1. Basics -- 1.0. Introductory remarks -- 1.1. Number systems -- 1.2. Coordinates in one dimension -- 1.3. Coordinates in two dimensions -- 1.4. The slope of a line in the plane -- 1.5. The equation of a line -- 1.6. Loci in the plane -- 1.7. Trigonometry -- 1.8. Sets and functions -- 1.8.1. Examples of functions of a real variable -- 1.8.2. Graphs of functions -- 1.8.3. Plotting the graph of a function -- 1.8.4. Composition of functions -- 1.8.5. The inverse of a function -- 1.9. A few words about logarithms and exponentials -- 2. Foundations of calculus -- 2.1. Limits -- 2.1.1. One-sided limits -- 2.2. Properties of limits -- 2.3. Continuity -- 2.4. The derivative -- 2.5. Rules for calculating derivatives -- 2.5.1. The derivative of an inverse -- 2.6. The derivative as a rate of change -- 3. Applications of the derivative -- 3.1. Graphing of functions -- 3.2. Maximum/minimum problems -- 3.3. Related rates -- 3.4. Falling bodies -- 4. The integral -- 4.0. Introduction -- 4.1. Antiderivatives and indefinite integrals -- 4.1.1. The concept of antiderivative -- 4.1.2. The indefinite integral -- 4.2. Area -- 4.3. Signed area -- 4.4. The area between two curves -- 4.5. Rules of integration -- 4.5.1. Linear properties -- 4.5.2. Additivity -- 5. Indeterminate forms -- 5.1. l'Hôpital's rule -- 5.1.1. Introduction -- 5.1.2. l'Hôpital's rule -- 5.2. Other indeterminate forms -- 5.2.1. Introduction -- 5.2.2. Writing a product as a quotient -- 5.2.3. The use of the logarithm -- 5.2.4. Putting terms over a common denominator -- 5.2.5. Other algebraic manipulations -- 5.3. Improper integrals : a first look -- 5.3.1. Introduction -- 5.3.2. Integrals with infinite integrands -- 5.3.3. An application to area -- 5.4. More on improper integrals -- 5.4.1. Introduction -- 5.4.2. The integral on an infinite interval -- 5.4.3. Some applications --