ch. 1. What it's all about -- 1.1. Introduction -- 1.2. Functions -- 1.3. Calculus : one basic idea -- 1.4. Conceptual development -- 1.5. About this book -- ch. 2. The derivative -- 2.1. Motivation -- 2.1.1. Slopes and tangent lines -- 2.1.2. Finding the instantaneous velocity -- 2.2. Definition of the derivative -- 2.3. Notation for the derivative -- 2.4. Calculating derivatives -- 2.5. Applications of the derivative -- Solved problems -- ch. 3. Applications of the derivative -- 3.1. Newton's method -- 3.1.1. Introduction --- 3.1.2. The method -- 3.2. Linear approximation and Taylor polynomials -- Solved problems -- ch. 4. The integral -- 4.1. Motivation -- 4.1.1. Velocity and distance -- 4.1.2. Work -- 4.1.3. Area -- 4.2. Definition of the integral -- 4.3. Notion for the integral -- 4.3.1. Riemann sums -- 4.4. Computational techniques -- 4.5. Applications of the integral -- Solved problems -- ch. 5. Applications of the integral -- 5.1. Arc length -- 5.2. Volume of a solid of revolution -- Solved problems -- ch. 6. Topics in integration -- 6.1. Improper integrals -- 6.2. Numerical integration -- 6.2.1. Trapezoidal rule -- 6.2.2. Simpson's rule -- Solved problems -- ch. 7. Infinite series -- 7.1. Motivation -- 7.2. Definition -- 7.3. Notation -- 7.4. Computational techniques -- 7.5. Applications of series -- Solved problems -- Index.