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
Website Video Clips with Solutions:
Pages 6 #
Rationalizing the denominator examples
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 #
Website Video Clips with Solutions:
Slope of a Tangent explanation Part 1
Slope of a Tangent Part 2
1.3 Rates of Change
Pages 22 #
Website Video Clips with Solutions:
1.4 Limit of a Function
Website Video Clips with Solutions:
Average Velocity Examples
Watch the concept Video and examples 1-3
Average Rate of Change Examples
Watch the concept Video and examples 1-3
Pages 34 #
Limit explanation Video
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 #
Website Video Clips with Solutions:
Limits of Rational Functions examples
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
Website Video Clips with Solutions:
Pages 48 #
Continuity examples 1
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 #
Website Video Clips with Solutions:
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
UNIT 2: Derivatives
2.1 The Derivative Function
Pages 65 #
Website Video Clips with Solutions:
The definition of a Derivative Explanation and examples
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
Functions
Pages 76 #
Website Video Clips with Solutions:
2.3 The Product Rule
Website Video Clips with Solutions:
Khan Academy Questions:
Derivative of Polynomial functions
Graphing the derivative Polynomial Functions
Derivative of Polynomial Functions examples
Watch the concept Video and examples 1-3
Pages 85 #
The Product Rule Explanation and example #1
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
Power Rule Practice Problems
2.4 The Quotient Rule
Pages 94 #
The Quotient Rule
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
Website Video Clips with Solutions:
2.5 The Derivatives of Composite
Functions
Pages 99 #
Website Video Clips with Solutions:
The Chain Rule explanation
The Chain Rule examples
The Chain Rule example 2
Review
Pages 109 #
UNIT 3: Derivatives and their Applications
3.1 Higher Order Derivatives, Velocity
and Acceleration
Website Video Clips with Solutions:
3.2 Minimum and Maximum on an
Interval
Website Video Clips with Solutions:
Pages 119 #
Application Problem with Velocity
Higher Order Derivatives application problems
Pages 130 #
Minimum and Maximum Application Problems
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 #
Website Video Clips with Solutions:
Optimization Application Problems: Volume Problem
Optimization Application Problem: Sum of numbers
Optimization Problem volume of a cube
3.4 Optimization Problems in
Economics and Science
Pages 148 #
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 #
Website Video Clips with Solutions:
Increasing and Decreasing functions examples
Increasing and Decreasing Functions examples 2
Watch the concept Video and examples 1 and 2 (Skip #3)
4.2 Critical Points, Local Maxima and
Local Minima
Website Video Clips with Solutions:
Pages 172 #
Critical Points, Local Maxima and Minima Examples
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 #
Website Video Clips with Solutions:
Vertical and Horizontal Asymptotes
Finding Horizontal Asymptotes example
Vertical Asymptote graphing example
4.4 Concavity and Points of Inflection
Pages 198 #
Website Video Clips with Solutions:
4.5 Algorithm for Curve Sketching
Website Video Clips with Solutions:
Review
Concavity and Points of Inflection
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)
Pages 207 #
Curve Sketching Examples
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
Pages 216 #
UNIT 5: Derivatives of Exponential and Trigonometric Functions
5.1 Derivatives of Exponential Functions
Pages 227#
Website Video Clips with Solutions:
Derivative of Exponential Functions
Derivative of Exponential Functions #2
Watch the concept Video and examples 2-3 (skip 1)
5.2 The Derivative of the General
Exponential Function
Website Video Clips with Solutions:
5.3 Optimization Problems Involving
Exponential Functions
Pages 235 #
Derivative of Exponential Functions
Derivative of Exponential Functions #2
Watch the concept Video and examples 1
Derivative of Exponential Functions #3
Pages 241 #
Exponential Functions and Optimization
Website Video Clips with Solutions:
5.4 The Derivatives of Sine and Cosine
Website Video Clips with Solutions:
Pages 250 #
Derivatives of Sine and Cosine
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
Website Video Clips with Solutions:
Review
Pages 258 #
The Derivative of Tangent Example
Trigonometric Derivatives
Go to Topic “Calculus” and click on “Trigonometric Functions”
Trigonometric Derivative Problem 1
Trigonometric Derivative Problem 2
Pages 263 #
UNIT 6: An Introduction to Vectors
6.1 An Introduction to Vectors
Pages 275 #
Website Video Clips with Solutions:
An introduction to Vectors
Vector Explanation and examples of Finding the magnitude
Watch the concept Video and examples 1-3
6.2 Vector Addition
Pages 282 #
Website Video Clips with Solutions:
6.3 Multiplication of a Vector by a
Scalar
Website Video Clips with Solutions:
Addition and Subtraction of Vectors
Vector Addition
Watch the concept Video and examples 1-3
Vector Addition the components of vectors
Watch the concept Video and examples 1-3
Pages 293 #
Multiplying a Vector by a Scalar
Finding the resultant vector example
Watch the concept Video and examples 1-3
6.4 Properties of Vectors
Website Video Clips with Solutions:
6.5 Vector in R2 and R3
Pages 302 #
Algebraic Representation of Vectors
Watch the concept Video and examples 1-3
Unit Vectors
Watch the concept Video and examples 1-3
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 #
Website Video Clips with Solutions:
Vectors in R3
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 #
Website Video Clips with Solutions:
Application Problems Navigation
Watch the concept Video and examples 1-3
7.3 The Dot Product: Geometric
Pages 371 #
Website Video Clips with Solutions:
7.4 The Dot Product: Algebraic
Website Video Clips with Solutions:
The Dot Product
Applications of Dot Product
The Dot Product Geometric Examples
Watch the concept Video and examples 1-3
Pages 379 #
The Dot Product
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
and Cross Product
Pages 409 #
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
Equations in R2
Website Video Clips with Solutions:
Pages 427 #
Equations of line in 2-D
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
Equations in R3
Website Video Clips with Solutions:
8.4 Vector and Parametric
Equations in a Plane
Website Video Clips with Solutions:
8.5 The Cartesian equation of a
Plane
Website Video Clips with Solutions:
8.6 Sketching Planes in R3
Pages 445 #
The intersection of Lines
R3 Problems
Watch the concept Video and examples 1-3
Pages 453 #
Properties of Planes
R3 Problems
Watch the concept Video and examples 1-3
Pages 461 #
Equation of a Plane
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
Pages 470 #
Website Video Clips with Solutions:
Graphing Planes in R3
Watch Concept and problem #2
Review
Pages 480 #
UNIT 9: Relationships between Points, Lines, Planes
9.1 Intersection of a Lines and
Planes
Pages 489 #
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
Line
Pages 534 #
Website Video Clips with Solutions:
9.6 The Distance from a Point to a
Plane
Pages 542 #
Website Video Clips with Solutions:
Review
Pages 551 #