ENGLISH

Calculus from Approximation to Theory

By Daniel C. Sloughter

Book information

Year
2020
ISBN
2020031331, 9781470455880, 9781470463052
Language
english
Format
PDF
Filesize
6 MB (6664426 bytes)
Pages
\584
Time added
2021-02-25 21:16:15

Description

Cover Title page Copyright Contents Preface Chapter 1. Sequences and Limits 1.1. Calculus: Areas and tangents Problems 1.1 1.2. Sequences Problems 1.2 1.3. The sum of a sequence Problems 1.3 1.4. Difference equations Problems 1.4 1.5. Nonlinear difference equations Problems 1.5 Chapter 2. Functions and Their Properties 2.1. Functions and their graphs Problems 2.1 2.2. Trigonometric functions Problems 2.2 2.3. Limits and the notion of continuity Problems 2.3 2.4. Continuous functions Problems 2.4 2.5. Some consequences of continuity Problems 2.5 Chapter 3. Derivatives and Best Affine Approximations 3.1. Best affine approximations Problems 3.1 3.2. Derivatives and rates of change Problems 3.2 3.3. Differentiation of rational functions Problems 3.3 3.4. Differentiation of compositions Problems 3.4 3.5. Differentiation of trigonometric functions Problems 3.5 3.6. Newton’s method Problems 3.6 3.7. The Mean Value Theorem Problems 3.7 3.8. Finding maximum and minimum values Problems 3.8 3.9. The geometry of graphs Problems 3.9 Chapter 4. Integrals 4.1. The definite integral Problems 4.1 4.2. Numerical approximations Problems 4.2 4.3. The Fundamental Theorem of Calculus Problems 4.3 4.4. Using the Fundamental Theorem Problems 4.4 4.5. More techniques of integration Problems 4.5 4.6. Improper integrals Problems 4.6 4.7. More on area Problems 4.7 4.8. Distance, position, and length Problems 4.8 Chapter 5. Taylor Polynomials and Series 5.1. Polynomial approximations Problems 5.1 5.2. Taylor’s theorem Problems 5.2 5.3. Infinite series revisited Problems 5.3 5.4. The comparison test Problems 5.4 5.5. The ratio test Problems 5.5 5.6. Absolute convergence Problems 5.6 5.7. Power series Problems 5.7 5.8. Taylor series Problems 5.8 5.9. Some limit calculations Problems 5.9 Chapter 6. More Transcendental Functions 6.1. The exponential function Problems 6.1 6.2. The natural logarithm function Problems 6.2 6.3. Models of growth and decay Problems 6.3 6.4. Integration of rational functions Problems 6.4 6.5. Inverse trigonometric functions Problems 6.5 6.6. Trigonometric substitutions Problems 6.6 6.7. Hyperbolic functions Problems 6.7 Chapter 7. The Complex Plane 7.1. The algebra of complex numbers Problems 7.1 7.2. The calculus of complex functions Problems 7.2 7.3. Motion in the plane Problems 7.3 7.4. The two-body problem Problems 7.4 Chapter 8. Differential Equations 8.1. Numerical solutions Problems 8.1 8.2. Separation of variables Problems 8.2 8.3. First-order linear equations Problems 8.3 8.4. Second-order linear equations Problems 8.4 8.5. Pendulums and mass-spring systems Problems 8.5 8.6. Phase planes Problems 8.6 8.7. Power series solutions Problems 8.7 Appendix A. Answers to Selected Problems A.1. Chapter 1 A.2. Chapter 2 A.3. Chapter 3 A.4. Chapter 4 A.5. Chapter 5 A.6. Chapter 6 A.7. Chapter 7 A.8. Chapter 8 Index Back Cover

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