Calculus : Early Transcendental Functions
Robert T. Smith, Roland Minton · Medical Entomology and Zoology · 2006
Calculus: Early Transcendental Chapter 0: Preliminaries 0.1, Polynomials and Rational 0.2, Graphing Calculators and Computer Algebra 0.3, 0.4, and Inverse Trigonometric 0.5, and Logarithmic 0.6, Transformations of Chapter 1: and 1.1, A Brief Preview of Calculus: and the Length of a Curve 1.2, Concept of Limit 1.3, Computation of 1.4, and Its Consequences 1.5, Limits Involving Infinity Asymptotes 1.6, Formal Definition of the Limit 1.7, Limits and Loss-of-Significance Errors Chapter 2: Differentiation 2.1, Tangent and Velocity 2.2, 2.3, Computation of Derivatives: The 2.4, and Quotient Rules 2.5, Chain 2.6, of Trigonometric 2.7, of Exponential and Logarithmic 2.8, Implicit Differentiation and Inverse Trigonometric 2.9, Hyperbolic 2.10, Mean Value Chapter 3: of the Derivative 3.1, and Newton's Method 3.2, Indeterminate Forms and L'Hopital's Rule 3.3, Maximum and Minimum Values 3.4, Increasing and Decreasing 3.5, Concavity and the Second Derivative Test 3.6, Overview of Curve Sketching 3.7, 3.8, Related 3.9, Rates of in Economics and the Sciences Chapter 4: 4.1, Antiderivatives 4.2, Sums and Sigma Notation 4.3, 4.4, Definite 4.5, Fundamental Theorem of 4.6, by Substitution 4.7, Numerical Integration 4.8, Natural Logarithm as an Chapter 5: of the Definite Integral 5.1, Between 5.2, Volume: Slicing, Disks and Washers 5.3, Volumes by Shells 5.4, Arc Length and 5.5, Projectile 5.6, Applications of to Physics and Engineering 5.7, Probability Chapter 6: 6.1, Review of Formulas and Techniques 6.2, by Parts 6.3, of Integration 6.4, of Rational Using Fractions 6.5, Tables and Computer Algebra 6.6, Improper Chapter 7: First-Order Differential 7.1, Modeling with Differential Equations 7.2, Separable Differential Equations 7.3, Direction and Euler's Method 7.4, Systems of First-Order Differential Equations Chapter 8: 8.1, Sequences of Real Numbers 8.2, Infinite Series 8.3, Integral and Comparison Tests 8.4, Alternating Series 8.5, Absolute Convergence and the Ratio Test 8.6, Power Series 8.7, Series 8.8, Applications of Taylor Series 8.9, Fourier Series Chapter 9: and 9.1, Curves and Equations 9.2, and Equations 9.3, Arc Length and Area in Equations 9.4, Polar Coordinates 9.5, and Coordinates 9.6, Conic 9.7, Conic Sections in Coordinates Chapter 10: and the Geometry of 10.1, in the Plane 10.2, in Space 10.3, Dot Product 10.4, Cross Product 10.5, Lines and Planes in Space 10.6, in Space Chapter 11: 11.1, Vector-Valued 11.2, Calculus of 11.3, Motion in Space 11.4, Curvature 11.5, Tangent and Normal Vectors 11.6, Parametric Surfaces Chapter 12: of Several and Differentiation 12.1, Functions of Several Variables 12.2, Limits and Continuity 12.3, Partial Derivatives 12.4, Tangent Planes and Linear Approximations 12.5, Chain 12.6, Gradient and Directional Derivatives 12.7, Extrema of of Several Variables 12.8, Constrained Optimization and and Lagrange Multipliers Chapter 13: Multiple Integrals 13.1, Double 13.2, Area, Volume and Center of Mass 13.3, Double Integrals in Coordinates 13.4, Surface 13.5, Triple 13.6, Cylindrical Coordinates 13.7, Spherical Coordinates 13.8, Change of in Multiple Chapter 14: Calculus 14.1, Vector Fields 14.2, Line 14.3, Independence of Path and Conservative Fields 14.4, Green's 14.5, Curl and 14.6, Surface 14.7, Divergence 14.8, Stokes' 14.9, Applications of Chapter 15: Second Order Differential 15.1, Second-Order With Constant Coefficients 15.2, Nonhomogeneous Equations: Undetermined Coefficients 15.3, Applications of Second-Order Equations 15.4, Power Solutions of Differential Equations Appendix A: Proofs of Selected Theorems Appendix B: Answers to Odd-Numbered Exercises