Calculus And Vectors 12: Study Guide And University Handbook by Chris KnowlesCalculus And Vectors 12: Study Guide And University Handbook by Chris Knowles

Calculus And Vectors 12: Study Guide And University Handbook

byChris Knowles, Antonietta Lenjosek

Paperback | August 25, 2008

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  • Extend practice and exercises, and build skills needed for university bound students
  • Includes key concepts with expanded examples
  • Consumable format which can serve as a reference tool for students as they enter university
Title:Calculus And Vectors 12: Study Guide And University HandbookFormat:PaperbackDimensions:10.8 × 8.4 × 0.8 inPublished:August 25, 2008Publisher:McGraw Hill School IndigeLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0070735891

ISBN - 13:9780070735897

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Table of Contents


Chapter 1 Rates of Change
1.1 Rates of Change and the Slope of a Curve
   Average Rate of Change
   Instantaneous Rate of Change
1.2 Rates of Change Using Equations
   Difference Quotient
   Estimate the Instantaneous Rate of Change
   Estimate the Slope of a Tangent
1.3 Limits
   Limit of a Sequence
   Limit of a Function
   One-sided Limits
1.4 Limits and Continuity
   Evaluate Limits Algebraically
   Limit Properties
   Continuous and Discontinuous Functions
   Limits Involving Asymptotes
   Indeterminate Forms
1.5 Introduction to Derivatives
   First Principles Definition
   Leibniz Notation
   Differentiate Rational Functions
   Non-Differentiable Functions
   Solve Rate and Tangent Problems Using First Principles
Challenge Questions
Chapter 1 Checklist

Chapter 2 Derivatives
2.1 Derivative of a Polynomial Function
   Derivative Rules: The Constant Rule, The Power Rule, The Sum and Difference Rules, The Constant Multiple Rule
   Rational Exponents and the Power Rule
   Differentiate Powers with Negative Exponents
   Applications of Polynomial Derivatives
2.2 The Product Rule
2.3 Velocity, Acceleration, and Second Derivatives
   Relationship Between the First and Second Derivative
   Determining the Second Derivative
   Relationship Between Displacement, Velocity, and Acceleration
2.4 The Chain Rule
   Differentiate Composite Functions
   Leibniz Form of the Chain Rule
   Power of a Function Rule
   Combining Derivative Rules and the Chain Rule
2.5 Derivatives of Quotients
   Differentiating a Simple Quotient Function
   The Quotient Rule
2.6 Rate of Change Problems
   Functions Pertaining to Business: Demand, Revenue, Cost, and Profit Functions
   Derivatives of Business Functions: Marginal Cost, Marginal Revenue, and Marginal Profit
   Applications of Derivatives in Physical Sciences: Kinetic Energy, Electrical Currents, Linear Density
Challenge Questions
Chapter 2 Checklist

Chapter 3 Curve Sketching
3.1 Increasing and Decreasing Functions
   Intervals of Increase and Decrease
   Sketch Functions Using the First Derivative
3.2 Maxima and Minima
   Critical Values
   Local Maximum and Minimum Values
   Absolute Maximum and Minimum Values
3.3 Concavity and the Second Derivative Test
   Second Derivative Test
   Point of Inflection
   Intervals of Concavity
3.4 Simple Rational Functions
   Vertical Asymptotes
   Derivatives of Rational Functions
   Concavity of Rational Functions
3.5 Putting It All Together
   Steps to Analyse a Function
   Analyse and Sketch Functions
3.6 Optimization Problems
   Area, Surface Area, Volume Problems
   Cost, Revenue Problems
Challenge Questions
Chapter 3 Checklist

Chapter 4 Derivatives of Sinusoidal Functions
4.1 Instantaneous Rates of Change of the Sinusoidal Functions
   Derivative of a Sinusoidal Function
4.2 Derivatives of the Sine and Cosine Functions
   Constant Multiple Rule
   Sum and Difference Rules
   Slope at a Point
   Equation of a Tangent Line
4.3 Differentiation Rules for Sinusoidal Functions
   Chain Rule
   Power of a Function Rule
   Product Rule
   Combining Derivative Rules
4.4 Applications of Sinusoidal Functions and Their Derivatives
   Models of Periodic Behaviour
Challenge Questions
Chapter 4 Checklist

