CONTENTS - 1. REVIEW OF ELEMENTARY ALGEBRA - Indices; Logarithms; Graphs-Solution of Linear Equations; Solution of Quadratic Equations in One Variable; Approximate Solution of Higher Order Equations; Solution of Exponential Equations - 2. REVIEW OF ELEMENTARY PLANE TRIGONOMETRY - The Circular Functions; Radian Measure; Simple Applications of Trigonometry; Solution of General Triangles; Circular Functions of the Sum and Difference of Two Angles; Solution of Trigonometric Equations; The Inverse Circular Functions - 3. CO-ORDINATE PLANE GEOMETRY OF THE STRAIGHT LINE - Cartesian and Polar Co-ordinates; Loci; Various Forms of the Equation of a Line; Distance from a Point to a Line; Angle between Two Lines; Point of Intersection of Two Lines; Pairs of Lines; Problems Involving Straight Lines - 4. CO-ORDINATE PLANE GEOMETRY OF THE CIRCLE - Equations of a Circle; Equation of the Tangent to a Circle; Equation of the Normal to a Circle; Length of the Tangent from a Point to a Circle; Intersection of a Circle with a Line; Intersection of Two Circles; Problems Involving Circles and Lines - 5.
THE BINOMIAL EXPANSION - Permutations and Combinations; The Binomial Expansion for Positive Integral Index; Some Properties of the Binomial Coefficients; The Binomial Expansion for any Index; Validity of the Binomial Expansion for any Index; Applications of the Binomial Expansion - 6. PARTIAL FRACTIONS - Rational Functions; Addition and Subtraction of Rational Functions; Partial Fractions Viewed as an Inverse Process; The Denominator g(a...') Containing Non-Repeated Linear Factors; The Denominator g(a...') Containing Repeated Linear Factors; The Denominator g(x) Containing Non-Repeated Quadratic Factors; The Denominator g(x) Containing Repeated Quadratic Factors; The General Denominator Applications of Partial Fractions - 7. FUNCTIONS AND LIMITS - Functional Relationships; Geometrical Representation of a Functional Relationship; Values and Limits of a Function; The Derivative of a Function - 8.
DIFFERENTIATION - Differentiation from First Principles; Differentiation of x"-Differentiation of sin x and cos x; Differentiation of Sums, Differences, Products, and Quotients; Differentiation of Compound Circular Functions; Differentiation of a Function of a Function-Differentiation of log x; The Exponential and Hyperbolic Functions; Differentiation of Inverse Circular and Inverse Hyperbolic Functions - 9. APPLICATIONS OF DIFFERENTIATION - Tangents and Normals to Curves; Estimation of Small Errors; Maclaurin and Taylor Series; Newton's Method for the Approximate Solution of Equations; Maxima and Minima - 10. INTEGRATION - Integration as the Inverse of Differentiation; Special Methods of Integration; Integration Using Partial Fractions; Integration by Substitution; Integration by Parts; The Definite Integral; Reduction Formulae - 11. APPLICATIONS OF INTEGRATION - Areas Bounded by Plane Curves; Mean Values; Arc Lengths of Plane Curves; Volumes of Solids of Revolution; Surfaces of Revolution; Centres of Gravity; Moments of Inertia; Hydrostatic Thrust and Centres of Pressure - 12. COMPLEX NUMBERS - 13. ORDINARY LINEAR DIFFERENTIAL EQUATIONS - 14 PARTIAL DIFFERENTIATION - 15.
STATISTICAL METHOD - 16. STANDARD NUMERICAL MEASURES FOR DESCRIBING FREQUENCY DIAGRAMS - 17. PROBABILITY THEORY AND ITS APPLICATIONS - 18. BINOMIAL AND POISSON DISTRIBUTIONS - 19. NORMAL DISTRIBUTION - 20. CONTROL CHARTS - 21. POPULATION AND SAMPLE - 22. DISTRIBUTION OF DIFFERENCES - 23. TESTS OF SIGNIFICANCE - 24. ANALYSIS OF VARIANCE - 25. REGRESSION AND CORRELATION (LINEAR RELATIONSHIPS) -