- ホーム
- > 洋書
- > 英文書
- > Science / Mathematics
Full Description
Calculus: Concepts & Computation achieves a clarity of style and presentation that provides a simple, yet rigorous, introduction to what are complicated and powerful concepts. It provides an "early transcendentals" version of calculus, with derivatives of trigonometric, exponential, and logarithmic functions covered early in the publication (Chapter 2).
The text and solutions manual package provides a predominant emphasis on traditional by hand computations and graphing while also employing Maple, a computer algebra system (or CAS), as an auxiliary tool. Maple provides a dynamical, visual illustration of the concepts, fostering a deeper understanding of these concepts. To make the transition to this publication virtually seamless for adopters, worksheets, a solutions manual, and lecture videos with views of the text material, examples being worked on, and animations and figures are provided.
Calculus: Concepts & Computation
Contains thoughtfully designed exercise sets, with exercises ranging from basic to hard, both computational and theoretical.
Can be bundled with a detailed and elaborate electronic solution manual for the odd-numbered exercises in Chapters 1-8. It contains most all of the steps in the progression toward the answer and many comments on the underlying algebra (and calculus). Our Solutions Manual is more detailed and elaborate than other solutions manuals that typically are seen or used.
Includes unique sections: An Alternative to Trig Substitutions, A New Class of Arc Length Problems, and An Overlooked Class of Solids of Revolution.
Contents
Chapter 1: Limits
1.1 Limits: An Informal View
1.2 Limit Tools: The Graphical Method
1.3 Limit Tools: The Numerical Method
1.4 Limit Tools: The Algebraic Method
1.5 Limit Laws
1.6 One-Sided Limits
1.7 Continuous Functions
1.8 Limits Involving Infinity
1.9 The Definition of a Limit
Chapter 2: Derivatives
2.1 The Tangent Line Problem
2.2 The Derivative Function
2.3 Derivatives of Power Functions
2.4 Velocity
2.5 Differentials and Higher Derivatives
2.6 The Product and Quotient Rules
2.7 Derivatives of Trig Functions
2.8 The Chain Rule
2.9 Derivatives of Exponential and Logarithmic Functions
2.10 Implicit Differentiation
2.11 Derivatives of Inverse Functions
2.12 Hyperbolic Functions
2.13 Related Rate
Chapter 3: Applications of Derivatives
3.1 Curve Sketching: 1st Derivatives
3.2 Curve Sketching: 2nd Derivatives
3.3 Maximum and Minimum Values
3.4 Optimization
3.5 The Mean Value Theorem
3.6 L' Hospital's Rule
3.7 Antiderivatives and Integrals
Chapter 4: Integrals
4.1 Areas and Sums
4.2 Riemann Sums
4.3 Definite Integrals
4.4 The Fundamental Theorem of Calculus
4.5 The Substitution Method
Chapter 5: Applications of Integrals
5.1 Areas of Planar Regions
5.2 Solids with Known Sectional Area
5.3 Solids of Revolutions-Disk Method
5.4 The Washer and Shell Methods
5.5 Lengths of Curves
5.6 Surface Area of Solids of Revolutions
5.7 Force and Work
5.8 Moments and Center of Mass
Chapter 6: Techniques of Integration
6.1 Integration by Parts
6.2 Trigonometric Integrals
6.3 Trigonometric Substitutions
6.4 Partial Fractions
6.5 Integrals via a Computer Algebra System
6.6 Improper Integrals
Chapter 7: Differential Equations
7.1 Introduction to Differential Equations
7.2 Separable DEs and Modeling
7.3 First-Order Linear DEs
Chapter 8: Sequences and Series
8.1 Sequences
8.2 Infinite Series
8.3 The nth Term and Integral Tests
8.4 The Comparison Tests
8.5 The Ratio and Root Tests
8.6 Absolute and Conditional Convergence
8.7 Power Series
8.8 Taylor and Maclaurin Series
8.9 Operations on Power Series
Chapter 9: Plane Curves and Polar Coordinates
9.1 Parametric Equations
9.2 Parametric Calculus - Derivatives
9.3 Parametric Calculus - Integrals
9.4 Polar Coordinates
9.5 Polar Coordinate Calculus
9.6 Conic Sections
Chapter 10: Vectors and Geometry
10.1 Three-Dimensional Coordinate Systems
10.2 Vectors
10.3 The Dot Product
10.4 The Cross Product
10.5 Lines and Planes in Space
10.6 Cylinders and Quadric Surfaces
Chapter 11: Partial Derivatives
11.1 Functions of Two or More Variables
11.2 Multivariable Limits and Continuity
11.3 Partial Derivatives
11.4 The Chain Rule
11.5 Directional Derivatives & Gradient
11.6 Tangent Planes
11.7 Local Extrema and Saddle Points
Chapter 12: Multiple Integrals
12.1 Double Integrals and Iterated Integrals
12.2 Double Integrals over General Regions
12.3 Double Integrals in Polar Coordinates
12.4 Applications of Double Integrals
12.5 Triple Integrals
12.6 Triple Integrals in Cylindrical and Spherical Coordinates
Answers to Odd Exercises
Index
