Machine generated contents note: 1.Quadratic Equations -- 1.1.Quadratic Equations -- 1.2.Further Consequences -- 1.3.Exercises -- 2.Diagrams -- 2.1.Graphs -- 2.2.Exercises -- 3.Functions -- 3.1.Functions -- 3.2.Generating New Functions -- 3.3.Exercises -- 4.Inverse Functions -- 4.1.Injective and Surjective Functions -- 4.2.Bijective Functions and Inverses -- 4.3.Increasing, Decreasing, Convex and Indicator Functions -- 4.4.Exercises -- 5.Numbers -- 5.1.The Positive Integers -- 5.2.The Integers and Rational Numbers -- 5.3.Arithmetic and Geometry -- 5.4.Exercises -- 6.Sets Of Real Numbers -- 6.1.Countable Sets -- 6.2.Uncountable Sets -- 6.3.Sets Which Are Bounded Above -- 6.4.Intervals -- 6.5.Exercises -- 7.Series With Positive Entries -- 7.1.Increasing and Decreasing Sequences -- 7.2.Series with Positive Entries -- 7.3.The Exponential Function -- 7.4.Multiplication of Series -- 7.5.The Log Function -- 7.6.Exercises -- 8.Review And Transition -- 8.1.Review and Preview --

Contents note continued: 8.2.Convergent Sequences -- 8.3.Convergent Series -- 8.4.Power Series -- 8.5.Exercises -- 9.Continuous Functions -- 9.1.Continuous Functions -- 9.2.Intermediate Value Theorem -- 9.3.Fundamental Existence Theorem for Maxima and Minima -- 9.4.Exercises -- 10.Differentiable Functions -- 10.1.Differentiable Functions -- 10.2.Basic Functions and Rules for Differentiation -- 10.3.Mean Value Theorem -- 10.4.Exercises -- 11.Applications Of Differentiation -- 11.1.Sequences -- 11.2.Limits -- 11.3.Curve Sketching -- 11.4.Applications of the Mean Value Theorem -- 11.5.In Retrospect -- 11.6.Exercises -- 12.The Real Numbers -- 12.1.Upper Bounds -- 12.2.Dyadic Sections and the Bisection Principle -- 12.3.Foundational Developments -- 12.4.Infinitesimals -- 12.5.Exercises -- 13.Integration Theory -- 13.1.The Riemann Integral -- 13.2.Fundamental Theorem of Calculus -- 13.3.Methods of Integration -- 13.4.Exercises -- 14.Applications Of Integration Theory --

Contents note continued: 14.1.Integral Inequalities -- 14.2.Integrals over Infinite Intervals -- 14.3.Taylor's Theorem -- 14.4.Exercises.