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Grade 12 - MCV4U - Calculus and Vectors_ University

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Grade 12 - MCV4U - Calculus and Vectors_ University Powered By Docstoc
					                               Calculus and Vectors, University (MCV4U)
                                          UNIT 1: Introduction to Calculus
                                                 UNIT 2: Derivatives
                                      UNIT 3: Derivatives and their Applications
                                              UNIT 4: Curve Sketching
                         UNIT 5: Derivatives of Exponential and Trigonometric Functions
                                         UNIT 6: An Introduction to Vectors
                                           UNIT 7: Application of Vectors
                                       UNIT 8: Equations of Lines and Planes
                                UNIT 9: Relationships between Points, Lines, Planes


                                          UNIT 1: Introduction to Calculus
1.1 Rationalizing the Denominator                                         Pages 6 #

                                                            Rationalizing the denominator examples
Website Video Clips with Solutions:                         Watch the concept Video and examples 1-2
                                                    Rationalizing the denominator with a Binomial example 2
                                                            Watch the concept Video and examples 1-2
                                                         How to rationalize a denominator explanation
                                                                         Review of skills
                                                         Simplifying Radical expressions explanation
       Additional Support:                             Simplifying Radical expressions of the same root
                                                       Simplifying radical expressions of different roots
   1.2 The Slope of a Tangent                                  Pages 10 #

                                                   Slope of a Tangent explanation Part 1
Website Video Clips with Solutions:                      Slope of a Tangent Part 2




      1.3 Rates of Change                                      Pages 22 #

                                                       Average Velocity Examples
Website Video Clips with Solutions:              Watch the concept Video and examples 1-3
                                                   Average Rate of Change Examples
                                                 Watch the concept Video and examples 1-3



     1.4 Limit of a Function                                   Pages 34 #

                                                           Limit explanation Video
Website Video Clips with Solutions:                      One sided-Limit examples
                                                  Watch the concept Video and examples 1-2
                                                 Using the Graphical for evaluating Limits
                                                  Watch the concept Video and examples 1-3
                                                   Limits of Rational Functions examples
                                                  Watch the concept Video and examples 1-3
                                      Evaluating Rational Functions examples (Similar Question 10-11)
                                                  Watch the concept Video and examples 1-3

    Khan Academy Questions:                            Limit Practice Questions #1
                                                       Limits Practice Questions #2



     1.5 Properties of Limits                                  Pages 40 #
                                                Limits of Rational Functions examples
Website Video Clips with Solutions:            Watch the concept Video and examples 1-3
                                           Evaluating limits of Rational Functions examples
                                               Watch the concept Video and examples 1-3
                                           Evaluating limits of Rational Functions Example 2



          1.6 Continuity                                     Pages 48 #

                                                        Continuity examples 1
Website Video Clips with Solutions:            Watch the concept Video and examples 1-3
                                           Determining if a function is Continuous examples
                                               Watch the concept Video and examples 1-3
                                              Evaluating Limits Algebraically Example 1
                                               Watch the concept Video and examples 1-3
                                              Evaluating Limits Algebraically Example 2
                                               Watch the concept Video and examples 1-3

    Khan Academy Questions:                          Limits Practice Questions #2



             Review                                          Pages 56 #
                                              Evaluating Limits Algebraically Example 1
                                              Watch the concept Video and examples 1-3
Website Video Clips with Solutions:
                                              Evaluating Limits Algebraically Example 2
                                              Watch the concept Video and examples 1-3



                                      UNIT 2: Derivatives


  2.1 The Derivative Function                                Pages 65 #
                                            The definition of a Derivative Explanation and examples
Website Video Clips with Solutions:                Watch the concept Video and examples 1-3
                                             Finding the derivative from First Principles example 1
                                             Finding the derivative from First Principles example 2
                                             Finding the derivative from First Principles example 3
                                                            Derivative Explanation 1
                                                            Derivative Explanation 2

    Khan Academy Questions:                              Derivative Practice Problems #1




2.2 The Derivative of Polynomial                                   Pages 76 #
           Functions
                                                      Derivative of Polynomial functions
Website Video Clips with Solutions:              Graphing the derivative Polynomial Functions
                                                 Derivative of Polynomial Functions examples
                                                   Watch the concept Video and examples 1-3



      2.3 The Product Rule                                         Pages 85 #

                                                  The Product Rule Explanation and example #1
Website Video Clips with Solutions:              Go to Topic “Calculus” and click on “Product Rule”
                                                                 The Product Rule
                                                                  The Power Rule
                                      Go to Topic “Calculus” and click on “Power Rule” and watch examples 1-7
                                                           The Product Rule example 1
                                                           The Product Rule example 2

    Khan Academy Questions:                              Power Rule Practice Problems
      2.4 The Quotient Rule                                                   Pages 94 #

