Calculus II

Calculus II

Detalles Bibliográficos
Otros Autores: Zegarelli, Mark, author (author)
Formato: Libro electrónico
Idioma:Inglés
Publicado: Hoboken, New Jersey : John Wiley & Sons, Inc 2023.
Edición:Third edition
Colección:--For dummies.
Materias:
Calculus.
Ver en Biblioteca Universitat Ramon Llull:https://discovery.url.edu/permalink/34CSUC_URL/1im36ta/alma991009752727606719
Tabla de Contenidos:
  • Intro
  • Title Page
  • Copyright Page
  • Table of Contents
  • Introduction
  • About This Book
  • Conventions Used in This Book
  • What You're Not to Read
  • Foolish Assumptions
  • Icons Used in This Book
  • Beyond the Book
  • Where to Go from Here
  • Part 1 Introduction to Integration
  • Chapter 1 An Aerial View of the Area Problem
  • Checking Out the Area
  • Comparing classical and analytic geometry
  • Finding definite answers with the definite integral
  • Slicing Things Up
  • Untangling a hairy problem using rectangles
  • Moving left, right, or center
  • Defining the Indefinite
  • Solving Problems with Integration
  • We can work it out: Finding the area between curves
  • Walking the long and winding road
  • You say you want a revolution
  • Differential Equations
  • Understanding Infinite Series
  • Distinguishing sequences and series
  • Evaluating series
  • Identifying convergent and divergent series
  • Chapter 2 Forgotten but Not Gone: Review of Algebra and Pre-Calculus
  • Quick Review of Pre-Algebra and Algebra
  • Working with fractions
  • Adding fractions
  • Subtracting fractions
  • Multiplying fractions
  • Dividing fractions
  • Knowing the facts on factorials
  • Polishing off polynomials
  • Powering through powers (exponents)
  • Understanding zero and negative exponents
  • Understanding fractional exponents
  • Expressing functions using exponents
  • Rewriting rational functions using exponents
  • Simplifying rational expressions by factoring
  • Review of Pre-Calculus
  • Trigonometry
  • Noting trig notation
  • Figuring the angles with radians
  • Identifying some important trig identities
  • Asymptotes
  • Graphing common parent functions
  • Linear and polynomial functions
  • Exponential and logarithmic functions
  • Trigonometric functions
  • Transforming continuous functions
  • Polar coordinates
  • Summing up sigma notation.
  • Chapter 3 Recent Memories: Review of Calculus I
  • Knowing Your Limits
  • Telling functions and limits apart
  • Evaluating limits
  • Hitting the Slopes with Derivatives
  • Referring to the limit formula for derivatives
  • Knowing two notations for derivatives
  • Understanding Differentiation
  • Memorizing key derivatives
  • Derivatives of the trig functions
  • Derivatives of the inverse trig functions
  • The Power rule
  • The Sum rule
  • The Constant Multiple rule
  • The Product rule
  • The Quotient rule
  • Evaluating functions from the inside out
  • Differentiating functions from the outside in
  • Finding Limits Using L'Hôpital's Rule
  • Introducing L'Hôpital's rule
  • Alternative indeterminate forms
  • Case #1: 0 ⋅ ∞
  • Case #2: ∞ - ∞
  • Case #3: Indeterminate powers
  • Part 2 From Definite to Indefinite Integrals
  • Chapter 4 Approximating Area with Riemann Sums
  • Three Ways to Approximate Area with Rectangles
  • Using left rectangles
  • Using right rectangles
  • Finding a middle ground: The Midpoint rule
  • Two More Ways to Approximate Area
  • Feeling trapped? The Trapezoid rule
  • Don't have a cow! Simpson's rule
  • Building the Riemann Sum Formula
  • Approximating the definite integral with the area formula for a rectangle
  • Widening your understanding of width
  • Limiting the margin of error
  • Summing things up with sigma notation
  • Heightening the functionality of height
  • Finishing with the slack factor
  • Chapter 5 There Must Be a Better Way - Introducing the Indefinite Integral
  • FTC2: The Saga Begins
  • Introducing FTC2
  • Evaluating definite integrals using FTC2
  • Your New Best Friend: The Indefinite Integral
  • Introducing anti-differentiation
  • Solving area problems without the Riemann sum formula
  • Understanding signed area
  • Distinguishing definite and indefinite integrals
  • FTC1: The Journey Continues.
  • Understanding area functions
  • Making sense of FTC1
  • Part 3 Evaluating Indefinite Integrals
  • Chapter 6 Instant Integration: Just Add Water (And C )
  • Evaluating Basic Integrals
  • Using the 17 basic antiderivatives for integrating
  • Three important integration rules
  • The Sum rule for integration
  • The Constant Multiple rule for integration
  • The Power rule for integration
  • What happened to the other rules?
  • Evaluating More Difficult Integrals
  • Integrating polynomials
  • Integrating more complicated-looking functions
  • Understanding Integrability
  • Taking a look at two red herrings of integrability
  • Computing integrals
  • Representing integrals as elementary functions
  • Getting an idea of what integrable really means
