Calculus hasn't changed, but your students have. Many of today's students have seen calculus before at the high school level. However, professors report nationwide that students come into their calculus courses with weak backgrounds in algebra and trigonometry, two areas of knowledge vital to the mastery of calculus. Thomas' Calculus Early Transcendentals, Part One, Media Upgrade, Eleventh Edition responds to the needs of today's students by developing their conceptual understanding while maintaining a rigor appropriate to the calculus course.
Thomas' Calculus Early Transcendentals, Part One, Media Upgrade, Eleventh Edition is now available with an enhanced MyMathLab (TM) course-the ultimate homework, tutorial and study solution for today's students. The enhanced MyMathLab (TM) course includes a rich and flexible set of course materials and features innovative Java (TM) Applets, Group Projects, and new MathXL (R) exercises. This text is also available with WebAssign (R) and WeBWorK (R).
1. Functions Functions and Their Graphs Identifying Functions; Mathematical Models Combining Functions; Shifting and Scaling Graphs Graphing with Calculators and Computers Exponential Functions Inverse Functions and Logarithms 2. Limits and Continuity Rates of Change and Limits Calculating Limits Using the Limit Laws Precise Definition of a Limit One-Sided Limits and Limits at Infinity Infinite Limits and Vertical Asymptotes Continuity Tangents and Derivatives 3. Differentiation The Derivative as a Function Differentiation Rules for Polynomials, Exponentials, Products and Quotients The Derivative as a Rate of Change Derivatives of Trigonometric Functions The Chain Rule and Parametric Equations Implicit Differentiation Derivatives of Inverse Functions and Logarithms Inverse Trigonometric Functions Related Rates Linearization and Differentials 4. Applications of Derivatives Extreme Values of Functions The Mean Value Theorem Monotonic Functions and the First Derivative Test Concavity and Curve Sketching Applied Optimization Problems Indeterminate Forms and L'Hopital's Rule Newton's Method Antiderivatives 5. Integration Estimating with Finite Sums Sigma Notation and Limits of Finite Sums The Definite Integral The Fundamental Theorem of Calculus Indefinite Integrals and the Substitution Rule Substitution and Area Between Curves 6. Applications of Definite Integrals Volumes by Slicing and Rotation About an Axis Volumes by Cylindrical Shells Lengths of Plane Curves Moments and Centers of Mass Areas of Surfaces of Revolution and The Theorems of Pappus Work Fluid Pressures and Forces 7. Integrals and Transcendental Functions The Logarithm Defined as an Integral Exponential Growth and Decay Relative Rates of Growth Hyperbolic Functions 8. Techniques of Integration Basic Integration Formulas Integration by Parts Integration of Rational Functions by Partial Fractions Trigonometric Integrals Trigonometric Substitutions Integral Tables and Computer Algebra Systems Numerical Integration Improper Integrals 9. Further Applications of Integration Slope Fields and Separable Differential Equations First-Order Linear Differential Equations Euler's Method Graphical Solutions of Autonomous Equations Applications of First-Order Differential Equations 10. Conic Sections and Polar Coordinates Conic Sections and Quadratic Equations Classifying Conic Sections by Eccentricity Quadratic Equations and Rotations Conics and Parametric Equations; The Cycloid Polar Coordinates Graphing in Polar Coordinates Area and Lengths in Polar Coordinates Conic Sections in Polar Coordinates 11. Infinite Sequences and Series Sequences Infinite Series The Integral Test Comparison Tests The Ratio and Root Tests Alternating Series, Absolute and Conditional Convergence Power Series Taylor and Maclaurin Series Convergence of Taylor Series; Error Estimates Applications of Power Series Fourier Series Appendices. Mathematical Induction Proofs of Limit Theorems Commonly Occurring Limits Theory of the Real Numbers Complex Numbers The Distributive Law for Vector Cross Products Determinants and Cramer's Rule The Mixed Derivative Theorem and the Increment Theorem The Area of a Parallelogram's Projection on a Plane