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For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it.
All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.
The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.
Serves as a companion to any single-variable calculus textbook
Informal, entertaining, and not intimidating
Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures
More than 475 examples (ranging from easy to hard) provide step-by-step reasoning
Theorems and methods justified and connections made to actual practice
Difficult topics such as improper integrals and infinite series covered in detail
Tried and tested by students taking freshman calculus
All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.
The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.
Serves as a companion to any single-variable calculus textbook
Informal, entertaining, and not intimidating
Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures
More than 475 examples (ranging from easy to hard) provide step-by-step reasoning
Theorems and methods justified and connections made to actual practice
Difficult topics such as improper integrals and infinite series covered in detail
Tried and tested by students taking freshman calculus
For many students, calculus can be the most mystifying and frustrating course they will ever take. The Calculus Lifesaver provides students with the essential tools they need not only to learn calculus, but to excel at it.
All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.
The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.
Serves as a companion to any single-variable calculus textbook
Informal, entertaining, and not intimidating
Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures
More than 475 examples (ranging from easy to hard) provide step-by-step reasoning
Theorems and methods justified and connections made to actual practice
Difficult topics such as improper integrals and infinite series covered in detail
Tried and tested by students taking freshman calculus
All of the material in this user-friendly study guide has been proven to get results. The book arose from Adrian Banner's popular calculus review course at Princeton University, which he developed especially for students who are motivated to earn A's but get only average grades on exams. The complete course will be available for free on the Web in a series of videotaped lectures. This study guide works as a supplement to any single-variable calculus course or textbook. Coupled with a selection of exercises, the book can also be used as a textbook in its own right. The style is informal, non-intimidating, and even entertaining, without sacrificing comprehensiveness. The author elaborates standard course material with scores of detailed examples that treat the reader to an "inner monologue"--the train of thought students should be following in order to solve the problem--providing the necessary reasoning as well as the solution. The book's emphasis is on building problem-solving skills. Examples range from easy to difficult and illustrate the in-depth presentation of theory.
The Calculus Lifesaver combines ease of use and readability with the depth of content and mathematical rigor of the best calculus textbooks. It is an indispensable volume for any student seeking to master calculus.
Serves as a companion to any single-variable calculus textbook
Informal, entertaining, and not intimidating
Informative videos that follow the book--a full forty-eight hours of Banner's Princeton calculus-review course--is available at Adrian Banner lectures
More than 475 examples (ranging from easy to hard) provide step-by-step reasoning
Theorems and methods justified and connections made to actual practice
Difficult topics such as improper integrals and infinite series covered in detail
Tried and tested by students taking freshman calculus
Über den Autor
Adrian Banner
Inhaltsverzeichnis
- Welcome
- How to Use This Book to Study for an Exam
- Two all-purpose study tips
- Key sections for exam review (by topic)
- Acknowledgments
- 1 Functions, Graphs, and Lines
- 1.1 Functions
- 1.1.1 Interval notation
- 1.1.2 Finding the domain
- 1.1.3 Finding the range using the graph
- 1.1.4 The vertical line test
- 1.2 Inverse Functions
- 1.2.1 The horizontal line test
- 1.2.2 Finding the inverse
- 1.2.3 Restricting the domain
