Calculus: Early Transcendentals Multivariable
Autor Jon Rogawski, Colin Adams, Robert Franzosaen Limba Engleză Paperback – 28 dec 2018
În această a patra ediție a volumului Calculus, autorii Colin Adams, Jon Rogawski și Robert Franzosa rafinează formula unui manual care a devenit standard în analiza matematică universitară. Schimbarea majoră față de edițiile precedente rezidă în optimizarea simbiozei dintre text, grafică și aranjarea în pagină, transformând suportul de curs într-un instrument vizual care ghidează natural fluxul logic al demonstrațiilor. Remarcăm introducerea unor secțiuni noi, precum „Assumptions Matter” și „Conceptual Insight”, menite să prevină erorile comune și să consolideze raționamentul matematic dincolo de simpla aplicare a unor formule. Cititorii familiarizați cu Thomas' Calculus vor aprecia în acest volum abordarea mai prietenoasă a expunerii, care anticipează activ punctele de blocaj ale studenților. Dacă lucrări precum Single Variable Essential Calculus: Early Transcendentals de James Stewart mizează pe concizie, Calculus alege să ofere o experiență bogată, cu peste 1200 de pagini ce includ perspective istorice și exerciții cu dificultate graduală. Poziționarea acestei lucrări în cariera lui Colin Adams este una centrală. Deși autorul explorează latura ludică a disciplinei în Do Androids Dream of Symmetric Sheaves? sau rigoarea extremă în Encyclopedia of Knot Theory, acest manual de analiză reprezintă punctul de echilibru perfect. Calculus reușește să integreze precizia academică necesară unui curriculum riguros cu stilul accesibil și intuitiv care l-a consacrat pe Adams ca un comunicator de excepție al științelor exacte.
Preț: 1561.59 lei
Preț vechi: 1904.38 lei
-18%
Carte indisponibilă temporar
Specificații
ISBN-10: 1319055923
Pagini: 624
Dimensiuni: 216 x 274 x 23 mm
Greutate: 1.16 kg
Ediția:4th edition
Editura: W. H. Freeman
De ce să citești această carte
Recomandăm acest manual studenților la facultățile de profil tehnic sau matematic care doresc o înțelegere profundă a analizei matematice. Prin rubricile de tip „Insight” și exercițiile structurate gradual, cititorul câștigă nu doar tehnici de calcul, ci și o perspectivă conceptuală solidă. Este resursa ideală pentru cei care preferă o învățare vizuală, sprijinită de diagrame clare și explicații care anticipează întrebările dificile.
Despre autor
Colin Adams este profesor de matematică „Thomas T. Read” la Williams College și o figură marcantă în comunitatea academică internațională. Expertiza sa vastă acoperă domenii diverse, de la topologie — fiind autorul volumului Encyclopedia of Knot Theory — până la popularizarea matematicii prin umor, fiind editorialist la „Mathematical Intelligencer”. Această versatilitate se reflectă în manualul Calculus, unde rigoarea matematică este dublată de o capacitate rară de a explica concepte abstracte într-un limbaj accesibil și captivant, adaptat nevoilor studenților contemporani.
Descriere scurtă
1. Clear, accessible exposition that anticipates and addresses student difficulties.
2. Layout and figures that communicate the flow of ideas.
3. Highlighted features that emphasize concepts and mathematical reasoning including Conceptual Insight, Graphical Insight, Assumptions Matter, Reminder, and Historical Perspective.
4. A rich collection of examples and exercises of graduated difficulty that teach basic skills as well as problem-solving techniques, reinforce conceptual understanding, and motivate calculus through interesting applications. Each section also contains exercises that develop additional insights and challenge students to further develop their skills.
