Chapter 1 - Functions and Models Section 1.1 - Four Ways to Represent a Function Section 1.2 - Mathematical Models Section 1.3 - New Functions from Old Functions Section 1.4 - Graphing Calculators and Computers Return to Top Chapter 2 - Limits and Rates of Change Section 2.1 - The Tangent and Velocity Problems Section 2.2 - The Limit of a Function Section 2.3 - Calculating Limits Using the Limit Laws Section 2.5 - Continuity Section 2.6 - Tangents, Velocities, and Other Rates of Change Return to Top Chapter 3 - Derivatives Section 3.1 - Derivatives Section 3.2 - The Derivative as a Function Section 3.3 - Differentiation Formulas Section 3.4 - Rates of Change in the Natural and Social Sciences Section 3.5 - Derivatives of Trigonometric Functions Section 3.6 - The Chain Rule Section 3.7 - Implicit Differentiation Section 3.8 - Higher Derivatives Section 3.9 - Related Rates Section 3.10 - Linear Approximations and Differentials Return to Top Chapter 4 - Applications of Differentiation Section 4.1 - Maximum and Minimum Values Section 4.2 - The Mean Value Theorem Section 4.3 - How Derivatives Affect the Shape of a Graph Section 4.4 - Limits at Infinity; Horizontal Asymptotes Section 4.5 - Summary of Curve Sketching Section 4.6 - Graphing with Calculus and Calculators Section 4.7 - Optimization Problems Section 4.8 - Applications to Economics Section 4.9 - Newton's Method Section 4.10 - Antiderivatives Return to Top Chapter 5 - Integrals Section 5.1 - Areas and Distances Section 5.2 - The Definite Integral Section 5.3 - The Fundamental Theorem of Calculus Section 5.4 - Indefinite Integrals and the Total Change Theorem Section 5.5 - The Substitution Rule Bonus Problems! Return to Top Chapter 6 - Applications of Integration Section 6.1 - Areas between Curves Section 6.2 - Volumes Bonus! (not really 6.3) Section 6.4 - Work Section 6.5 - Average Value of a Function Return to Top Chapter 7 - Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions Section 7.1 - Inverse Functions Section 7.2 - Exponential Functions and Their Derivatives Section 7.3 - Logarithmic Functions Section 7.2* - The Natural Logarithmic Function Section 7.3* - The Natural Exponential Function Section 7.4 - Derivatives of Logarithmic Functions Section 7.4* - General Logarithmic and Exponential Functions Section 7.5 - Inverse Trigonometric Functions Section 7.7 - Indeterminate Forms and L'Hospital's Rule Return to Top Chapter 8 - Techniques of Integration Section 8.1 - Integration by Parts Section 8.2 - Trigonometric Integrals Section 8.4 - Integration of Rational Functions by Partial Fractions Section 8.6 - Integration Using Tables and Computer Algebra Systems Section 8.7 - Approximate Integration Section 8.8 - Improper Integrals Return to Top Chapter 9 - Further Applications of Integration Section 9.1 - Arc Length Section 9.3 - Applications to Physics and Engineering Section 9.4 - Applications to Economics and Biology Section 9.5 - Probability Return to Top Chapter 10 - Differential Equations Section 10.1 - Modeling with Differential Equations Section 10.2 - Direction Fields and Euler's Method Section 10.3 - Separable Equations Section 10.4 - Exponential Growth and Decay Section 10.5 - The Logistic Function Section 10.7 - Predator-Prey Systems Return to Top Chapter 11 - Parametric Equations and Polar Coordinates Section 11.1 - Curves Defined by Parametric Equations Section 11.2 - Tangents and Areas Section 11.3 - Arc Length and Surface Area Section 11.4 - Polar Coordinates Return to Top Chapter 12 - Infinite Sequences and Series Section 12.1 - Sequences Section 12.2 - Series Section 12.3 - The Integral Test and Estimates of Sums Section 12.4 - The Comparison Tests Section 12.5 - Alternating Series Section 12.6 - Absolute Convergence and the Ratio and Root Tests Section 12.8 - Power Series Section 12.9 - Representations of Functions as Power Series Section 12.10 - Taylor and Maclaurin Series Section 12.11 - The Binomial Series Section 12.12 - Applications of Taylor Polynomials Return to Top Chapter 18 - Second-Order Differential Equations Section 18.4 - Series Solutions Return to Top