                                                                            The Quotient Rule
Website Video Clips with Solutions:                           Watch the concept Video and examples 1(b), 3
                                                                           The Quotient Rule 2
                                                Go to Topic “Calculus” and click on “Quotient Rule” and watch examples 1-5
                                                                          The Quotient example



2.5 The Derivatives of Composite                                              Pages 99 #
           Functions
                                                                      The Chain Rule explanation
Website Video Clips with Solutions:                                    The Chain Rule examples
                                                                       The Chain Rule example 2



             Review                                                           Pages 109 #


                                        UNIT 3: Derivatives and their Applications
3.1 Higher Order Derivatives, Velocity                                          Pages 119 #
          and Acceleration
                                                                    Application Problem with Velocity
  Website Video Clips with Solutions:                         Higher Order Derivatives application problems




  3.2 Minimum and Maximum on an                                                 Pages 130 #
              Interval
                                                               Minimum and Maximum Application Problems
  Website Video Clips with Solutions:                              Finding the local min/max problem 1
                                                                   Finding the local min/max Problem 2
                                                                     Local Min/Max Explanation video
     3.3 Optimization Problems                                         Pages 141 #

                                                   Optimization Application Problems: Volume Problem
  Website Video Clips with Solutions:              Optimization Application Problem: Sum of numbers
                                                         Optimization Problem volume of a cube



    3.4 Optimization Problems in                                       Pages 148 #
       Economics and Science
                                            Optimization Application Problems for Earth sciences and economics
  Website Video Clips with Solutions:




             Review                                                 Pages 156 #


                                          UNIT 4: Curve Sketching
4.1 Increasing and Decreasing Functions                                 Pages 165 #

                                                      Increasing and Decreasing functions examples
   Website Video Clips with Solutions:               Increasing and Decreasing Functions examples 2
                                                    Watch the concept Video and examples 1 and 2 (Skip #3)



 4.2 Critical Points, Local Maxima and                                  Pages 172 #
              Local Minima
                                                     Critical Points, Local Maxima and Minima Examples
   Website Video Clips with Solutions:                  The First Derivative test to find local min/max
                                                           Watch the concept Video and examples 1-3
                                                      Critical Points Explanation and example problem
                                                    Watch the concept Video and examples 1 (Skip 2 and 3)



4.3 Vertical and Horizontal Asymptote                                   Pages 181 #

                                                            Vertical and Horizontal Asymptotes
  Website Video Clips with Solutions:                     Finding Horizontal Asymptotes example
                                                           Vertical Asymptote graphing example



4.4 Concavity and Points of Inflection                                  Pages 198 #

                                                              Concavity and Points of Inflection
  Website Video Clips with Solutions:                          Concavity and inflection points
                                                          Watch the concept Video and examples 1-3
                                                     The second Derivative Test examples and concept
                                                    Watch the concept Video and examples 1 and 3 (Skip #2)



 4.5 Algorithm for Curve Sketching                                      Pages 207 #

                                                                 Curve Sketching Examples
  Website Video Clips with Solutions:              Sketching Polynomial and Rational Functions examples
                                                     Watch the concept Video and examples 1,2,4 (Skip #3)
                                                          Finding Horizontal Asymptotes example
                                                           Vertical Asymptote graphing example
                                                           Graphing a Rational Function example



               Review                                                   Pages 216 #


                        UNIT 5: Derivatives of Exponential and Trigonometric Functions
5.1 Derivatives of Exponential Functions                          Pages 227#

                                                    Derivative of Exponential Functions
   Website Video Clips with Solutions:             Derivative of Exponential Functions #2
                                               Watch the concept Video and examples 2-3 (skip 1)



   5.2 The Derivative of the General                              Pages 235 #
         Exponential Function
                                                     Derivative of Exponential Functions
   Website Video Clips with Solutions:              Derivative of Exponential Functions #2
                                                    Watch the concept Video and examples 1
                                                    Derivative of Exponential Functions #3



  5.3 Optimization Problems Involving                             Pages 241 #
         Exponential Functions
                                                    Exponential Functions and Optimization
   Website Video Clips with Solutions:




5.4 The Derivatives of Sine and Cosine                            Pages 250 #

                                                         Derivatives of Sine and Cosine
   Website Video Clips with Solutions:             Trigonometric Derivatives (Skip Tangent)
                                           Go to Topic “Calculus” and click on “Trigonometric Functions”
                                                Derivatives of Trigonometric Practice Problems
                                                  Do Examples 1-7 by yourself and see solutions
        5.5 The Derivative of tan                                            Pages 258 #

                                                                 The Derivative of Tangent Example
   Website Video Clips with Solutions:                                Trigonometric Derivatives
                                                      Go to Topic “Calculus” and click on “Trigonometric Functions”
                                                                 Trigonometric Derivative Problem 1
                                                                 Trigonometric Derivative Problem 2



                Review                                                       Pages 263 #


                                         UNIT 6: An Introduction to Vectors
 6.1 An Introduction to Vectors                                          Pages 275 #

