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THÔNG TIN TÀI LIỆU
Cấu trúc
Contents
Preface
To the Student
Diagnostic Tests
Ch 1: Functions and Limits
1.1 Functions and Their Representations
1.1 Exercises
1.2 A Catalog of Essential Functions
1.2 Exercises
1.3 The Limit of a Function
1.3 Exercises
1.4 Calculating Limits
1.4 Exercises
1.5 Continuity
1.5 Exercises
1.6 Limits Involving Infinity
1.6 Exercises
Chapter 1: Review
Ch 2: Derivatives
2.1 Derivatives and Rates of Change
2.1 Exercises
2.2 The Derivative as a Function
2.2 Exercises
2.3 Basic Differentiation Formulas
2.3 Exercises
2.4 The Product and Quotient Rules
2.4 Exercises
2.5 The Chain Rule
2.5 Exercises
2.6 Implicit Differentiation
2.6 Exercises
2.7 Related Rates
2.7 Exercises
2.8 Linear Approximations and Differentials
2.8 Exercises
Chapter 2: Review
Ch 3: Applications of Differentiation
3.1 Maximum and Minimum Values
3.1 Exercises
3.2 The Mean Value Theorem
3.2 Exercises
3.3 Derivatives and the Shapes of Graphs
3.3 Exercises
3.4 Curve Sketching
3.4 Exercises
3.5 Optimization Problems
3.5 Exercises
3.6 Newton's Method
3.6 Exercises
3.7 Antiderivatives
3.7 Exercises
Chapter 3: Review
Ch 4: Integrals
4.1 Areas and Distances
4.1 Exercises
4.2 The Definite Integral
4.2 Exercises
4.3 Evaluating Definite Integrals
4.3 Exercises
4.4 The Fundamental Theorem of Calculus
4.4 Exercises
4.5 The Substitution Rule
4.5 Exercises
Chapter 4: Review
Ch 5: Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions
5.1 Inverse Functions
5.1 Exercises
5.2 The Natural Logarithmic Function
5.2 Exercises
5.3 The Natural Exponential Function
5.3 Exercises
5.4 General Logarithmic and Exponential Functions
5.4 Exercises
5.5 Exponential Growth and Decay
5.5 Exercises
5.6 Inverse Trigonometric Functions
5.6 Exercises
5.7 Hyperbolic Functions
5.7 Exercises
5.8 Indeterminate Forms and L'Hospital's Rule
5.8 Exercises
Chapter 5: Review
Ch 6: Techniques of Integration
6.1 Integration by Parts
6.1 Exercises
6.2 Trigonometric Integrals and Substitutions
6.2 Exercises
6.3 Partial Fractions
6.3 Exercises
6.4 Integration with Tables and Computer Algebra Systems
6.4 Exercises
6.5 Approximate Integration
6.5 Exercises
6.6 Improper Integrals
6.6 Exercises
Chapter 6: Review
Ch 7: Applications of Integration
7.1 Areas between Curves
7.1 Exercises
7.2 Volumes
7.2 Exercises
7.3 Volumes by Cylindrical Shells
7.3 Exercises
7.4 Arc Length
7.4 Exercises
7.5 Area of a Surface of Revolution
7.5 Exercises
7.6 Applications to Physics and Engineering
7.6 Exercises
7.7 Differential Equations
7.7 Exercises
Chapter 7: Review
Ch 8: Series
8.1 Sequences
8.1 Exercises
8.2 Series
8.2 Exercises
8.3 The Integral and Comparison Tests
8.3 Exercises
8.4 Other Convergence Tests
8.4 Exercises
8.5 Power Series
8.5 Exercises
8.6 Representing Functions as Power Series
8.6 Exercises
8.7 Taylor and Maclaurin Series
8.7 Exercises
8.8 Applications of Taylor Polynomials
8.8 Exercises
Chapter 8: Review
Ch 9: Parametric Equations and Polar Coordinates
9.1 Parametric Curves
9.1 Exercises
9.2 Calculus with Parametric Curves
9.2 Exercises
9.3 Polar Coordinates
9.3 Exercises
9.4 Areas and Lengths in Polar Coordinates
9.4 Exercises
9.5 Conic Sections in Polar Coordinates
9.5 Exercises
Chapter 9: Review
Ch 10: Vectors and the Geometry of Space
10.1 Three-Dimensional Coordinate Systems
10.1 Exercises
10.2 Vectors
10.2 Exercises
10.3 The Dot Product
10.3 Exercises
10.4 The Cross Product
10.4 Exercises
10.5 Equations of Lines and Planes
10.5 Exercises
10.6 Cylinders and Quadric Surfaces
10.6 Exercises
10.7 Vector Functions and Space Curves
10.7 Exercises
10.8 Arc Length and Curvature
10.8 Exercises
10.9 Motion in Space: Velocity and Acceleration
10.9 Exercises
Chapter 10: Review
Ch 11: Partial Derivatives
11.1 Functions of Several Variables
11.1 Exercises
11.2 Limits and Continuity
11.2 Exercises
11.3 Partial Derivatives
11.3 Exercises
11.4 Tangent Planes and Linear Approximations
11.4 Exercises
11.5 The Chain Rule
11.5 Exercises
11.6 Directional Derivatives and the Gradient Vector
11.6 Exercises
11.7 Maximum and Minimum Values
11.7 Exercises
11.8 Lagrange Multipliers
11.8 Exercises
Chapter 11: Review
Ch 12: Multiple Integrals
12.1 Double Integrals over Rectangles
12.1 Exercises
12.2 Double Integrals over General Regions
12.2 Exercises
12.3 Double Integrals in Polar Coordinates
12.3 Exercises
12.4 Applications of Double Integrals
12.4 Exercises
12.5 Triple Integrals
12.5 Exercises
12.6 Triple Integrals in Cylindrical Coordinates
12.6 Exercises
12.7 Triple Integrals in Spherical Coordinates
12.7 Exercises
12.8 Change of Variables in Multiple Integrals
12.8 Exercises
Chapter 12: Review
Ch 13: Vector Calculus
13.1 Vector Fields
13.1 Exercises
13.2 Line Integrals
13.2 Exercises
13.3 The Fundamental Theorem for Line Integrals
13.3 Exercises
13.4 Green's Theorem
13.4 Exercises
13.5 Curl and Divergence
13.5 Exercises
13.6 Parametric Surfaces and Their Areas
13.6 Exercises
13.7 Surface Integrals
13.7 Exercises
13.8 Stokes' Theorem
13.8 Exercises
13.9 The Divergence Theorem
13.9 Exercises
Chapter 13: Review
Appendixes
Appendix A: Trigonometry
Appendix B: Sigma Notation
Appendix C: Proofs
Appendix D: Answers to Odd-Numbered Exercises
Index
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