Chapter 5 Exponential and Logarithmic Functions
5.1 Rate of Change and the Number e
   Nature of the Rate of Change
   Value of Number e
5.2 The Natural Logarithm
   Value of Number e
   Natural Logarithm
5.3 Derivatives of Exponential Functions
   Derivative of f(x) = bx
   Equation of a Tangent Line
5.4 Differentiation Rules for Exponential Functions
   Product Rule
   Chain Rule
   Difference Rule
   Combining Rules
   Extreme Values
5.5 Making Connections: Exponential Models
   Modelling Using Exponential Functions and their Derivatives
   Representations of Exponential Models
Challenge Questions
Chapter 5 Checklist

Chapter 6 Geometric Vectors
6.1 Introduction to Vectors
   Vectors and Scalars
   True Bearings
   Quadrant Bearings
   Equivalent and Opposite Vectors
6.2 Addition and Subtraction of Vectors
   Parallel Vectors
   Opposite Vectors
   The Zero Vector
   Parallelogram Method of Adding Vectors
   Properties of Vector Addition and Subtraction
6.3 Multiplying a Vector by a Scalar
   Scalar Multiplication
   Distributive Property
   Collinear Vectors
   Vector Properties for Scalar Multiplication
   Linear Combinations of Vectors
6.4 Applications of Vector Addition
   Rectangular Vector Components
   Resultant Vector
   Equilibrant Vector
   Applications Involving Velocities and Forces
6.5 Resolution of Vectors into Rectangular Components
  Horizontal and Vertical Components of a Force
Challenge Questions
Chapter 6 Checklist

Chapter 7 Cartesian Vectors
7.1 Cartesian Vectors
   Position Vector
   Unit Vectors
   Magnitude of a Vector
   Operations With Cartesian Vectors
   Cartesian Vectors Between Two Points
   Forces and Velocities as Cartesian Vectors
7.2 Dot Product
  Properties of the Dot Product
  Calculate Dot Products of Vectors
7.3 Applications of the Dot Product
   Work in Cartesian Form
   The Angle Between Two Cartesian Vectors
   Vector Projections
7.4 Vectors in Three-Space
   Octants in a 3-D Graph
   Plot Points in 3-D
   3-D Cartesian Vectors
   Magnitude of a Cartesian Vector
   Operations with Cartesian Vectors in 3-D
   Collinear Vectors
   Orthogonal Vectors
   Properties of Cartesian Vector Operations in Three-Space
7.5 The Cross Product and Its Properties
   Cross Product in Cartesian Form
   Properties of the Cross Product of Cartesian Vectors
7.6 Applications of the Dot Product and Cross Product
   Vector Projections and Work in Three-Space
   Triple Scalar Product
   Volume of a Parallelepiped
Challenge Questions
Chapter 7 Checklist

Chapter 8 Lines and Planes
8.1 Equations of Lines in Two-Space and Three-Space
   Vector Equation of a Line in Two-Space
   Parametric Equations of a Line in Two-Space
   Vector Equations of Lines in Three-Space
   Parametric Equations of Lines in Three-Space
8.2 Equations of Planes
   Vector Equations of Planes in Three-Space
   Parametric Equations of Planes in Three-Space
   Scalar Equations of Planes in Three-Space
8.3 Properties of Planes
   Scalar Equations of Planes in Three-Space
8.4 Intersections of Lines in Two-Space and Three-Space
   Linear Systems in Two-Space
   Linear Systems in Three-Space
   Intersection of Lines
   Distance Between Two Skew Lines
8.5 Intersections of Lines and Planes
   Intersection of a Line and a Plane
   Distance From a Point to a Plane
8.6 Intersection of Planes
   Intersection of Two Planes
   Consistent and Inconsistent Systems of Three Planes
   Solving Systems With Three Planes
   Analysing Inconsistent Solutions
   Solving Systems of Equations Using Matrices
   Elementary Row Operations
   Row Reduced Echelon Form
   Solve Dependent or Inconsistent Systems
Challenge Questions
Chapter 8 Checklist

University Preparation

Implicit Differentiation
Derivatives of Logarithmic Differentiation
Related Rates
Integration: The Substitution Rule and Integration by Parts

Solving Systems of Equations
Practice Exam