Book:Frank Ayres, Jr./Theory and Problems of Differential and Integral Calculus/SI Edition

Subject Matter

 * Calculus

Contents

 * Preface to Second Edition (March 1964)


 * Chapter 1: Variables and Functions
 * Chapter 2: Limits
 * Chapter 3: Continuity
 * Chapter 4: The Derivative
 * Chapter 5: Differentiation of Algebraic Functions
 * Chapter 6: Implicit Differentiation
 * Chapter 7: Tangents and Normals
 * Chapter 8: Maximum and Minimum Values
 * Chapter 9: Applied Problems in Maxima and Minima
 * Chapter 10: Rectilinear and Circular Motion
 * Chapter 11: Related Rates
 * Chapter 12: Differentiation of Trigonometric Functions
 * Chapter 13: Differentiation of Inverse Trigonometric Functions
 * Chapter 14: Differentiation of Exponential and Logarithmic Functions
 * Chapter 15: Differentiation of Hyperbolic Functions
 * Chapter 16: Parametric Representation of Curves
 * Chapter 17: Curvature
 * Chapter 18: Plane Vectors
 * Chapter 19: Curvilinear Motion
 * Chapter 20: Polar Coordinates
 * Chapter 21: The Law of the Mean
 * Chapter 22: Indeterminate Forms
 * Chapter 23: Differentials
 * Chapter 24: Curve Tracing
 * Chapter 25: Fundamental Integration Formulas
 * Chapter 26: Integration by Parts
 * Chapter 27: Trigonometric Integrals
 * Chapter 28: Trigonometric Substitutions
 * Chapter 29: Integration by Parts
 * Chapter 30: Miscellaneous Substitutions
 * Chapter 31: Integration of Hyperbolic Functions
 * Chapter 32: Applications of Indefinite Integrals
 * Chapter 33: The Definite Integral
 * Chapter 34: Plane Areas by Integration
 * Chapter 35: Volumes of Solids of Revolution
 * Chapter 36: Volumes of Solids with Known Cross Sections
 * Chapter 37: Centroids
 * Chapter 38: Moments of Inertia
 * Chapter 39: Fluid Pressure
 * Chapter 40: Work
 * Chapter 41: Length of Arc
 * Chapter 42: Area of Surface of Revolution
 * Chapter 43: Centroid and Moment of Inertia
 * Chapter 44: Plane Area and Centroid of Area
 * Chapter 45: Length and Centroid of Arc. Area of Surface of Revolution
 * Chapter 46: Improper Integrals
 * Chapter 47: Infinite Sequences and Series
 * Chapter 48: Tests for Convergence and Divergence of Positive Series
 * Chapter 49: Series with Negative Terms
 * Chapter 50: Computation with Series
 * Chapter 51: Power Series
 * Chapter 52: Series Expansion of Functions
 * Chapter 53: Maclaurin's and Taylor's Formulas with Remainders
 * Chapter 54: Computations using Power Series
 * Chapter 55: Approximate Integration
 * Chapter 56: Partial Derivatives
 * Chapter 57: Total Differentials and Total Derivatives
 * Chapter 58: Implicit Functions
 * Chapter 59: Space Curves and Surfaces
 * Chapter 60: Directional Derivatives. Maximum and Minimum Values
 * Chapter 61: Space Vectors
 * Chapter 62: Vector Differentiation and Integration
 * Chapter 63: Double and Iterated Integrals
 * Chapter 64: Centroids and Moments of Inertia of Plane Areas
 * Chapter 65: Volume under a Surface. Double Integration
 * Chapter 66: Area of a Curved Surface. Double Integration
 * Chapter 67: Triple Integrals
 * Chapter 68: Masses of Variable Density
 * Chapter 69: Differential Equations
 * Chapter 70: Differential Equations of Order Two
 * INDEX



Source work progress
* : Chapter $1$: Variables and Functions

Working through standard lists of integrals -- there is a problem in the below page which needs to be resolved:
 * : Chapter $25$: Fundamental Integration Formulas: $24$.