Essential Calculus with Applications

To the Instructor; To the Student Chapter 1. Mathematical Background 1.1 Introductory Remarks 1.2 Sets 1.3 Numbers 1.4 Inequalities 1.5 The Absolute Value 1.6 Intervals and Neighborhoods 1.7 Rectangular Coordinates 1.8 Straight Lines 1.9 More about Straight Lines Chapter 2. Differential Calculus 2.1 Functions 2.2 More about Functions 2.3 Graphs 2.4 Derivatives and Limits 2.5 More about Derivatives 2.6 More about Limits 2.7 Differentiation Technique 2.8 Further Differentiation Technique 2.9 Other Kinds of Limits Chapter 3. Differentiation as a Tool 3.1 Velocity and Acceleration 3.2 Related Rates and Business Applications 3.3 Properties of Continuous Functions 3.4 Properties of Differentiable Functions 3.5 Applications of the Mean Value Theorem 3.6 Local Extrema 3.7 Concavity and Inflection Points 3.8 Optimization Problems Chapter 4. Integral Calculus 4.1 The Definite Integral 4.2 Properties of Definite Integrals 4.3 The Logarithm 4.4 The Exponential 4.5 More about the Logarithm and Exponential 4.6 Integration Technique 4.7 Improper Integrals Chapter 5. Integration as a Tool 5.1 Elementary Differential Equations 5.2 Problems of Growth and Decay 5.3 Problems of Motion Chapter 6. Functions of Several Variables 6.1 From Two to n Dimensions 6.2 Limits and Differentiation 6.3 The Chain Rule 6.4 Extrema in n Dimensions Tables; Selected Hints and Answers; Supplementary Hints and Answers; Index