Calculus and Vectors Notes and Information

Course Outline

Learning Goals

Reassessment Criteria

Classroom Expectations

Part 1: Vectors (Chapters 6 - 9)

Chapter 6 - Introduction to Vectors (GA1 & GA2)

 Getting Ready for Vectors Complete Note

 6.1 An Introduction to Vectors     Complete Note

 6.2 Vector Addition Complete Note

 6.3 Multiplication of a Vector by a Scalar  Complete Note

 6.4 Properties of Vectors Complete Note

 6.5 Vectors in R^2 and R^3 Complete Note

 6.6 & 6.7 Operations with Vectors in R^2 and R^3 Complete Note

 6.8 Linear Combinations and Spanning Sets Complete Note

 Chapter 6 Review

Chapter 7 - Applications of Vectors (GA1 & GA2)

 7.1 Vectors as Forces & 7.2 Velocity Complete Note

 7.3 The Dot Product of Geometric Vectors Complete Note

 7.4 The Dot Product of Algebraic Vectors    Complete Note

 7.5 Scalar and Vector Projections (Partially Complete) Last part 

 7.6 The Cross Product Complete Note

 Start Test Review

Chapter 8 - Equations of Lines and Planes (GA3 & GA4)

 8.1 Vector and Parametric Equations of a Line in R^2 Complete Note

 8.2 The Cartesian Equation of a Line  Complete Note

 8.3 Vector, Parametric & Symmetric Equations of a Line in R^3 Complete Note

 8.4 Vector and Parametric Equations of a Plane Complete Note

 8.5 The Cartesian Equation of a Plane Complete Note

8.6 Sketching Planes in R^3 (You are going to make your own note, and then we will discuss the concepts together.)

 Chapter 8 Review

Chapter 9 - Relationships Between Points, Lines and Planes (GA3 & GA4)

 Vector Appendix to prepare for Chapter 9 Complete Note

 9.1 The Intersection of a Line with a Plane and the Intersection of Two Lines Complete Note

 9.2 Systems of Equations; 9.5 The Distance from a Point to a Line Complete Note

 9.3 The Intersection of Two Planes; 9.6 The Distance from a Point to a Plane Complete Note

Oct. 26 - 9.4 The Intersection of Three Planes (This will be a handout/guided reading activity; I will have models in the room); Quiz 9.1, 9.2 & 9.5

 Chapter 9 Review

 Vectors Review 

Part 2: Calculus (Chapters 1 - 5) 

Chapter 1: Introduction to Calculus (RC1)

 1.1 Radical Expressions: Rationalizing Denominators Complete Note

 Advanced Functions Review/Preview & 1.2 The Slope of a Tangent Line Complete Note

 1.3 Rates of Change Complete Note

 1.4 The Limit of a Function Complete Note

 1.5 The Properties of Limits          Complete Note

 1.6 Continuity Complete Note

 Chapter 1 Review

Chapter 2: Derivatives & Chapter 5: Derivative of Exponential and Trigonometric Functions (RC2 & RC3)

 2.1 The Derivative Function Complete Note

 2.2 The Derivatives of Polynomial Functions Complete Note

2.3 The Product Rule Complete Note

 2.4 The Quotient Rule Complete Note

 2.5 The Derivatives of Composite Functions  Complete Note

 5.4 The Derivatives of y=sinx and y=cos x  Complete Note (There will also be a handout on the 5th to look at characteristics of graphs) Note from Dec. 5

 5.5 The Derivative of y = tan x Complete Note

 3.1 Higher Order Derivatives, Velocity, and Acceleration Complete note

 Derivatives Review

Chapter 3: Derivatives and Their Applications (AD2)

3.2 Maximum and Minimum Values on an Interval Complete Note

3.3 Optimization Problems Complete Note

3.4 Optimization Problems in Economics and Science Complete Note

Chapter 4: Curve Sketching (AD1)

 4.1 Increasing and Decreasing Functions & 4.2 Critical Points, Local Maxima, and Local Minima Complete Note

4.3 Vertical and Horizontal Asymptotes  Complete note

 4.4 Concavity and Points of Inflection  Complete Note

 4.5 An Algorithm for Curve Sketching Complete Note

 Test Review

 5.1 & 5.2 Derivatives of Exponential Functions Complete Note

 Exam Review

Additional Materials

Weeks 1 & 2 - Implicit Differentiation

Weeks 3 to 6 - Related Rate Problems

Weeks 7 & 8 - Antiderivatives

Weeks 9 to13 - Definite Integrals

Last week! - Indefinite Integrals (A quick look)

Those of you that took this course first semester, please remember that we have plans for Thursdays at lunch so that you can get ahead for next year!

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