College Algebra and Calculus

0. FUNDAMENTAL CONCEPTS OF ALGEBRA. Real Numbers: Order and Absolute Value. The Basic Rules of Algebra. Integer Exponents. Radicals and Rational Exponents. Polynomials and Special Products. Factoring. Fractional Expressions. 1. EQUATIONS AND INEQUALITIES. Linear Equations. Mathematical Modeling. Quadratic Equations. The Quadratic Formula. Other Types of Equations. Linear Inequalities. Other Types of Inequalities. 2. FUNCTIONS AND GRAPHS. Graphs of Equations. Lines in the Plane. Linear Modeling and Direct Variation. Functions. Graphs of Functions. Transformations of Functions. The Algebra of Functions. 3. POLYNOMIAL AND RATIONAL FUNCTIONS. Quadratic Functions and Models. Polynomial Functions of Higher Degree. Polynomial Division. Real Zeros of Polynomial Functions. Complex Numbers. The Fundamental Theorem of Algebra. Rational Functions. 4. EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Inverse Functions. Exponential Functions. Logarithmic Functions. Properties of Logarithms. Solving Exponential and Logarithmic Equations. Exponential and Logarithmic Models. 5. SYSTEMS OF EQUATIONS AND INEQUALITIES. Solving Linear Systems Using Substitution. Solving Linear Systems Using Elimination. Linear Systems in Three or More Variables. Systems of Inequalities. Linear Programming. 6. MATRICES AND DETERMINANTS. Matrices and Linear Systems. Operations with Matrices. The Inverse of a Square Matrix. The Determinant of a Square Matrix. Applications of Matrices and Determinants. 7. LIMITS AND DERIVATIVES. Limits. Continuity. The Derivative and the Slope of a Graph. Some Rules for Differentiation. Rates of Change: Velocity and Marginals. The Product and Quotient Rules. The Chain Rule. 8. APPLICATIONS OF THE DERIVATIVE. Higher-Order Derivatives. Implicit Differentiation. Related Rates. Increasing and Decreasing Functions. Extrema and the First-Derivative Test. Concavity and the Second-Derivative Test. 9. FURTHER APPLICATIONS OF THE DERIVATIVE. Optimization Problems. Business and Economics Applications. Asymptotes. Curve Sketching: A Summary. Differentials and Marginal Analysis. 10. DERIVATIVES OF EXPONENTIAL AND LOGARITHMIC FUNCTIONS. Exponential Functions. Natural Exponential Functions. Derivatives of Exponential Functions. Logarithmic Functions. Derivatives of Logarithmic Functions. Exponential Growth and Decay. 11. INTEGRATION AND ITS APPLICATIONS. Antiderivatives and Indefinite Integrals. Integration by Substitution and The General Power Rule. Exponential and Logarithmic Integrals. Area and the Fundamental Theorem of Calculus. The Area of a Region Bounded by Two Graphs. The Definite Integral as the Limit of a Sum. 12. TECHNIQUES OF INTEGRATION. Integration by Parts and Present Value. Integration Tables. Numerical Integration. Improper Integrals. 13. FUNCTIONS OF SEVERAL VARIABLES. The Three-Dimensional Coordinate System. Surfaces in Space. Functions of Several Variables. Partial Derivatives. Extrema of Functions of Two Variables. Lagrange Multipliers. Least Squares Regression Analysis. Double Integrals and Area in the Plane. Applications of Double Integrals. 14. TRIGONOMETRIC FUNCTIONS. Radian Measure of Angles. The Trigonometric Functions. Graphs of Trigonometric Functions. Derivatives of Trigonometric Functions. Integrals of Trigonometric Functions. 15. SERIES AND TAYLOR POLYNOMIALS. Sequences and Summation Notation. Arithmetic Sequences and Partial Sums. Geometric Sequences and Series. Series and Convergence. p-Series and the Ratio Test. Power Series and Taylor's Theorem. Taylor Polynomials. Newton's Method. 16. PROBABILITY. Counting Principles. Probability. Discrete and Continuous Random Variables. Expected Value and Variance. Mathematical Induction. The Binomial Theorem. Appendix A: An Introduction to Graphing Utilities. Appendix B: Conic Sections. Conic Sections. Conic Sections and Translations. Appendix C: Further Concepts in Statistics. Data and Linear Modeling. Measures of Central Tendency and Dispersion. Appendix D: Precalculus Review. The Real Number Line and Order. Absolute Value and Distance on the Real Number Line. Exponents and Radicals. Factoring Polynomials. Fractions and Rationalization. Appendix E: Alternate Introduction to the Fundamental Theorem of Calculus. Appendix F: Differential Equations. Solutions of Differential Equations. Separation of Variables. First-Order Linear Differential Equations. Applications of Differential Equations. Appendix G: Formulas. Differentiation and Integration Formulas. Formulas from Business and Finance. Appendix H: Properties and Measurement. Review of Algebra, Geometry, and Trigonometry. Units of Measurements. Appendix I: Graphing Utility Programs. Appendix J: Mathematical Induction. Supplements: