Table
of Contents:
1. PRELIMINARIES.
-
1.1 Precalculus Review I.
-
1.2 Precalculus Review II.
-
1.3 The Cartesian Coordinate System.
-
1.4 Straight Lines.
2. FUNCTIONS, LIMITS, AND THE DERIVATIVE.
-
2.1 Functions and Their Graphs.
-
2.2 The Algebra of Functions.
-
2.3 Functions and Mathematical Models.
-
2.4 Limits.
-
2.5 One-Sided Limits and Continuity.
-
2.6 The Derivative.
3. DIFFERENTIATION.
-
3.1 Basic Rules of Differentiation.
-
3.2 The Product and Quotient Rules.
-
3.3 The Chain Rule.
-
3.4 Marginal Functions in Economics.
-
3.5 Higher-Order Derivatives.
-
3.6 Implicit Differentiation and Related Rates.
-
3.7 Differentials.
4. APPLICATIONS OF THE DERIVATIVE.
5. EXPONENTIAL AND LOGARITHMIC FUNCTIONS.
-
5.1 Exponential Functions.
-
5.2 Logarithmic Functions.
-
5.3 Compound Interest.
-
5.4 Differentiation of Exponential Functions.
-
5.5 Differentiation of Logarithmic Functions.
-
5.6 Exponential Functions as Mathematical Models.
6. INTEGRATION.
-
6.1 Antiderivatives and the Rules of Integration.
-
6.2 Integration by Substitution.
-
6.3 Area and the Definite Integral.
-
6.4 The Fundamental Theorem of Calculus.
-
6.5 Evaluating Definite Integrals.
-
6.6 Area between Two Curves.
-
6.7 Applications of the Definite Integral to Business and Economics.
7. ADDITIONAL TOPICS IN INTEGRATION.
-
7.1 Integration by Parts.
-
7.2 Integration Using Tables of Integrals.
-
7.3 Numerical Integration.
-
7.4 Improper Integrals.
-
7.5 Volumes of Solids of Revolution.
8. CALCULUS OF SEVERAL VARIABLES.
-
8.1 Functions of Several Variables.
-
8.2 Partial Derivatives.
-
8.3 Maxima and Minima of Functions of Several Variables.
-
8.4 The Method of Least Squares.
-
8.5 Constrained Maxima and Minima and the Method of Lagrange Multipliers.
-
8.6 Total Differentials.
-
8.7 Double Integrals.
-
8.8 Applications of Double Integrals.
9. DIFFERENTIAL EQUATIONS.
-
9.1 Differential Equations.
-
9.2 Separation of Variables.
-
9.3 Applications of Separable Differential Equations.
-
9.4 Approximate Solutions of Differential Equations.
10. PROBABILITY AND CALCULUS.
-
10.1 Probability Distributions of Random Variables.
-
10.2 Expected Value and Standard Deviation.
-
10.3 Normal Distributions.
11. TAYLOR POLYNOMIALS AND INFINITE SERIES.
-
11.1 Taylor Polynomials.
-
11.2 Infinite Sequences.
-
11.3 Infinite Series.
-
11.4 Series with Positive Numbers.
-
11.5 Power Series and Taylor Series.
-
11.6 More on Taylor Series.
-
11.7 Newton's Method.
12. TRIGONOMETRIC FUNCTIONS.
-
12.1 Measurement of Angles.
-
12.2 The Trigonometric Functions.
-
12.3 Differentiation of Trigonometric Functions.
-
12.4 Integration of Trigonometric Functions
APPENDIX
本書其它內容…
| 