- 1.2.4 Inverses of inverse functions
- 1.3 Composition of Functions
- 1.4 Odd and Even Functions
- 1.5 Graphs of Linear Functions
- 1.6 Common Functions and Graphs
- 2 Review of Trigonometry
- 2.1 The Basics
- 2.2 Extending the Domain of Trig Functions
- 2.2.1 The ASTC method
- 2.2.2 Trig functions outside [0, 2π]
- 2.3 The Graphs of Trig Functions
- 2.4 Trig Identities
- 3 Introduction to Limits
- 3.1 Limits: The Basic Idea
- 3.2 Left-Hand and Right-Hand Limits
- 3.3 When the Limit Does Not Exist
- 3.4 Limits at ∞ and −∞
- 3.4.1 Large numbers and small numbers
- 3.5 Two Common Misconceptions about Asymptotes
- 3.6 The Sandwich Principle
- 3.7 Summary of Basic Types of Limits
- 4 How to Solve Limit Problems Involving Polynomials
- 4.1 Limits Involving Rational Functions as x → a
- 4.2 Limits Involving Square Roots as x → a
- 4.3 Limits Involving Rational Functions as x → ∞
- 4.3.1 Method and examples
- 4.4 Limits Involving Poly-type Functions as x → ∞
- 4.5 Limits Involving Rational Functions as x → −∞
- 4.6 Limits Involving Absolute Values
- 5 Continuity and Differentiability
- 5.1 Continuity
- 5.1.1 Continuity at a point
- 5.1.2 Continuity on an interval
- 5.1.3 Examples of continuous functions
- 5.1.4 The Intermediate Value Theorem
- 5.1.5 A harder IVT example
- 5.1.6 Maxima and minima of continuous functions
- 5.2 Differentiability
- 5.2.1 Average speed
- 5.2.2 Displacement and velocity
- 5.2.3 Instantaneous velocity
- 5.2.4 The graphical interpretation of velocity
- 5.2.5 Tangent lines
- 5.2.6 The derivative function
- 5.2.7 The derivative as a limiting ratio
- 5.2.8 The derivative of linear functions
- 5.2.9 Second and higher-order derivatives
- 5.2.10 When the derivative does not exist
- 5.2.11 Differentiability and continuity
- 6 How to Solve Differentiation Problems
- 6.1 Finding Derivatives Using the Definition
- 6.2 Finding Derivatives (the Nice Way)
- 6.2.1 Constant multiples of functions
- 6.2.2 Sums and differences of functions
- 6.2.3 Products of functions via the product rule
- 6.2.4 Quotients of functions via the quotient rule
- 6.2.5 Composition of functions via the chain rule
- 6.2.6 A nasty example
- 6.2.7 Justification of the product rule and the chain rule
- 6.3 Finding the Equation of a Tangent Line
- 6.4 Velocity and Acceleration
- 6.4.1 Constant negative acceleration
- 6.5 Limits Which Are Derivatives in Disguise
- 6.6 Derivatives of Piecewise-Defined Functions
- 6.7 Sketching Derivative Graphs Directly
- 7 Trig Limits and Derivatives
- 7.1 Limits Involving Trig Functions
- 7.1.1 The small case
- 7.1.2 Solving problems—the small case
- 7.1.3 The large case
- 7.1.4 The “other” case
- 7.1.5 Proof of an important limit
- 7.2 Derivatives Involving Trig Functions
- 7.2.1 Examples of differentiating trig functions
- 7.2.2 Simple harmonic motion
- 7.2.3 A curious function
- 8 Implicit Differentiation and Related Rates
- 8.1 Implicit Differentiation
- 8.1.1 Techniques and examples
- 8.1.2 Finding the second derivative implicitly
- 8.2 Related Rates
- 8.2.1 A simple example
- 8.2.2 A slightly harder example
- 8.2.3 A much harder example
- 8.2.4 A really hard example
- 9 Exponentials and Logarithms
- 9.1 The Basics
- 9.1.1 Review of exponentials
- 9.1.2 Review of logarithms
- 9.1.3 Logarithms, exponentials, and inverses
- 9.1.4 Log rules
- 9.2 Definition of e
- 9.2.1 A question about compound interest
- 9.2.2 The answer to our question
- 9.2.3 More about e and logs
- 9.3 Differentiation of Logs and Exponentials
- 9.3.1 Examples of differentiating exponentials and logs
- 9.4 How to Solve Limit Problems Involving Exponentials or Logs
- 9.4.1 Limits involving the definition of e
- 9.4.2 Behavior of exponentials near 0
- 9.4.3 Behavior of logarithms near 1
- 9.4.4 Behavior of exponentials near ∞ or −∞
- 9.4.5 Behavior of logs near ∞
- 9.4.6 Behavior of logs near 0
- 9.5 Logarithmic Differentiation
- 9.5.1 The derivative of xa
- 9.6 Exponential Growth and Decay
- 9.6.1 Exponential growth
- 9.6.2 Exponential decay
- 9.7 Hyperbolic Functions
- 10 Inverse Functions and Inverse Trig Functions
- 10.1 The Derivative and Inverse Functions
- 10.1.1 Using the derivative to show that an inverse exists
- 10.1.2 Derivatives and inverse functions: what can go wrong
- 10.1.3 Finding the derivative of an inverse function
- 10.1.4 A big example
- 10.2 Inverse Trig Functions
- 10.2.1 Inverse sine
- 10.2.2 Inverse cosine
