This is an expanded version of Calculus and its Applications, Tenth Edition, by Bittinger, Ellenbogen, and Surgent. This edition adds coverage of trigonometric functions, differential equations, sequences and series, probability distributions, and matrices.
Calculus and Its Applications has become a best-selling text because of its accessible presentation that anticipates your needs. The writing style provides intuitive explanations that build on earlier mathematical experiences. Explanations are often coupled with figures to help you visualize new calculus concepts. Additionally, the text’s numerous and up-to-date applications from business, economics, life sciences, and social sciences help motivate you. Algebra diagnostic and review material is available for those who need to strengthen basic skills. Every aspect of this text is designed to motivate and help you to more readily understand and apply the mathematics.
Table of Contents
R. Functions, Graphs, and Models
R.1 Graphs and Equations
R.2 Functions and Models
R.3 Finding Domain and Range
R.4 Slope and Linear Functions
R.5 Nonlinear Functions and Models
R.6 Mathematical Modeling and Curve Fitting
1.1 Limits: A Numerical and Graphical Approach
1.2 Algebraic Limits and Continuity
1.3 Average Rates of Change
1.4 Differentiation Using Limits of Difference Quotients
1.5 Differentiation Techniques: The Power and Sum-Difference Rules
1.6 Differentiation Techniques: The Product and Quotient Rules
1.7 The Chain Rule
1.8 Higher-Order Derivatives
2. Applications of Differentiation
2.1 Using First Derivatives to Find Maximum and Minimum Values and Sketch Graphs
2.2 Using Second Derivatives to Find Maximum and Minimum Values and Sketch Graphs
2.3 Graph Sketching: Asymptotes and Rational Functions
2.4 Using Derivatives to Find Absolute Maximum and Minimum Values
2.5 Maximum-Minimum Problems; Business and Economic Applications
2.6 Marginals and Differentials
2.7 Implicit Differentiation and Related Rates
3. Exponential and Logarithmic Functions
3.1 Exponential Functions
3.2 Logarithmic Functions
3.3 Applications: Uninhibited and Limited Growth Models
3.4 Applications: Decay
3.5 The Derivatives of ax and loga x
3.6 An Economics Application: Elasticity of Demand
4.2 Antiderivatives as Areas
4.3 Area and Definite Integrals
4.4 Properties of Definite Integrals
4.5 Integration Techniques: Substitution
4.6 Integration Techniques: Integration by Parts
4.7 Integration Techniques: Tables
5. Applications of Integration
5.1 An Economics Application: Consumer Surplus and Producer Surplus
5.2 Applications of Integrating Growth and Decay Models
5.3 Improper Integrals
5.4 Numerical Integration
6. Functions of Several Variables
6.1 Functions of Several Variables
6.2 Partial Derivatives
6.3 Maximum-Minimum Problems
6.4: An Application: The Least-Squares Technique
6.5 Constrained Optimization
6.6 Double Integrals
7. Trigonometric Functions
7.1 Basics of Trigonometry
7.2 Derivatives of Trigonometric Functions
7.3 Integration of Trigonometric Functions
7.4 Inverse Trigonometric Functions and Applications
8. Differential Equations
8.1 Differential Equations
8.2 Separable Differential Equations
8.3 Applications: Inhibited Growth Models
8.4 First-Order Linear Differential Equations
8.5 Higher-Order Differential Equations and a Trigonometry Connection
9. Sequences and Series
9.1 Arithmetic Sequences and Series
9.2 Geometric Sequences and Series
9.3 Simple and Compound Interest
9.4 Annuities and Amortization
9.5 Power Series and Linearization
9.6 Taylor Series and a Trigonometry Connection
10. Probability Distributions
10.1 A Review of Sets
10.3 Discrete Probability Distributions
10.4 Continuous Probability Distributions
10.5 Mean, Variance, Standard Deviation, and the Normal Distribution
11. Systems and Matrices (online)
11.1 Systems of Linear Equations
11.2 Gauss-Jordan Elimination
11.3 Matrices and Row Operations
11.4 Matrix Arithmetic: Equality, Addition and Scalar Multiples
11.5 Matrix Multiplication, Multiplicative Identities and Inverses
11.6 Determinants and Cramer’s Rule
11.7 Systems of Linear Inequalities and Linear Programming
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