Calculus with Analytic Geometry
Published on 10. May 2014
1054 pages
978-1-4832-6240-6 (ISBN)
Description
Calculus with Analytic Geometry presents the essentials of calculus with analytic geometry. The emphasis is on how to set up and solve calculus problems, that is, how to apply calculus. The initial approach to each topic is intuitive, numerical, and motivated by examples, with theory kept to a bare minimum. Later, after much experience in the use of the topic, an appropriate amount of theory is presented. Comprised of 18 chapters, this book begins with a review of some basic pre-calculus algebra and analytic geometry, paying particular attention to functions and graphs. The reader is then introduced to derivatives and applications of differentiation; exponential and trigonometric functions; and techniques and applications of integration. Subsequent chapters deal with inverse functions, plane analytic geometry, and approximation as well as convergence, and power series. In addition, the book considers space geometry and vectors; vector functions and curves; higher partials and applications; and double and multiple integrals. This monograph will be a useful resource for undergraduate students of mathematics and algebra.
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Harley Flanders | Justin Jesse Price
Calculus with Analytical Geometry
Book
01/1978
2nd Edition
Academic Press
€28.79
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Content
¿Preface1. Functions and Graphs 1. Introduction 2. Real Numbers 3. Coordinates 4. Functions and Graphs 5. Linear Functions 6. Quadratic Functions 7. More on Graphing 8. Polynomials and Rational Functions 9. Distance Formula and Applications 10. Tangents 11. Miscellaneous Exercises2. Derivatives 1. The Slope Problem 2. Limits 3. The Derivative 4. Sums and Products 5. Quotients and Square Roots 6. The Chain Rule 7. The Tangent Line 8. Antiderivatives 9. Higher Derivatives 10. Limits and Continuity 11. Differentiable Functions 12. Miscellaneous Exercises3. Applications of Differentiation 1. Curve Sketching 2. Rectilinear Motion 3. Related Rates 4. Maxima and Minima 5. Applications of Max and Min 6. Second Derivative Test 7. On Problem Solving 8. Extrema and Convexity 9. Miscellaneous Exercises4. Exponential and Trigonometric Functions 1. The Exponential Function 2. Properties of Exponential Functions 3. Approximation and Growth Rates 4. Applications 5. Trigonometric Functions 6. Additional Trigonometric Functions 7. Derivatives 8. Applications 9. Miscellaneous Exercises5. Integration 1. The Area Problem 2. Examples of Integrals 3. The Definite Integral and the Fundamental Theorem 4. Applications 5. Approximate Integration 6. Integration of Products 7. Symmetry 8. Inequalities and Estimates 9. Insights into Integration 10. Miscellaneous Exercises6. Applications of Integration 1. Introduction 2. Area 3. Volume 4. Work 5. Fluid Pressure 6. Miscellaneous Applications 7. Miscellaneous Exercises7. Inverse Functions 1. Inverse Functions and Their Derivatives 2. The Logarithm Function 3. Further Properties of Logarithms 4. Applications of Logarithms 5. Inverse Trigonometric Functions 6. Derivatives and Applications 7. Hyperbolic Functions 8. Basic Properties 9. Miscellaneous Exercises8. Techniques of Integration 1. Indefinite Integrals 2. Substitutions and Differentials 3. Other Substitutions 4. Use of Identities 5. Partial Fractions 6. Trigonometric Substitutions 7. Integration by Parts 8. Reduction Formulas 9. Integral Tables 10. Miscellaneous Exercises9. Plane Analytic Geometry 1. Translation and Circles 2. Locus 3. Parabola and Ellipse 4. Hyperbola 5. Polar Coordinates 6. Polar Graphs 7. Rotation of Axes 8. Calculus Applied to Conics 9. Miscellaneous Exercises10. Approximation 1. Introduction 2. First and Second Degree Approximations 3. Taylor Approximations 4. Taylor's Formula 5. Rolle's Theorem 6. Mean Value Theorems and Lhospital's Rule 7. Interpolation 8. Lagrange Interpolation 9. Approximate Integration 10. Root Approximation and Hill Climbing 11. Iteration and Newton's Method 12. Miscellaneous Exercises11. Convergence 1. Sequences and Limits 2. Properties of Limits 3. Infinite Series 4. Series with Positive Terms 5. Series with Positive and Negative Terms 6. Improper Integrals 7. Convergence and Divergence Tests 8. Relation between Integrals and Series 9. Other Improper Integrals 10. Miscellaneous Exercises12. Power Series 1. Basic Properties 2. Taylor Series 3. Expansion of Functions 4. Further Techniques 5. Binomial Series 6. Numerical Applications 7. Sequences and Series of Functions 8. Miscellaneous Exercises13. Space Geometry and Vectors 1. Rectangular Coordinates 2. Vector Algebra 3. Length and Inner Product 4. Lines and Planes 5. Linear Systems 6. Cross Poduct 7. Applications of the Cross Product 8. Miscellaneous Exercises14. Vector Functions and Curves 1. Differentiation 2. Arc Length 3. Plane Curves 4.