- 10.2.3 Inverse tangent
- 10.2.4 Inverse secant
- 10.2.5 Inverse cosecant and inverse cotangent
- 10.2.6 Computing inverse trig functions
- 10.3 Inverse Hyperbolic Functions
- 10.3.1 The rest of the inverse hyperbolic functions
- 11 The Derivative and Graphs
- 11.1 Extrema of Functions
- 11.1.1 Global and local extrema
- 11.1.2 The Extreme Value Theorem
- 11.1.3 How to find global maxima and minima
- 11.2 Rolle’s Theorem
- 11.3 The Mean Value Theorem
- 11.3.1 Consequences of the Mean Value Theorem
- 11.4 The Second Derivative and Graphs
- 11.4.1 More about points of inflection
- 11.5 Classifying Points Where the Derivative Vanishes
- 11.5.1 Using the first derivative
- 11.5.2 Using the second derivative
- 12 Sketching Graphs
- 12.1 How to Construct a Table of Signs
- 12.1.1 Making a table of signs for the derivative
- 12.1.2 Making a table of signs for the second derivative
- 12.2 The Big Method
- 12.3 Examples
- 12.3.1 An example without using derivatives
- 12.3.2 The full method: example 1
- 12.3.3 The full method: example 2
- 12.3.4 The full method: example 3
- 12.3.5 The full method: example 4
- 13 Optimization and Linearization
- 13.1 Optimization
- 13.1.1 An easy optimization example
- 13.1.2 Optimization problems: the general method
- 13.1.3 An optimization example
- 13.1.4 Another optimization example
- 13.1.5 Using implicit differentiation in optimization
- 13.1.6 A difficult optimization example
- 13.2 Linearization
- 13.2.1 Linearization in general
- 13.2.2 The differential
- 13.2.3 Linearization summary and examples
- 13.2.4 The error in our approximation
- 13.3 Newton’s Method
- 14 L’Hôpital’s Rule and Overview of Limits
- 14.1 L’Hôpital’s Rule
- 14.1.1 Type A: 0/0 case
- 14.1.2 Type A: ±∞/±∞ case
- 14.1.3 Type B1 (∞ − ∞)
- 14.1.4 Type B2 (0 × ±∞)
- 14.1.5 Type C (1±∞ 00, or ∞0)
- 14.1.6 Summary of l’Hôpital’s Rule types
- 14.2 Overview of Limits
- 15 Introduction to Integration
- 15.1 Sigma Notation
- 15.1.1 A nice sum
- 15.1.2 Telescoping series
- 15.2 Displacement and Area
- 15.2.1 Three simple cases
- 15.2.2 A more general journey
- 15.2.3 Signed area
- 15.2.4 Continuous velocity
- 15.2.5 Two special approximations
- 16 Definite Integrals
- 16.1 The Basic Idea
- 16.1.1 Some easy examples
- 16.2 Definition of the Definite Integral
- 16.2.1 An example of using the definition
- 16.3 Properties of Definite Integrals
- 16.4 Finding Areas
- 16.4.1 Finding the unsigned area
- 16.4.2 Finding the area between two curves
- 16.4.3 Finding the area between a curve and the y-axis
- 16.5 Estimating Integrals
- 16.5.1 A simple type of estimation
- 16.6 Averages and the Mean Value Theorem for Integrals
- 16.6.1 The Mean Value Theorem for integrals
- 16.7 A Nonintegrable Function
- 17 The Fundamental Theorems of Calculus
- 17.1 Functions Based on Integrals of Other Functions
- 17.2 The First Fundamental Theorem
- 17.2.1 Introduction to antiderivatives
- 17.3 The Second Fundamental Theorem
- 17.4 Indefinite Integrals
- 17.5 How to Solve Problems: The First Fundamental Theorem
- 17.5.1 Variation 1: variable left-hand limit of integration
- 17.5.2 Variation 2: one tricky limit of integration
- 17.5.3 Variation 3: two tricky limits of integration
- 17.5.4 Variation 4: limit is a derivative in disguise
- 17.6 How to Solve Problems: The Second Fundamental Theorem
- 17.6.1 Finding indefinite...
- 16.1 The Basic Idea
- 15.1 Sigma Notation
- 14.1 L’Hôpital’s Rule
- 13.1 Optimization
- 12.1 How to Construct a Table of Signs
- 11.1 Extrema of Functions
- 10.1 The Derivative and Inverse Functions
- 9.1 The Basics
- 8.1 Implicit Differentiation
- 7.1 Limits Involving Trig Functions
- 5.1 Continuity
- 1.1 Functions
- How to Use This Book to Study for an Exam
Details
| Erscheinungsjahr: | 2007 |
|---|---|
| Fachbereich: | Analysis |
| Genre: | Importe, Mathematik |
| Rubrik: | Naturwissenschaften & Technik |
| Medium: | Taschenbuch |
| Inhalt: | Einband - flex.(Paperback) |
| ISBN-13: | 9780691130880 |
| ISBN-10: | 0691130884 |
| Sprache: | Englisch |
| Einband: | Kartoniert / Broschiert |
| Autor: | Banner, Adrian |
| Hersteller: | Princeton University Press |
| Verantwortliche Person für die EU: | Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de |
| Maße: | 254 x 178 x 40 mm |
| Von/Mit: | Adrian Banner |
| Erscheinungsdatum: | 25.03.2007 |
| Gewicht: | 1,391 kg |
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