Solutions Manual for Calculus A Complete Course 9th Edition by Robert Adams ISBN 0134154363 9780134154367

Solutions Manual for Calculus: A Complete Course 9th Edition by Robert Adams – Ebook PDF Instant Download/Delivery: 0134154363, 978-0134154367

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Product details:

ISBN 10: 0134154363

ISBN 13: 978-0134154367

Author:  Robert Adams 

Calculus: A Complete Course 9th Edition: 

Proven in North America and abroad, this classic text has earned a reputation for excellent accuracy and mathematical rigour. Previous editions have been praised for providing complete and precise statements of theorems, using geometric reasoning in applied problems, and for offering a range of applications across the sciences. Written in a clear, coherent, and readable form, Calculus: A Complete Course makes student comprehension a clear priority.

KEY TOPICS:

Limits and Continuity; Differentiation; Transcendental Functions; More Applications of Differentiation; Integration; Techniques of Integration; Applications of Integration; Conics, Parametric Curves, and Polar Curves; Sequence, Series, and Power Series; Vectors and Coordinate Geometry in 3-Space; Vector Functions and Curves; Partial Differentiation; Applications of Partial Derivatives; Multiple Integration; Vector Fields; Vector Calculus; Differential forms and Exterior Calculus; Ordinary Differential Equations

MARKET:

Appropriate for the three-semester calculus course.

 

Calculus: A Complete Course 9th Edition Table of contents:

1. Limits and Continuity

1.1. Examples of Velocity, Growth Rate, and Area

• Average Velocity and Instantaneous Velocity

• The Growth of an Algal Culture

• The Area of a Circle

1.2. Limits of Functions

• One-Sided Limits

• Rules for Calculating Limits

• The Squeeze Theorem

1.3. Limits at Infinity and Infinite Limits

• Limits at Infinity

• Limits at Infinity for Rational Functions

• Infinite Limits

• Using Maple to Calculate Limits

1.4. Continuity

• Continuity at a Point

• Continuity on an Interval

• Continuous Functions on Closed, Finite Intervals

1.5. The Formal Definition of Limit

• Using the Definition of Limit to Prove Theorems

• Other Kinds of Limits

2. Differentiation

2.1. Tangent Lines and Their Slopes

• Normals

2.2. The Derivative

• Some Important Derivatives

• Leibniz Notation

• Differentials

2.3. Differentiation Rules

• Sums and Constant Multiples

• The Product Rule

• The Reciprocal Rule

• The Quotient Rule

2.4. The Chain Rule

• Finding Derivatives with Maple

• Building the Chain Rule into Differentiation Formulas

• Proof of the Chain Rule (Theorem 6)

2.5. Derivatives of Trigonometric Functions

• Some Special Limits

• The Derivatives of Sine and Cosine

• The Derivatives of the Other Trigonometric Functions

2.6. Higher-Order Derivatives

2.7. Using Differentials and Derivatives

• Approximating Small Changes

• Average and Instantaneous Rates of Change

2.8. The Mean-Value Theorem

• Increasing and Decreasing Functions

2.9. Implicit Differentiation

• Higher-Order Derivatives

• The General Power Rule

2.10. Antiderivatives and Initial-Value Problems

• Antiderivatives

• The Indefinite Integral

• Differential Equations and Initial-Value Problems

2.11. Velocity and Acceleration

• Velocity and Speed

• Acceleration

• Falling Under Gravity

3. Transcendental Functions

3.1. Inverse Functions

• Inverting Non–One-to-One Functions

• Derivatives of Inverse Functions

3.2. Exponential and Logarithmic Functions

• Exponentials

• Logarithms

3.3. The Natural Logarithm and Exponential

• The Natural Logarithm

• The Exponential Function

3.4. Growth and Decay

• Exponential Growth and Decay Models

• Interest on Investments

• Logistic Growth

3.5. The Inverse Trigonometric Functions

• The Inverse Sine (or Arcsine) Function

• The Inverse Tangent (or Arctangent) Function

3.6. Hyperbolic Functions

• Inverse Hyperbolic Functions

3.7. Second-Order Linear DEs with Constant Coefficients

• Recipe for Solving ay” + by’ + cy = 0

• Simple Harmonic Motion

• Damped Harmonic Motion

4. More Applications of Differentiation

4.1. Related Rates

• Procedures for Related-Rates Problems

4.2. Finding Roots of Equations

• Discrete Maps and Fixed-Point Iteration

• Newton’s Method

4.3. Indeterminate Forms

• L’Hopital’s Rule

4.4. Extreme Values

• Maximum and Minimum Values

• Critical Points, Singular Points, and Endpoints

4.5. Concavity and Inflections

• The Second Derivative Test

4.6. Sketching the Graph of a Function

• Asymptotes

4.7. Graphing with Computers

• Numerical Monsters and Computer Graphing

4.8. Extreme-Value Problems

• Procedure for Solving Extreme-Value Problems

4.9. Linear Approximations

• Approximating Values of Functions

• Error Analysis

4.10. Taylor Polynomials

• Taylor’s Formula

• Big-O Notation

4.11. Roundoff Error, Truncation Error, and Computers

• Taylor Polynomials in Maple

5. Integration

5.1. Sums and Sigma Notation

• Evaluating Sums

5.2. Areas as Limits of Sums

• The Basic Area Problem

• Some Area Calculations

5.3. The Definite Integral

• Partitions and Riemann Sums

• The Definite Integral

5.4. Properties of the Definite Integral

• A Mean-Value Theorem for Integrals

5.5. The Fundamental Theorem of Calculus

5.6. The Method of Substitution

• Trigonometric Integrals

5.7. Areas of Plane Regions

• Areas Between Two Curves

6. Techniques of Integration

6.1. Integration by Parts

• Reduction Formulas

6.2. Integrals of Rational Functions

• Linear and Quadratic Denominators

• Partial Fractions

6.3. Inverse Substitutions

• The Inverse Trigonometric Substitutions

6.4. Other Methods for Evaluating Integrals

• The Method of Undetermined Coefficients

6.5. Improper Integrals

• Improper Integrals of Type I

• Improper Integrals of Type II

6.6. The Trapezoid and Midpoint Rules

• The Trapezoid Rule

• The Midpoint Rule

6.7. Simpson’s Rule

7. Applications of Integration

7.1. Volumes by Slicing—Solids of Revolution

• Volumes by Slicing

• Solids of Revolution

7.2. More Volumes by Slicing

7.3. Arc Length and Surface Area

• Arc Length

• The Arc Length of the Graph of a Function

• Areas of Surfaces of Revolution

7.4. Mass, Moments, and Centre of Mass

• Mass and Density

• Moments and Centres of Mass

7.5. Centroids

• Pappus’s Theorem

7.6. Other Physical Applications

• Hydrostatic Pressure

• Work

• Potential Energy and Kinetic Energy

7.7. Applications in Business, Finance, and Ecology

• The Present Value of a Stream of Payments

• The Economics of Exploiting Renewable Resources

7.8. Probability

• Discrete Random Variables

• Expectation, Mean, Variance, and Standard Deviation

7.9. First-Order Differential Equations

• Separable Equations

• First-Order Linear Equations

 

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