A Course of Mathematics for Engineers and Scientists

Chapter I. Introductory Concepts Functional Notation and Fundamental Definitions The Roots of Equations Elementary Two-Dimensional Coordinate Geometry Limits and Continuity Orders of MagnitudeChapter II. The Technique of Differentiation Differentiation from First Principles The Rules of Differentiation Repeated Differentiation Exponentials, Logarithms and Hyperbolic Functions Inverse Functions Differentiation of Equations Leibniz's Theorem on Repeated Differentiations Elementary Partial Differentiation DifferentialsChapter III. The Technique of Integration Definitions and Standard Forms The Definite Integral as the Limit of a Sum Elementary Rules and Examples Integration by Substitution Integration by Parts Partial Fractions Integration of Rational Functions Miscellaneous Methods Reduction FormulaChapter IV. Geometry of Two Dimensions Introduction Gradient, Tangent and Normal Points of Inflexion The Arc Length of a Curve Curvature Envelopes The Loaded Cable Polar Coordinates Curve Sketching Translation and Rotation of Axes The Area of a Triangle The General Equation of the Second Degree The Properties of the Ellipse The Properties of the Hyperbola The Properties of the Parabola The Polar Equation of a ConicChapter V. Applications of Differentiation Convergence of Series Inequalities The Mean Value Theorem and Linear Approximations Taylor's and Maclaurin's Theorems Expansions in Power Series Maxima and Minima Small Increments and Proportional Errors Approximate Solution of Equations KinematicsChapter VI. Applications of Integration Introduction-The Area Bounded by a Plane Curve Volumes and Surfaces of Revolution Polar Coordinates First Moments The Theorems of Pappus Mean Values-Root Mean Square Second Moments-Moments of Inertia Applications to Hydrostatics Numerical IntegrationChapter VII. Complex Numbers Introduction-The Argand Diagram De Moivre's Theorem Multiplication and Division on the Argand Diagram The Roots of Complex Numbers Trigonometric Expansions Functions of x + iyAnswers to ExercisesIndex