(3)
7.4 Applications to Business and Industry
215(8)
7.4.1 Present and Future Values
215(3)
7.4.2 Annuity
218(1)
7.4.3 Applications in Business
219(4)
7.5 Applications to Mechanics and Engineering
223(5)
7.6 Integrals and Probability
228(6)
7.7 Exercises
234(5)
8 Functions of Several Variables
239(68)
8.1 Introduction
239(6)
8.2 Situations Modeled by Functions of More Than One Variable
245(2)
8.3 Continuity of Functions of Several Variables
247(4)
8.4 Partial Derivatives with Applications
251(22)
8.5 Optimization of Functions of Two Variables
273(15)
8.5.1 Unconstrained Optimization
273(12)
8.5.2 Constrained Optimization
285(3)
8.6 Taylor Expansion in Two Variables
288(3)
8.7 Integration of Functions of Several Variables
291(7)
8.8 Applications of Double Integrals
298(4)
8.8.1 Population of a City
298(1)
8.8.2 Average Value of a Function of Two Variables
299(1)
8.8.3 Joint Probability Density Functions
300(2)
8.9 Exercises
302(5)
9 Vector Calculus
307(76)
9.1 Introduction
307(1)
9.2 Vectors
308(12)
9.3 Differential Calculus of Vector Fields
320(20)
9.3.1 Curves
321(5)
9.3.2 Vector Fields in Several Dimensions
326(11)
9.3.3 Surfaces
337(3)
9.4 Integration in Vector Fields
340(12)
9.4.1 Line Integrals
340(7)
9.4.2 Surface Integrals
347(5)
9.5 Fundamental Theorems of Vector Calculus
352(11)
9.5.1 The Theorem of Green and Ostrogradski
352(3)
9.5.2 The Divergence Theorem of Gauss
355(5)
9.5.3 The Theorem of Stokes
360(3)
9.6 Applications of Vector Calculus to Engineering Problems
363(15)
9.6.1 Elements of Vector Calculus and the Physical World
364(8)
9.6.2 Applications of Line Integrals
372(2)
9.6.3 An Example of Planar Fluid Flow-Hurricane
374(4)
9.7 Exercises
378(5)
10 Fourier Methods with Applications
383(44)
10.1 Introduction
383(1)
10.2 Orthonormal Systems and Fourier Series
384(27)
10.2.1 Orthonormal Systems
384(6)
10.2.2 Fourier Series
390(12)
10.2.3 Further Properties of Fourier Series
402(9)
10.3 The Fourier Transform
411(11)
10.3.1 Basic Properties of the Fourier Transform
411(8)
10.3.2 Convolution
419(2)
10.3.3 The Discrete Fourier Transform
421(1)
10.4 Application of Fourier Methods to Signal Analysis
422(2)
10.5 Exercises
424(3)
11 Differential Equations
427(48)
11.1 Introduction and Basic Notions
428(6)
11.2 Separation of Variables
434(3)
11.3 First-Order Linear Equations
437(2)
11.4 Solution by Substitution
439(9)
11.4.1 Homogeneous Equations
439(2)
11.4.2 Bernoulli Equations
441(2)
11.4.3 Reduction of Order
443(1)
11.4.4 Homogeneous Linear Equations with Constant Coefficients
444(4)
11.5 Modeling with Differential Equations
448(12)
11.5.1 Growth and Decay
448(1)
11.5.2 Population Growth
449(4)
11.5.3 Pollution of Lakes
453(1)
11.5.4 The Quantity of a Drug in the Body
454(1)
11.5.5 Spread of Diseases, Technologies and Rumor
455(2)
11.5.6 Application of Newton's Law of Cooling
457(1)
11.5.7 Application of Newton's Cooling Law for Determining Time of Death
458(2)
11.6 Introduction to Partial Differential Equations
460(4)
11.7 Applications of Fourier Methods to Partial Differential Equations
464(7)
11.7.1 Fourier Methods for the Wave Equation
465(4)
11.7.2 Fourier Methods for the Heat Equation
469(1)
11.7.3 Fourier Methods for the Laplace Equation
470(1)
11.8 Exercises
471(4)
12 Calculus with MATLAB
475(34)
12.1 Introduction
475(1)
12.2 Important Elements of MATLAB
476(6)
12.2.1 Advantages of MATLAB
476(1)
