This course builds on students’ previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions; and apply these concepts and skills to the modelling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics, and some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course.
Most material will be provided in the form of lecture notes (slideshows) and handouts. Copies of the textbook will be provided for in-class use and for overnight sign-out. Additional resources may be found online at the following sites:
- Paul Dawkin’s Online Calculus Notes
- University of British Columbia Calculus Notes
- UofW Online Courseware
- Differential Calculus on Khan Academy
Topics Covered
- Geometric and Algebraic Vectors
- Unit Outline
- Prerequisite Skills
- Vector Basics
- Adding and Subtracting Vectors
- Multiplying Vectors By Scalars
- Forces as Vectors
- Velocities as Vectors
- Resolving Vectors Into Components
- Algebraic Vectors In Two- and Three-Space
- Magnitudes and Direction Angles
- Operations with Algebraic Vectors
- Dot Product
- Cross Product
- Geometric Applications of Dot/Cross Products
- Work and Torque
- Equations and Intersections of Lines and Planes
- Parametric and Vector Equations of Lines in 2-Space | Video Lesson (not mine)
- Symmetric and Scalar Equations of Lines in 2-Space | Video Lesson (not mine)
- Equations of Lines in 3-Space | Video Lesson (not mine)
- Vector and Parametric Equations of Planes | Video Lesson (not mine)
- Scalar Equation of a Plane | Video Lesson (not mine)
- Sketching Planes
- Intersections of Lines in 2-Space
- Intersections of Lines in 3-Space | Video Lesson (not mine)
- Intersections of Lines and Planes | Video Lesson (not mine)
- Solving Linear Systems with 3 Variables
- Solving Linear Systems Using Matrices | Video Lesson (not mine)
- Intersections of Two Planes | Video Lesson (not mine)
- Intersections of Three Planes | Video Lesson (not mine)
- Distance From a Point To a Line/Plane | Video Lesson (not mine)
- Rates of Change and Limits
- Derivative Rules
- Basic Derivative Rules
- Product Rule
- Chain Rule | (Proof)
- Quotient Rule
- Implicit Differentiation
- Higher-Order Derivatives
- Derivatives of Sinusoidal Functions
- Derivatives of Other Trigonometric Functions
- Derivative of the Exponential Function, y=ex
- Derivative of the Natural Logarithmic Function, y=ln(x)
- Derivative of General Exponential and Logarithmic Functions
- Logarithmic Differentiation
- Curve Sketching and Applications of Derivatives