Includes index.

Introduction: Calculus: A New Horizon from Ancient Roots -- Chapter 1. Functions -- 1.1. Functions and the Analysis of Graphical Information -- 1.2. Properties of Functions -- 1.3. Graphing Functions on Calculators and Computers; Computer Algebra Systems -- 1.4. New Functions from Old -- 1.5. Lines -- 1.6. Families of Functions -- 1.7. Mathematical Models -- 1.8. Parametric Equations -- Horizon Module: Iteration and Dynamical Systems -- Chapter 2. Limits and Continuity -- 2.1. Limits (An Intuitive Approach) -- 2.2. Computing Limits -- 2.3. Computing Limits: End Behavior -- 2.4. Limits (Discussed More Rigorously) -- 2.5. Continuity -- 2.6. Limits and Continuity of Trigonometric Functions -- Chapter 3. The Derivative -- 3.1. Slopes and Rates of Change -- 3.2. The Derivative -- 3.3. Techniques of Differentiation -- 3.4. Derivatives of Trigonometric Functions -- 3.5. The Chain Rule -- 3.6. Implicit Differentiation -- 3.7. Related Rates -- 3.8. Local Linear Approximation; Differentials -- Horizon Module: Robotics -- Chapter 4. The Derivative in Graphing and Applications -- 4.1. Analysis of Functions I: Increase, Decrease, and Concavity -- 4.2. Analysis of Functions II: Relative Extrema; First and Second Derivative Tests -- 4.3. Analysis of Functions III: Applying Technology and the Tools of Calculus -- 4.4. Rectilinear Motion (Motion Along a Line) -- 4.5. Absolute Maxima and Minima -- 4.6. Applied Maximum and Minimum Problems -- 4.7. Newton's Method -- 4.8. Rolle's Theorem; Mean-Value Theorem -- Chapter 5. Integration -- 5.1. An Overview of the Area Problem -- 5.2. The Indefinite Integral; Integral Curves and Direction Fields -- 5.3. Integration by Substitution -- 5.4. Sigma Notation; Area as a Limit -- 5.5. The Definite Integral -- 5.6. The Fundamental Theorem of Calculus -- 5.7. Rectilinear Motion Revisited; Average Value -- 5.8. Evaluating Definite Integrals by Substitution -- Horizon Module: Blammo the Human Cannonball -- Chapter 6. Applications of the Definite Integral in Geometry, Science, and Engineering -- 6.1. Area Between Two Curves -- 6.2. Volumes by Slicing; Disks and Washers -- 6.3. Volumes by Cylindrical Shells -- 6.4. Length of a Plane Curve -- 6.5. Area of a Surface of Revolution -- 6.6. Work -- 6.7. Fluid Pressure and Force -- Chapter 7. Exponential, Logarithmic, and Inverse Trigonometric Functions -- 7.1. Inverse Functions -- 7.2. Exponential and Logarithmic Functions -- 7.3. Derivatives and Integrals Involving Logarithmic and Exponential Functions -- 7.4. Graphs and Applications Involving Logarithmic and Exponential Functions -- 7.5. Logarithmic Functions from the Integral Point of View -- 7.6. Derivatives and Integrals Involving Inverse Trigonometric Functions -- 7.7. L'Hopital's Rule; Indeterminate Forms -- 7.8. Hyperbolic Functions and Hanging Cables -- Chapter 8. Principles of Integral Evaluation -- 8.1. An Overview of Integration Methods -- 8.2. Integration by Parts -- 8.3. Trigonometric Integrals -- 8.4. Trigonometric Substitutions -- 8.5. Integrating Rational Functions by Partial Fractions -- 8.6. Using Tables of Integrals and Computer Algebra Systems -- 8.7. Numerical Integration; Simpson's Rule -- 8.8. Improper Integrals -- Horizon Module: Railroad Design -- Chapter 9. Mathematical Modeling with Differential Equations -- 9.1. First-Order Differential Equations and Applications -- 9.2. Direction Fields; Euler's Method -- 9.3. Modeling with First-Order Differential Equations -- 9.4. Second-Order Linear Homogeneous Differential Equations; The Vibrating Spring -- Chapter 10. Infinite Series -- 10.1. Maclaurin and Taylor Polynomial Approximations -- 10.2. Sequences -- 10.3. Monotone Sequences -- 10.4. Infinite Series -- 10.5. Convergence Tests -- 10.6. The Comparison, Ratio, and Root Tests -- 10.7. Alternating Series; Conditional Convergence -- 10.8. Maclaurin and Taylor Series; Power Series -- 10.9. Convergence of Taylor Series; Computational Methods -- 10.10. Differentiating and Integrating Power Series; Modeling with Taylor Series -- Chapter 11. Analytic Geometry in Calculus -- 11.1. Polar Coordinates -- 11.2. Tangent Lines and Arc Length for Parametric and Polar Curves -- 11.3. Area in Polar Coordinates -- 11.4. Conic Sections in Calculus -- 11.5. Rotation of Axes; Second-Degree Equations -- 11.6. Conic Sections in Polar Coordinates -- Horizon Module: Comet Collision -- Appendix A. Real Numbers, Intervals, and Inequalities -- Appendix B. Absolute Value -- Appendix C. Coordinate Planes and Lines -- Appendix D. Distance, Circles, and Quadratic Equations -- Appendix E. Trigonometry Review -- Appendix F. Solving Polynomial Equations -- Appendix G. Selected Proofs.

First year undergraduate calculus courses. The difference between Early Transcendentals (ET) and Late Transcendentals (LT) is the placement of logs and exponentials (aka trancendentals) in the table of contents and therefore where those topics are covered in the course------either early or late.