Cuprins
1.1 Real Numbers, Functions, and Graphs
1.2 Linear and Quadratic Functions
1.3 The Basic Classes of Functions
1.4 Trigonometric Functions
1.5 Technology: Calculators and Computers
Chapter Review Exercises
Chapter 2: Limits
2.1 The Limit Idea: Instantaneous Velocity and Tangent Lines
2.2 Investigating Limits
2.3 Basic Limit Laws
2.4 Limits and Continuity
2.5 Indeterminate Forms
2.6 The Squeeze Theorem and Trigonometric Limits
2.7 Limits at Infinity
2.8 The Intermediate Value Theorem
2.9 The Formal Definition of a Limit
Chapter Review Exercises
Chapter 3: Differentiation
3.1 Definition of the Derivative
3.2 The Derivative as a Function
3.3 Product and Quotient Rules
3.4 Rates of Change
3.5 Higher Derivatives
3.6 Trigonometric Functions
3.7 The Chain Rule
3.8 Implicit Differentiation
3.9 Related Rates
Chapter Review Exercises
Chapter 4: Applications of the Derivative
4.1 Linear Approximation and Applications
4.2 Extreme Values
4.3 The Mean Value Theorem and Monotonicity
4.4 The Second Derivative and Concavity
4.5 Analyzing and Sketching Graphs of Functions
4.6 Applied Optimization
4.7 Newton's Method
Chapter Review Exercises
Chapter 5: Integration
5.1 Approximating and Computing Area
5.2 The Definite Integral
5.3 The Indefinite Integral
5.4 The Fundamental Theorem of Calculus, Part I
5.5 The Fundamental Theorem of Calculus, Part II
5.6 Net Change as the Integral of a Rate of Change
5.7 The Substitution Method
Chapter Review Exercises
Chapter 6: Applications of the Integral
6.1 Area Between Two Curves
6.2 Setting Up Integrals: Volume, Density, Average Value
6.3 Volumes of Revolution: Disks and Washers
6.4 Volumes of Revolution: Cylindrical Shells
6.5 Work and Energy
Chapter Review Exercises
Chapter 7: Exponential and Logarithmic Functions
7.1 The Derivative of f (x) = bx and the Number e
7.2 Inverse Functions
7.3 Logarithmic Functions and Their Derivatives
7.4 Applications of Exponential and Logarithmic Functions
7.5 L'Hopital's Rule
7.6 Inverse Trigonometric Functions
7.7 Hyperbolic Functions
Chapter Review Exercises
Chapter 8: Techniques of Integration
8.1 Integration by Parts
8.2 Trigonometric Integrals
8.3 Trigonometric Substitution
8.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
8.5 The Method of Partial Fractions
8.6 Strategies for Integration
8.7 Improper Integrals
8.8 Numerical Integration
Chapter Review Exercises
Chapter 9: Further Applications of the Integral
9.1 Probability and Integration
9.2 Arc Length and Surface Area
9.3 Fluid Pressure and Force
9.4 Center of Mass
Chapter Review Exercises
Chapter 10: Introduction to Differential Equations
10.1 Solving Differential Equations
10.2 Models Involving y=k(y-b)
10.3 Graphical and Numerical Methods
10.4 The Logistic Equation
10.5 First-Order Linear Equations
Chapter Review Exercises
Chapter 11: Infinite Series
11.1 Sequences
11.2 Summing an Infinite Series
11.3 Convergence of Series with Positive Terms
11.4 Absolute and Conditional Convergence
11.5 The Ratio and Root Tests and Strategies for Choosing Tests
11.6 Power Series
11.7 Taylor Polynomials
11.8 Taylor Series
Chapter Review Exercises
Chapter 12: Parametric Equations, Polar Coordinates, and Conic Sections
12.1 Parametric Equations
12.2 Arc Length and Speed
12.3 Polar Coordinates
12.4 Area and Arc Length in Polar Coordinates
12.5 Conic Sections
Chapter Review Exercises
Chapter 13: Vector Geometry
13.1 Vectors in the Plane
13.2 Three-Dimensional Space: Surfaces, Vectors, and Curves
13.3 Dot Product and the Angle Between Two Vectors
13.4 The Cross Product
13.5 Planes in 3-Space
13.6 A Survey of Quadric Surfaces
13.7 Cylindrical and Spherical Coordinates
Chapter Review Exercises
Chapter 14: Calculus of Vector-Valued Functions
14.1 Vector-Valued Functions
14.2 Calculus of Vector-Valued Functions
14.3 Arc Length and Speed
14.4 Curvature
14.5 Motion in 3-Space
14.6 Planetary Motion According to Kepler and Newton
Chapter Review Exercises
Chapter 15: Differentiation in Several Variables
15.1 Functions of Two or More Variables
15.2 Limits and Continuity in Several Variables
15.3 Partial Derivatives
15.4 Differentiability, Tangent Planes, and Linear Approximation
15.5 The Gradient and Directional Derivatives
15.6 Multivariable Calculus Chain Rules
15.7 Optimization in Several Variables
15.8 Lagrange Multipliers: Optimizing with a Constraint
Chapter Review Exercises
Chapter 16: Multiple Integration
16.1 Integration in Two Variables
16.2 Double Integrals over More General Regions
16.3 Triple Integrals
16.4 Integration in Polar, Cylindrical, and Spherical Coordinates
16.5 Applications of Multiple Integrals
16.6 Change of Variables
Chapter Review Exercises
Chapter 17: Line and Surface Integrals
17.1 Vector Fields
17.2 Line Integrals
17.3 Conservative Vector Fields
17.4 Parametrized Surfaces and Surface Integrals
17.5 Surface Integrals of Vector Fields
Chapter Review Exercises
Chapter 18: Fundamental Theorems of Vector Analysis
18.1 Green's Theorem
18.2 Stokes' Theorem
18.3 Divergence Theorem
Chapter Review Exercises
Appendices
A. The Language of Mathematics
B. Properties of Real Numbers
C. Induction and the Binomial Theorem
D. Additional Proofs
ANSWERS TO ODD-NUMBERED EXERCISES
REFERENCES
INDEX
Additional content can be accessed online at www.macmillanlearning.com/calculuset4e:
Additional Proofs:
L'Hôpital's Rule
Error Bounds for Numerical
Integration
Comparison Test for Improper
Integrals
Additional Content:
Second-Order Differential
Equations
Complex Numbers