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# Nelson Calculus and Vectors/Grade 12

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## Nelson Calculus and Vectors/Grade 12

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The Nelson Calculus and Vectors - Student Textbook supports the Ontario Ministry of Education
CourseCalculus and Vectors, Grade 12, University Prepration, Course Code: MCV4U
Author Team: Robert Donato, Ruth Malinowski, Dean Murray, Jeffrey Shifrin, Lorine Wilson, Dave Wright
Chapter 1: Introduction to Calculus
1.2 The Slope of a Tangent
1.3 Rates of Change
1.4 Limit of a Function
1.5 Properties of Limits
1.6 Continuity
Chapter 2: Derivatives
2.1 The Derivative Function
2.2 The Derivatives of Polynomial Functions
2.3 The Product Rule
2.4 The Quotient Rule
2.5 The Derivatives of Composite Functions
Chapter 3: Derivatives and their Applications
3.1 Higher Order Derivaties, Velocity and Accerleration
3.2 Minimum and Maximum on an Interval (Extreme Values)
3.3 Optimization Problems
3.4 Optimization Problems in Economics and Science
Chapter 4: Curve Sketching
4.1 Increasing and Decreasing Functions
4.2 Critical Points, Local Maxima, and Local Minima
4.3 Vertical and Horizontal Asymptotes
4.4 Concavity and Points of Inflection
4.5 An Algorithm for Curve Sketching
Chapter 5: Derivatives of Exponential and Trigonometric Functions
5.1 Derivaties of Exponential Functions, y= ex
5.2 The Derivatie of the General Exponential Function, y= bx
5.3 Optimization Problems Involving Exponential Functions
5.4 The Derivatives of y = sin x and y = cos x
5.5 The Derivative of y = tan x
Chapter 6: An Introduction to Vectors
6.1 An Introduction to Vectors
6.3 Multiplication of a Vector by a Scalar
6.4 Properties of Vectors
6.5 Vectors in R2 and R3
6.6 Operations with Algebraic Vectors R2
6.7 Operations with Vectors R3
6.8 Linear Combinations and Spanning Sets
Chapter 7: Applications of Vectors
7.1 Vectors as Forces
7.2 Velocity
7.3 The Dot Product of Two Geometric Vectors
7.4 The Dot Product of Algebraic Vectors
7.5 Scalar and Vector Projections
7.6 The Cross Product of Two Vectors
7.7 Applications of the Dot Product and Cross Product
Chapter 8: Equations of Lines and Planes
8.1 Vector and Parametric Equations of a Line in R2
8.2 Cartesian Equation of a Line
8.3 Vector, Parametric and Synmetric Equations of a Line in R3
8.4 Vector and Parametric Equations of a Plane
8.5 The Cartesian Equation of a Plane
8.6 Sketching Planes in R3
Chapter 9: Relationships between Points, Lines and Planes
9.1 The Intersection of a Line with a Plane and the Intersection of Two Lines
9.2 Systems of Equations
9.3 The Intersection of Two Planes
9.4 The Intersection of Three Planes
9.5 The Distance from a Point to a Line in R2 and R3
9.6 The Distance from a Point to a Plane
Each chapter has Review, Self-Test, and Task (or Math Project).
Answers are at the end of book.
Hardcover, 696 pages, book size: 21 cm x 26 cm x 3 cm

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