  • Chapter 7 Sharpening Your Integration Moves
  • Integrating Rational and Radical Functions
  • Integrating simple rational functions
  • Integrating radical functions
  • Using Algebra to Integrate Using the Power Rule
  • Integrating by using inverse trig functions
  • Integrating Trig Functions
  • Recalling how to anti-differentiate the six basic trig functions
  • Using the Basic Five trig identities
  • Applying the Pythagorean trig identities
  • Using to integrate trig functions
  • Using to integrate trig functions
  • Using to integrate trig functions
  • Integrating Compositions of Functions with Linear Inputs
  • Understanding how to integrate familiar functions that have linear inputs
  • Integrating the function composed with a linear input
  • Integrating the six basic trig functions with linear inputs
  • Integrating power functions composed with a linear input
  • Knowing the handy arctan formula
  • Using algebra to solve more complex problems
  • Using trig identities to integrate more complex functions
  • Understanding why integrating compositions of functions with linear inputs actually works.
  • Chapter 8 Here's Looking at U-Substitution
  • Knowing How to Use U-Substitution
  • Recognizing When to Use U-Substitution
  • The simpler case: f (x) · f '(x)
  • The more complex case: g(  f (x)) · f '(x) when you know how to integrate g (x)
  • Using Substitution to Evaluate Definite Integrals
  • Part 4 Advanced Integration Techniques
  • Chapter 9 Parting Ways: Integration by Parts
  • Introducing Integration by Parts
  • Reversing the Product rule
  • Knowing how to integrate by parts
  • Knowing when to integrate by parts
  • Integrating by Parts with the DI-agonal Method
  • Looking at the DI-agonal chart
  • Using the DI-agonal method
  • L is for logarithm
  • I is for inverse trig
  • A is for algebraic
  • T is for trig
  • Chapter 10 Trig Substitution: Knowing All the (Tri)Angles
  • Integrating the Six Trig Functions
  • Integrating Powers of Sines and Cosines
  • Odd powers of sines and cosines
  • Even powers of sines and cosines
  • Integrating Powers of Tangents and Secants
  • Even powers of secants
  • Odd powers of tangents
  • Other tangent and secant cases
  • Integrating Powers of Cotangents and Cosecants
  • Integrating Weird Combinations of Trig Functions
  • Using Trig Substitution
  • Distinguishing three cases for trig substitution
  • Integrating the three cases
  • The sine case
  • The tangent case
  • The secant case
  • Knowing when to avoid trig substitution
  • Chapter 11 Rational Solutions: Integration with Partial Fractions
  • Strange but True: Understanding Partial Fractions
  • Looking at partial fractions
  • Using partial fractions with rational expressions
  • Solving Integrals by Using Partial Fractions
  • Case 1: Distinct linear factors
  • Setting up partial fractions
  • Solving for unknowns A, B, and C
  • Evaluating the integral
  • Case 2: Repeated linear factors
  • Setting up partial fractions
  • Solving for unknowns A and B.
  • Evaluating the integral
  • Case 3: Distinct quadratic factors
  • Setting up partial fractions
  • Solving for unknowns A, B, and C
  • Evaluating the integral
  • Case 4: Repeated quadratic factors
  • Setting up partial fractions
  • Solving for unknowns A, B, C, and D
  • Evaluating the integral
  • Beyond the Four Cases: Knowing How to Set Up Any Partial Fraction
  • Integrating Improper Rationals
  • Distinguishing proper and improper rational expressions
  • Trying out an example
  • Part 5 Applications of Integrals
  • Chapter 12 Forging into New Areas: Solving Area Problems
  • Breaking Us in Two
  • Improper Integrals
  • Getting horizontal
  • Going vertical
  • Handling asymptotic limits of integration
  • Piecing together discontinuous integrands
  • Finding the Unsigned Area of Shaded Regions on the xy-Graph
  • Finding unsigned area when a region is separated horizontally
  • Crossing the line to find unsigned area
  • Calculating the area under more than one function
  • Measuring a single shaded region between two functions
  • Finding the area of two or more shaded regions between two functions
  • The Mean Value Theorem for Integrals
  • Calculating Arc Length
  • Chapter 13 Pump Up the Volume: Using Calculus to Solve 3-D Problems
  • Slicing Your Way to Success
  • Finding the volume of a solid with congruent cross sections
  • Finding the volume of a solid with similar cross sections
  • Measuring the volume of a pyramid
  • Measuring the volume of a weird solid
  • Turning a Problem on Its Side
  • Two Revolutionary Problems
  • Solidifying your understanding of solids of revolution
  • Skimming the surface of revolution
  • Finding the Space Between
  • Playing the Shell Game
  • Peeling and measuring a can of soup
  • Using the shell method without inverses
  • Knowing When and How to Solve 3-D Problems
  • Chapter 14 What's So Different about Differential Equations?.
  • Basics of Differential Equations.

Ejemplares similares