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Full Description
Designed specifically for biology and life/social sciences majors, this applied calculus program motivates students while fostering understanding and mastery. The authors emphasize integrated and engaging applications that show students the real-world relevance of topics and concepts. Several pedagogical features--from algebra review to study tips--provide extra guidance and practice.Applied Calculus for the Life and Social Sciences features current, relevant examples drawn from government sources, industry, recent events, and other disciplines that appeal to diverse interests. In addition, the program offers a strong support package--including CL MATHSpace Instructor/Student websites and course management tools, instructional DVDs, and solutions manuals--that allows students to review the material independently and retain key concepts.
Contents
0. A Precalculus Review0.1 The Real Number Line and Order0.2 Absolute Value and Distance on the Real Number Line0.3 Exponents and Radicals0.4 Factoring Polynomials0.5 Fractions and Rationalization1. Functions, Graphs, and Limits1.1 The Cartesian Plane and the Distance Formula1.2 Graphs of Equations1.3 Lines in the Plane and Slope1.4 Functions1.5 Limits1.6 Continuity2. Differentiation2.1 The Derivative and the Slope of a Graph2.2 Some Rules for Differentiation2.3 Rates of Change2.4 The Product and Quotient Rules2.5 The Chain Rule2.6 Higher-Order Derivatives3. Applications of the Derivative3.1 Increasing and Decreasing Functions3.2 Extrema and the First-Derivative Test3.3 Concavity and the Second-Derivative3.4 Optimization Problems3.5 Asymptotes3.6 Curve Sketching: A Summary3.7 Differentials: Linear Approximation4. Exponential and Logarithmic Functions4.1 Exponential Functions4.2 Natural Exponential Functions4.3 Derivatives of Exponential Functions4.4 Logarithmic Functions4.5 Derivatives of Logarithmic Functions4.6 Exponential Growth and Decay5. Trigonometric Functions5.1 Radian Measure of Angles5.2 The Trigonometric Functions5.3 Graphs of Trigonometric Functions5.4 Derivatives of Trigonometric Functions6. Integration and Its Applications6.1 Antiderivatives and Indefinite Integrals6.2 Integration by Substitution and The General Power Rule6.3 Exponential and Logarithmic Integrals6.4 Area and the Fundamental Theorem of Calculus6.5 The Area of a Region Bounded by Two Graphs6.6 Volumes of Solids of Revolution7. Techniques of Integration7.1 Integration by Parts7.2 Partial Fractions and Logistic Growth7.3 Integrals of Trigonometric Functions7.4 The Definite Integral as the Limit of a Sum7.5 Numerical Integration7.6 Improper Integrals8. Matrices8.1 Systems of Linear Equations in Two Variables8.2 Systems of Linear Equations in More Than Two Variables8.3 Matrices and Systems of Linear Equations8.4 Operations with Matrices8.5 The Inverse of a Matrix9. Functions of Several Variables9.1 The Three-Dimensional Coordinate System9.2 Surfaces in Space9.3 Functions of Several Variables9.4 Partial Derivatives9.5 Extrema of Functions of Two Variables9.6 Least Squares Regression Analysis9.7 Double Integrals and Area in the Plane9.8 Applications of Double Integrals10. Differential Equations10.1 Solutions of Differential Equations10.2 Separation of Variables10.3 First-Order Linear Differential Equations10.4 Applications of Differential Equations11. Probability and Calculus11.1 Discrete Probability11.2 Continuous Random Variables11.3 Expected Value and VarianceAppendix A. Differentiation and Integration FormulasAppendix B. Additional Topics in DifferentiationB.1 Implicit DifferentiationB.2 Related RatesAppendic C. Probability and Probability Distributions (web only)C.1 ProbabilityC.2 Probability ComputationsC.3 Conditional ProbabilityC.4 Tree Diagrams and Bayes'' TheoremC.5 Probability DistributionsC.6 Normal DistributionC.7 Binomial DistributionAppendix D. Properties and Measurement (web only)D.1 Review of AlgebraD.2 Units of MeasurementsAppendix E. Graphing Utility Programs (web only)E.1 Graphing Utility Programs
