Elementary Calculus with Applications

Contents
1. Elementary Functions
1.1 Definition, Domain and Range of a Function
1.2 Algebra of Functions
1.3 Transformations of Graphs
1.4 Polynomial, Rational and Power Functions
1.5 Exponential Functions
1.6 Logarithmic Functions
2. Limits
2.1 The Limit of a Function at a Point
2.2 Properties of Limits
2.3 Limits at Infinity
2.4 Continuous Functions
2.4.1 The Intermediate Value Theorem
3. The Derivative and Rules of Differentiation
3.1 The Derivative
3.1.1 The rate of change of a function and the slope of its graph
3.2.1 The derivative as the slope of the tangent line
3.1.3 The derivative as a rate of change
3.2 Rules of Differentiation
3.2.1 Basic rules of differentiation
3.2.2 The Product and Quotient Rules
3.2.3 The Chain Rule
3.2.4 Implicit Differentiation
3.3 Higher Order Derivatives
4. Applications of the Derivative
4.1 Determining the Intervals Where a Function is Increasing or Decreasing
4.2 Marginal Concepts in Economics
4.3 Elasticity of Demand
4.4 Related Rates
4.5 Maximum and Minimum Rules
4.6 Applications of the Second Derivative
4.7 Curve Sketching
4.8 Some Optimization Problems
4.9 Exponential Models
4.9.1 Continuously Compounded Interest
4.9.2 Exponential Growth and Decay
4.9.3 Learning Curves
5. Functions of Several Variables
5.1 Examples of Functions of Two and Three Variables
5.2 Partial Derivatives
5.3 Maxima and Minima of Functions of Two Variables
5.4 Lagrange Multipliers. Constrained Optimization
6. Integration
6.1 Antiderivatives and the Rules of Integration
6.2 Integration by Substitution
6.3 The Definite Integral
6.4 The Fundamental Theorem of Calculus
6.5 Evaluating Definite Integrals
Answers to Exercises
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6