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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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