TY  - BOOK
AU  - Stewart,James
TI  - Single variable calculus: concepts and context 
SN  - 9781337687805
AV  - QA303 .S88264 2019
U1  - 515 St49 2019 23
CY  - Calculus
KW  - Calculus
N1  - "4e."; Includes index; "New! Enhanced edition. Cengage has dramatically enhanced the online experience. Interactive activities, animations, exercises, and topic-based lecture videos have been added to Stewart's Calculus : concepts & contexts, 4e, WebAssign component"--Cover; Preface.To the Student.Diagnostic Tests.A Preview of Calculus.1. FUNCTIONS AND MODELS.Four Ways to Represent a Function. Mathematical Models: A Catalog of Essential Functions. New Functions from Old Functions. Graphing Calculators and Computers. Exponential Functions. Inverse Functions and Logarithms. Parametric Curves. Laboratory Project: Running Circles around Circles. Review. Principles of Problem Solving.2. LIMITS AND DERIVATIVES.The Tangent and Velocity Problems. The Limit of a Function. Calculating Limits Using the Limit Laws. Continuity. Limits Involving Infinity. Derivatives and Rates of Change. Writing Project: Early Methods for Finding Tangents. The Derivative as a Function. What Does f? ? Say about f ? Review. Focus on Problem Solving.3. DIFFERENTIATION RULES.Derivatives of Polynomials and Exponential Functions. Applied Project: Building a Better Roller Coaster. The Product and Quotient Rules. Derivatives of Trigonometric Functions. The Chain Rule. Laboratory Project: Bezier Curves. Applied Project: Where Should a Pilot Start Descent? Implicit Differentiation. Inverse Trigonometric Functions and their Derivatives. Derivatives of Logarithmic Functions. Discovery Project: Hyperbolic Functions. Rates of Change in the Natural and Social Sciences. Linear Approximations and Differentials. Laboratory Project: Taylor Polynomials. Review. Focus on Problem Solving.4. APPLICATIONS OF DIFFERENTIATION.Related Rates. Maximum and Minimum Values. Applied Project: The Calculus of Rainbows. Derivatives and the Shapes of Curves. Graphing with Calculus and Calculators. Indeterminate Forms and l'Hospital's Rule. Writing Project: The Origins of l'Hospital's Rule. Optimization Problems. Applied Project: The Shape of a Can. Newton's Method. Antiderivatives. Review. Focus on Problem Solving.5. INTEGRALS.Areas and Distances. The Definite Integral. Evaluating Definite Integrals. Discovery Project: Area Functions. The Fundamental Theorem of Calculus. Writing Project: Newton, Leibniz, and the Invention of Calculus. The Substitution Rule. Integration by Parts. Additional Techniques of Integration. Integration Using Tables and Computer Algebra Systems. Discovery Project: Patterns in Integrals. Approximate Integration. Improper Integrals. Review. Focus on Problem Solving.6. APPLICATIONS OF INTEGRATION.More about Areas. Volumes. Discovery Project: Rotating on a Slant. Volumes by Cylindrical Shells. Arc Length. Discovery Project: Arc Length Contest. Average Value of a Function. Applied Project: Where to Sit at the Movies. Applications to Physics and Engineering. Discovery Project: Complementary Coffee Cups. Applications to Economics and Biology. Probability. Review. Focus on Problem Solving.7. DIFFERENTIAL EQUATIONS.Modeling with Differential Equations. Direction Fields and Euler's Method. Separable Equations. Applied Project: How Fast Does a Tank Drain? Applied Project: Which Is Faster, Going Up or Coming Down? Exponential Growth and Decay. Applied Project: Calculus and Baseball. The Logistic Equation. Predator-Prey Systems. Review. Focus on Problem Solving.8. INFINTE SEQUENCES AND SERIES.Sequences. Laboratory Project: Logistic Sequences. Series. The Integral and Comparison Tests; Estimating Sums. Other Convergence Tests. Power Series. Representations of Functions as Power Series. Taylor and Maclaurin Series. Laboratory Project: An Elusive Limit. Writing Project: How Newton Discovered the Binomial Series. Applications of Taylor Polynomials. Applied Project: Radiation from the Stars. Review. Focus on Problem Solving.APPENDIXES.A. Intervals, Inequalities, and Absolute Values.B. Coordinate Geometry.C. Trigonometry.D. Precise Definitions of Limits.E. A Few Proofs.F. Sigma Notation.G. Integration of Rational Functions by Partial Fractions.H. Polar Coordinates.I. Complex Numbers.J. Answers to Odd-Numbered Exercises; COECS; Bachelor of Science in Civil Engineering; COECS; Bachelor of Science in Computer Engineering; COECS; Bachelor of Science in Electronics Engineering; CoED; Bachelor of Secondary Education major in Mathematics
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