Calculus & Its Applications, Global Edition

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Table of Contents

Calculus & Its Applications builds intuition with key concepts of calculus before the analytical material. For example, the authors explain the derivative geometrically before they present limits, and they introduce the definite integral intuitively via the notion of net change before they discuss Riemann sums.

The strategic organisation of topics makes it easy to adjust the level of theoretical material covered. The significant applications introduced early in the course serve to motivate students and make the mathematics more accessible. Another unique aspect of the text is its intuitive use of differential equations to model a variety of phenomena in Chapter 5, which addresses applications of exponential and logarithmic functions.

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0. Functions
0.1 Functions and Their Graphs
0.2 Some Important Functions
0.3 The Algebra of Functions
0.4 Zeros of Functions - The Quadratic Formula and Factoring
0.5 Exponents and Power Functions
0.6 Functions and Graphs in Applications
1. The Derivative
1.1 The Slope of a Straight Line
1.2 The Slope of a Curve at a Point
1.3 The Derivative and Limits
1.4 Limits and the Derivative
1.5 Differentiability and Continuity
1.6 Some Rules for Differentiation
1.7 More About Derivatives
1.8 The Derivative as a Rate of Change
2. Applications of the Derivative
2.1 Describing Graphs of Functions
2.2 The First and Second Derivative Rules
2.3 The First and Section Derivative Tests and Curve Sketching
2.4 Curve Sketching (Conclusion)
2.5 Optimization Problems
2.6 Further Optimization Problems
2.7 Applications of Derivatives to Business and Economics
3. Techniques of Differentiation
3.1 The Product and Quotient Rules
3.2 The Chain Rule
3.3 Implicit Differentiation and Related Rates
4. The Exponential and Natural Logarithm Functions
4.1 Exponential Functions
4.2 The Exponential Function ex
4.3 Differentiation of Exponential Functions
4.4 The Natural Logarithm Function
4.5 The Derivative of ln x 4.6 Properties of the Natural Logarithm Function
5. Applications of the Exponential and Natural Logarithm Functions
5.1 Exponential Growth and Decay
5.2 Compound Interest
5.3. Applications of the Natural Logarithm Function to Economics
5.4. Further Exponential Models
6. The Definite Integral
6.1 Anti-differentiation
6.2 The Definite Integral and Net Change of a Function
6.3 The Definite Integral and Area Under a Graph
6.4 Areas in the xy-Plane
6.5 Applications of the Definite Integral
7. Functions of Several Variables
7.1 Examples of Functions of Several Variables
7.2 Partial Derivatives
7.3 Maxima and Minima of Functions of Several Variables
7.4 Lagrange Multipliers and Constrained Optimization
7.5 The Method of Least Squares
7.6 Double Integrals
8. The Trigonometric Functions
8.1 Radian Measure of Angles
8.2 The Sine and the Cosine
8.3 Differentiation and Integration of sin t and cos t
8.4 The Tangent and Other Trigonometric Functions
9. Techniques of Integration
9.1 Integration by Substitution
9.2 Integration by Parts
9.3 Evaluation of Definite Integrals
9.4 Approximation of Definite Integrals
9.5 Some Applications of the Integral
9.6 Improper Integrals
10. Differential Equations
10.1 Solutions of Differential Equations
10.2 Separation of Variables
10.3 First-Order Linear Differential Equations
10.4 Applications of First-Order Linear Differential Equations
10.5 Graphing Solutions of Differential Equations
10.6 Applications of Differential Equations
10.7 Numerical Solution of Differential Equations