## Grade 12 Calculus and Vectors

Comprehensive list of FREE video tutorials for Canada and North America's grade 12 Calculus and Vectors

Calculus was developed by German mathematician and philosopher Gottfried Wilhelm Leibniz and English mathematician and physicist Sir Isaac Newton (concurrently, but from different parts of the world).

Calculus has two main parts: Derivatives and Integrals. Derivatives, the component of Calculus that is taught in Calculus and Vectors, mainly assist with solving problems that involves rates of changes and curve sketching. Meanwhile, integration is used to find areas and volumes made by the most complicated curves and shapes. Thus, Calculus is most useful in solving problems that presents itself in a state of continuum.

There are many different notations used in Calculus to indicate derivative of a function. Leibniz introduced the df(x)/dx or dy/dx notation (read as ‘d’ ‘y’ by ‘d’ ‘x’ or ‘derivative of ‘y’ with respect to ‘x’), while Newton came up with the ‘dot notation’
(ė or ë) which is now primarily used to indicate derivatives with respect to time. Leonhard Euler’s notation uses a prefix ‘D’ as a differential operator with the function ‘f(x)’ following it (i.e. Df and D^{2}f, D^{3}f...D^{n}f used for higher order of differentials). He also introduced the D_{x}f(x) or D_{x}y notation which reads exactly as Leibniz’s notation, above. Most popular notation to date belongs to Joseph Louis Lagrange, as he coined the ‘prime notation’ such as f’(x) (read as "f" "prime of" "x"), and f’’(x), f’’’(x)...f^{n}(x) for higher order of differentiation.

Please refer to high school math prerequisite tree to see the recommended courses and materials one should be familiar with prior to taking up Calculus and Vectors.

NB:

Each topic in a section has at least 3 different presenters. This provides access to different educating strategies on any one topic. (Please also note that the topics are not listed in any particular or recommended order). We advise you to use our compiled sources with discretion. They are outside sources. If you find errors or mistakes with the videos you access, please inform us via
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## Grade 12 Calculus and Vectors

Chapter 1: Introduction to* Calculus *and Vectors

1.1 Rationalizing Denominators

1.2 Average Rate of Change

1.3 Slope of Tangents

1.4 Limit of a Function

1.5 Properties of Limits

1.6 Continuity

Chapter 2: Derivatives

2.1 Introduction to Derivatives (limit of f(x) as h→0)

2.2 Derivatives: Power and Constant Multiple Rules

2.3 Derivatives: Sum and Difference Rules

2.4 Derivatives: Product Rule

2.5 Derivatives: Quotient Rule

2.6 Derivatives: Chain Rule [Composite functions]

2.7 Derivatives: Power Rule for Composite Functions

Chapter 3: Applications of Derivatives

3.1 Higher order Derivatives

Position, Velocity, and Acceleration

3.2 Extreme Value Problems

Local and Absolute Maxima and Minima

3.3 Optimization Problems

Distances, Areas, Volumes, Velocity &more

3.4 Optimization Problems - Economics and Science

Chapter 4: Curve Sketching

4.1 Intervals of Increase and Decrease

4.2 First Derivative Test

Critical points, Local Maxima and Local Minima

4.3 Vertical Asymptotes and Horizontal Asymptotes

4.4 Second Derivatives

Concavity and Points of Inflection

4.5 Oblique or Slant Asymptotes

Chapter 5: Derivatives of Trigonometric Functions

5.01 Review of Trigonometric Identities/Functions

5.1 Derivatives of f(x)= sin x and f(x)= cos x

5.2 Derivatives of f(x)= tan x

Chapter 6: Derivatives of Exponential Functions

6.1 Derivative of Exponential Functions f(x)=e^{x}

6.2 Derivative of General Exponential Functions f(x)=b^{x}

6.3 Optimization Problems - Exponential Functions ^{.}

Chapter 7: Introduction to * Vectors *

7.1 Review of Trigonometric Identities

7.2 Introduction to Vectors

7.3 Adding and Subtracting Vectors

7.4 Multiplication of Vector by Scalar

7.5 Computational Properties of Vectors

7.6 Three-Dimensional Vectors

7.7 2-D Vector Representations & Operations -

Using Unit Vector and Component Form

7.8 3-D Vector Representations & Operations -

Using Unit Vector and Component Form

7.9 Linear Combinations and Span of Vectors

Chapter 8: Vector Operations and Applications

8.1 Resolving Vectors

8.2 Resultant (Total) Vectors -

Problems involving Velocity and Forces

8.3 Dot (Scalar) Product of Vectors

8.4 Distributive Property of Dot Products

8.5 Angle Between Two Vectors

8.6 Scalar and Vector Projections

8.7 Cross (Vector) Product of Vectors

8.8 Applications of Dot Products

8.9 Applications of Cross Product

Chapter 9: Equations of Lines

9.1 Vector and Parametric Equations in 2-D

9.2 Vector and Scalar Equations of Lines in 2-D

9.3 Equations of Lines in 3-D

Vector, Parametric and Symmetric Equations

Chapter 10: Equations of Planes

10.1 Vector and Parametric Equations of Planes

10.2 Scalar or Cartesian Equations of Planes

10.3 Graphing Planes on 3-D Coordinate System

Chapter 11: Points, Lines and Planes

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