12.2.2 How to Run MATLAB?
476(4)
12.2.3 MATLAB Functions
480(2)
12.3 Visualization of Scalar- and Vector-Valued Function
482(7)
12.3.1 Plotting Scalar Functions with MATLAB
482(5)
12.3.2 Plots for Vector-Valued Functions in 2D and 3D
487(2)
12.4 Certain Topics of Calculus with MATLAB
489(18)
12.4.1 Differentiation and Integration
489(2)
12.4.2 Finding Limits of Functions
491(2)
12.4.3 Sequences and Series
493(1)
12.4.4 Solving Ordinary Differential Equations (ODEs)
494(4)
12.4.5 Animated Phase Portraits of Nonlinear and Chaotic Dynamical Systems
498(4)
12.4.6 Finding Minima and Maxima
502(1)
12.4.7 Fourier Analysis
503(4)
12.5 Exercises
507(2)
Appendix A Real Numbers and Inequalities 509(4)
Appendix B Analytic Geometry 513(4)
Appendix C Trigonometry 517(6)
Appendix D 523(20)
Solutions of Selected Exercises 543(98)
References 641(2)
Index 643
MARTIN BROKATE is Professor of Applied Mathematics at the Technical University, Munich, Germany. He received his PhD in Mathematics at Freie Universität, Berlin, Germany, in 1980, and was appointed to the Chair of Numerical Analysis and Control Theory in 1999. He was the spokesman of Special Research Area 438 Mathematical Modeling, Simulation and Verification in Material-Oriented Processes and Intelligent Systems from 2001 to 2004. He was the Dean of the Department of Mathematics in 20032006. His interests lie in applied analysis and control theory, with a focus on the mathematical analysis of rate-independent evolutions and hysteresis operators.   PAMMY MANCHANDA is Senior Professor in the Department of Mathematics at the Guru Nanak Dev University, Amritsar, India and Secretary of the Indian Society of Industrial and Applied Mathematics (ISIAM). She has published more than 50 research papers in several international journals of repute, edited4 proceedings for international conferences of the ISIAM and co-authored 3 books. She has visited the International Centre for Theoretical Physics (ICTP) (a UNESCO institution) at Trieste, Italy, many times to carry out her research activities, attended and delivered talks and chaired sessions at several international conferences and workshops across the globe, including the International Council for Industrial and Applied Mathematics (ICIAM) during 19992015 and the International Congress of Mathematicians (ICM). She is the managing editor of the Indian Journal of Industrial and Applied Mathematics and a member of the editorial board of the Springer book series Industrial and Applied Mathematics. ABUL HASAN SIDDIQI is a distinguished scientist and Adjunct Professor at the School of Basic Sciences and Research, and Coordinator at the Centre for Advanced Research in Applied Mathematics and Physics (CARAMP) at Sharda University, Greater Noida, India. He was a visiting consultant at ICTP; Sultan Qaboos University, Muscat, Oman; MIMOS, Kuala Lumpur, Malaysia; and a professor at several reputed universities including Aligarh Muslim University, Aligarh, India; and King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia. He has a long association with ICTP (a regular associate, guests of the director and senior associate). He was awarded the German Academic exchange Fellowship thrice to carry out mathematical research in Germany. He has published more than 100 research papers jointly with his research collaborators, 13 books and edited proceedings of 17 international conferences, as well as supervised 29 PhD scholars. He is the founder secretary and the current President of the ISIAM, which celebrated its Silver Jubilee in January 2016. He is the editor-in-chief of the Indian Journal of Industrial and Applied Mathematics (published by ISIAM) and the Springers book series Industrial and Applied Mathematics.
Daugiau apie elektronines knygas Daugiau apie elektronines knygas
Pastovi nuoroda: https://www.kriso.lt/db/97898113846462e.html