                                                                  An introduction to Vectors
Website Video Clips with Solutions:               Vector Explanation and examples of Finding the magnitude
                                                           Watch the concept Video and examples 1-3



       6.2 Vector Addition                                               Pages 282 #

                                                            Addition and Subtraction of Vectors
Website Video Clips with Solutions:                                    Vector Addition
                                                          Watch the concept Video and examples 1-3
                                                         Vector Addition the components of vectors
                                                          Watch the concept Video and examples 1-3



6.3 Multiplication of a Vector by a                                      Pages 293 #
              Scalar
                                                                Multiplying a Vector by a Scalar
Website Video Clips with Solutions:                          Finding the resultant vector example
                                       Watch the concept Video and examples 1-3




    6.4 Properties of Vectors                        Pages 302 #

                                        Algebraic Representation of Vectors
Website Video Clips with Solutions:    Watch the concept Video and examples 1-3
                                                     Unit Vectors
                                       Watch the concept Video and examples 1-3



     6.5 Vector in R2 and R3                         Pages 310 #



Website Video Clips with Solutions:




6.6 Operation with Vectors in R2                     Pages 319 #

                                                Graphing Vectors in R2
Website Video Clips with Solutions:




6.7 Operations with Vectors in R3                    Pages 327 #

                                                     Vectors in R3
Website Video Clips with Solutions:   An Introduction to the R3 coordinate system
                                       Watch the concept Video and examples 1-3
             Review                                              Pages 343 #


                                      UNIT 7: Application of Vectors
     7.1 Vectors as Forces                                       Pages 352 #



Website Video Clips with Solutions:




           7.2 Velocity                                          Pages 365 #

                                                       Application Problems Navigation
Website Video Clips with Solutions:                 Watch the concept Video and examples 1-3




7.3 The Dot Product: Geometric                                   Pages 371 #

                                                                The Dot Product
Website Video Clips with Solutions:                       Applications of Dot Product
                                                     The Dot Product Geometric Examples
                                                    Watch the concept Video and examples 1-3



 7.4 The Dot Product: Algebraic                                  Pages 379 #

                                                                The Dot Product
Website Video Clips with Solutions:                       Applications of Dot Product
                                                         Dot Product (Angle Property)
                                                    Watch the concept Video and examples 1-3
7.5 Scalar and vector Projections                                      Pages 390#



 Website Video Clips with Solutions:




7.6 Cross Product of Two Vectors                                       Pages 401 #

                                                                    The cross product
 Website Video Clips with Solutions:




7.7 Applications of the Dot Product                                    Pages 409 #
        and Cross Product
                                                       Applications of dot product and cross product
 Website Video Clips with Solutions:




              Review                                                   Pages 418 #




                                       UNIT 8: Equations of Lines and Planes
    8.1 Vectors and Parametric                                         Pages 427 #
          Equations in R2
                                                                 Equations of line in 2-D
 Website Video Clips with Solutions:                            Vector Equation of a Line
                                                         Watch the concept Video and examples 1-3
                                                              Parametric Equation of Lines
                                          Watch the concept Video and examples 1-3



8.2 Cartesian Equation of a Line                        Pages 435 #

                                                     Equation of a Plane
Website Video Clips with Solutions:




   8.3 Vectors and Parametric                           Pages 445 #
         Equations in R3
                                                  The intersection of Lines
Website Video Clips with Solutions:                     R3 Problems
                                          Watch the concept Video and examples 1-3



   8.4 Vector and Parametric                            Pages 453 #
      Equations in a Plane
                                                    Properties of Planes
Website Video Clips with Solutions:                     R3 Problems
                                          Watch the concept Video and examples 1-3



8.5 The Cartesian equation of a                         Pages 461 #
             Plane
                                                    Equation of a Plane
Website Video Clips with Solutions:       Watch the concept Video and examples 1-3
                                      Problems for equations of a Plane (Find the angle)
                                          Watch the concept Video and examples 1-3



   8.6 Sketching Planes in R3                           Pages 470 #
                                                                Graphing Planes in R3
Website Video Clips with Solutions:                          Watch Concept and problem #2




             Review                                                  Pages 480 #


                                UNIT 9: Relationships between Points, Lines, Planes


 9.1 Intersection of a Lines and                                     Pages 489 #
             Planes
                                                            Intersection of Lines and Planes
Website Video Clips with Solutions:




   9.2 Systems of Equations                                          Pages 499 #



Website Video Clips with Solutions:




 9.3 Intersection of Two Planes                                      Pages 510 #

                                                                 Intersection of Planes
Website Video Clips with Solutions:




9.4 Intersection of Three Planes                                     Pages 520 #
Website Video Clips with Solutions:




9.5 The Distance from a Point to a    Pages 534 #
              Line

Website Video Clips with Solutions:




9.6 The Distance from a Point to a    Pages 542 #
              Plane

Website Video Clips with Solutions:




             Review                   Pages 551 #

				
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