Succeeding in Applied Calculus

Warren B. Gordon has been Chair of the Mathematics Department at Baruch College since 1985. He received his MS and his Ph.D., from the Courant Institute of Mathematics at New York University.

1. REAL NUMBERS AND THEIR PROPERTIES. Pretest. The Real Number System. Variables, Algebraic Expressions, Terms, Coefficients and Factors. Order of Operations. Associative, Commutative, Distributive, Identity, and Inverse Properties. Exercises. Posttest. 2. A REVIEW OF THE LAWS OF EXPONENTS. Pretest. Exponents. Negative Exponents. Sum Rule. Product Rule. Quotient Rule. Zero Rule. Distributive Rules. Exercises. Posttest. 3. RADICALS. Pretest. Roots. Simplification of Radicals. Pythagoras" Theorem. The Distance Formula. Combining Radicals. Exercises. Posttest. 4. MULTIPLICATION AND RATIONALIZATION OF RADICALS. Pretest. Basic Operations. Product of Two Binomials. Conjugates. Rationalization. Indeterminate Forms. Exercises. Posttest. 5. COMPLEX NUMBERS. Pretest. Imaginary Number i. Complex Numbers. Exercises. Posttest. 6. FRACTIONAL EXPONENTS. Pretest. Fractional Roots. Equations with Fractional Exponents. Products of Radicals. Compound Interest. Rule of 72. Simple Pendulum. Exercises. Posttest. 7. A REVIEW OF FACTORING. Pretest. GCF. Monomial Factors. Factoring Trinomials. Perfect Squares. Conjugates - The Difference of Two Squares. Factoring by Grouping. Quadratic Equations and Factoring. Exercises. Posttest. 8. SOLVING LINEAR EQUATIONS. Pretest. Addition and Multiplication Properties. Linear Equations with Fractions. Linear Equations with Decimals. Solving for a Particular Variable. Applications of Linear Equations. Exercise. Posttest. 9. SOLVING EQUATIONS OF THE FORM ax^2 - b = 0. Pretest. Isolation of Squared Term. Isolation of Squared Binomial Term. Exercises. Posttest. 10. COMPLETING THE SQUARE. Pretest. Completion of the Square. Exercise. Posttest. 11. THE QUADRATIC FORMULA AND APPLICATIONS. Pretest. Quadratic Formula. Clearing Fractions. Applications. Equations Reducible to Quadratics. Exercises. Posttest. 12. OBSERVATIONS AND EXTENSIONS. Pretest. Discriminant. Sum and Product of Roots. Exercises. Posttest. 13. EQUATIONS CONTAINING RADICALS. Pretest. Isolation and Extraneous Roots. Multiple Square Roots. Exercises. Posttest. 14. SOLVING NON-LINEAR INEQUALITIES. Pretest. Sign Analysis. Interval Notation. Exercises. Posttest. 15. THE LINE. Pretest. Two Dimensional Coordinate System. Horizontal and Vertical Lines. The Slope Intercept Form. Graphing. The Point Slope Form. The Slope Formula. The General Linear Equation. An Economic Application. Exercise. Posttest. 16. THE CIRCLE. Pretest. Definition of a Circle. Equation of a Circle. Graphing a Circle. The Tangent Line. The Ellipse. Exercises. Posttest. 17. SOLVING TWO EQUATIONS IN TWO UNKNOWNS. Pretest. Method of Elimination. Method of Substitution. Exercises. Posttest. 18. NON-LINEAR SYSTEMS OF EQUATIONS. Pretest. Number of Solutions. Method of Substitution. Method of Elimination. A Calculus Application. Exercises. Posttest. 19. APPENDIX - ARITHMETIC OF SIGNED NUMBERS. Pretest. Absolute Value. Addition of Signed Numbers. Subtraction of Signed Numbers. Multiplication of Signed Numbers. Division of Signed Numbers. Exercises. Posttest. 20. Answers to Pre and Post Tests. 21. Answers to Exercises. 22. Index.