Calculus

0 Preliminaries 0.1 The Real Numbers and the Cartesian Plane 0.2 Lines and Functions 0.3 Graphing Calculators and Computer Algebra Systems 0.4 Solving Equations 0.5 Trigonometric Functions 0.6 Exponential and Logarithmic Functions 0.7 Transformations of Functions 0.8 Preview of Calculus 1 Limits and Continuity 1.1 The Concept of Limit 1.2 Computation of Limits 1.3 Continuity and its Consequences 1.4 Limits Involving Infinity 1.5 Formal Definition of the Limit 1.6 Limits and Loss-of-Significance Errors 2 Differentiation 2.1 Tangent Lines and Velocity 2.2 The Derivative 2.3 Computation of Derivatives: The Power Rule 2.4 The Product and Quotient Rules 2.5 Derivatives of Trigonometric Functions 2.6 Derivatives of Exponential and Logarithmic Functions 2.7 The Chain Rule 2.8 Implicit Differentiation and Related Rates 2.9 The Mean Value Theorem 3 Applications of Differentiation 3.1 Linear Approximations adn L'Hopital's Rule 3.2 Newton's Method 3.3 Maximum and Minimum Values 3.4 Increasing and Decreasing Functions 3.5 Concavity 3.6 Overview of Curve Sketching 3.7 Optimization 3.8 Rates of Change in Applications 4 Integration 4.1 Antiderivatives 4.2 Sums and Sigma Notation 4.3 Area 4.4 The Definite Integral 4.5 The Fundamental Theorem of Calculus 4.6 Integration by Substitution 4.7 Numerical Integration 5 Applications of the Definite Integral 5.1 Area Between Curves 5.2 Volume 5.3 Volumes by Cylindrical Shells 5.4 Arc Length and Surface Area 5.5 Projectile Motion 5.6 Work, Moments, and Hydrostatic Force 5.7 Probability 6 Exponentials, Logarithms, and Other Transcendental Functions 6.1 The Natural Logarithm Revisited 6.2 Inverse Functions 6.3 The Exponential Function Revisited 6.4 Growth and Decay Problems 6.5 Separable Differential Equations 6.6 Euler's Method 6.7 The Inverse Trigonometric Functions 6.8 The Calculus of the Inverse Trigonometric Functions 6.9 The Hyperbolic Functions 7 Integration Techniques 7.1 Review of Formulas and Techniques 7.2 Integration by Parts 7.3 Trigonometric Techniques of Integration 7.4 Integration of Rational Functions using Partial Fractions 7.5 Integration Tables and Computer Algebra Systems 7.6 Indeterminate Forms and L'Hopital's Rule 7.7 Improper Integrals 8 Infinite Series 8.1 Sequences of Real Numbers 8.2 Infinite Series 8.3 The Integral Test and Comparison Tests 8.4 Alternating Series 8.5 Absolute Convergence and the Ratio Test 8.6 Power Series 8.7 Taylor Series 8.8 Fourier Series 9 Parametric Equations and Polar Coordinates 9.1 Plane Curves and Parametric Equations 9.2 Calculus and Parametric Equations 9.3 Arc Length and Surface Area in Parametric Equations 9.4 Polar Coordinates 9.5 Calculus and Polar Coordinates 9.6 Conic Sections 9.7 Conic Sections in Polar Coordinates 10 Vectors and the Geometry of Space 10.1 Vectors in the Plane 10.2 Vectors in Space 10.3 The Dot Product 10.4 The Cross Product 10.5 Lines and Planes in Space 10.6 Surfaces in Space 11 Vector-Valued Functions 11.1 Vector-Valued Functions 11.2 The Calculus of Vector-Valued Functions 11.3 Motion in Space 11.4 Curvature 11.5 Tangent and Normal Vectors 12 Functions of Several Variables 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 The Chain Rule 12.6 The Gradient and Directional Derivatives 12.7 Extrema of Functions of Several Variables 12.8 Constrained Optimization and Lagrange Multipliers 13 Multiple Integrals 13.1 Double Integrals 13.2 Area, Volume and Center of Mass 13.3 Double Integrals in Polar Coordinates 13.4 Surface Area 13.5 Triple Integrals 13.6 Cylindrical CoordinatesSmith, Robert T. is the author of 'Calculus' with ISBN 9780072830934 and ISBN 007283093X.