Chapter 7: Limits and Derivatives
7.1 Limits and Convergence
Introduction to Limits
Introduction to Calculus
7.2 The Definition of the Derivative
Understanding the Definition of the Derivative
Sketching the Derivative of a Function
Visualizing Graphs of Functions and their Derivatives
Derivative Intuition
Recognizing Slopes of Curves
Graphs of Functions and Their Derivatives
Finding a Derivative from First Principles
Example 1 Example 2
The Power Rule
Example 1 Example 2 Example 3
Example 4 Example 5 Example 6
Finding the Equation of the Tangent Line
Tangent Line Parallel to Given Line
Finding the Tangent Line with the TI-84 Casio
Finding the Equation of the Normal Line
7.3 More Rules for Derivatives
The Product Rule
Introduction Examples Proof
The Quotient Rule
Introduction Examples
Proofs of Derivatives of ln x and ex
Finding the Equation of the Tangent and Normal Line
7.4 The Chain Rule
General Explanation: Part 1 Part 2 Examples
Simple Examples: Ex 1 Ex 2 Ex 3
Harder Examples: Ex 1 Ex 2 Ex 3
With Product Rule: Ex 1 Ex 2
With Quotient Rule
Mixed Derivatives: Ex 1 Ex 2 Ex 3
7.5 The Derivative and Kinematics
Position, Velocity, and Acceleration
Various Examples
7.6 The Derivative and Graphing
Critical Numbers Definition Ex 1 Ex 2
Local Max/Min, Inc/Dec: From a Function
Local Max/Min – Second Derivative Test
Concavity and Second Derivatives
Sketching the Curve Using Calculus Part 1 Part 2
Sketching the Curve Summary Part 1 Part 2
Part 3 Part 4
7.7 Optimization
Optimization Problem #1
Optimization Problem #2
Optimization Problem #3 – Making a Rain Gutter!
Chapter 9a: Integration Rules9.1 Antiderivatives and Indefinite Integration
Basic Integration Rules
Basic Integration examples
9.2 More on Indefinite Integrals
Integral of 1/x (watch only until 2:30)
Integral of ex
Integrals: Exponential Functions – Ex 1 and 2
Integrals: Exponential Functions – Ex 3 and 4
9.2 Integration by Substitution
Simple examples (ignore the third example...)
Another 2 Examples
Multiply / divide by a constant
Multiply / divide by a constant
Example with ex
Example with 1/x
More Complicated
Chapter 14: Calculus with Trigonometric Functions14.1 Derivatives of Sine, Cosine, and Tangent
Example 1 Example 2
14.2 More Practice with Derivatives
14.3 Integrals of Sine and Cosine
Trigonometric integrals - Basic examples
14.4 Revisiting Linear Motion
Chapter 9b: Applications of Integration9.3 Area and Definite Integrals
Definite Integral – Understanding the Definition
Approximating a Definite Integral Using Rectangles
9.4 The Fundamental Theorem of Calculus
Properties of Integrals
9.5 Area Between Curves
Areas Between Curves
9.6 Volumes of Revolution
Example 1 Example 2
9.7 Integrals and Kinematics
Example 1 Example 2
Chapter 12: Vectors12.1 Vectors: Basic Concepts
12.2 Addition and Subtraction of Vectors
Introduction to Vectors
Adding vectors
Subtracting vectors
Scalar multiplication
Magnitude and unit vector
Finding a Unit Vector
Vector algebra
Vectors in 3D
Magnitude and Direction of a Vector
Components of a Vector
12.3 Scalar Product
Intro to the Scalar Product
Perpendicular vectors
Exam Question
Perpendicular to two vectors
12.4 Vector Equation of a Line
Vector Equation of a Line: Introduction
Example 1 Example 2
Vector Equations to Cartesian Equations
Parallel Lines
Intersecting and Skew Lines
Exam Question 1 Exam Question 2
Exam Question 3 Exam Question 4
12.5 Applications of Vectors
Position and Time
Constant Velocity
Exam Question 1 Exam Question 2
Exam Question 3
7.1 Limits and Convergence
Introduction to Limits
Introduction to Calculus
7.2 The Definition of the Derivative
Understanding the Definition of the Derivative
Sketching the Derivative of a Function
Visualizing Graphs of Functions and their Derivatives
Derivative Intuition
Recognizing Slopes of Curves
Graphs of Functions and Their Derivatives
Finding a Derivative from First Principles
Example 1 Example 2
The Power Rule
Example 1 Example 2 Example 3
Example 4 Example 5 Example 6
Finding the Equation of the Tangent Line
Tangent Line Parallel to Given Line
Finding the Tangent Line with the TI-84 Casio
Finding the Equation of the Normal Line
7.3 More Rules for Derivatives
The Product Rule
Introduction Examples Proof
The Quotient Rule
Introduction Examples
Proofs of Derivatives of ln x and ex
Finding the Equation of the Tangent and Normal Line
7.4 The Chain Rule
General Explanation: Part 1 Part 2 Examples
Simple Examples: Ex 1 Ex 2 Ex 3
Harder Examples: Ex 1 Ex 2 Ex 3
With Product Rule: Ex 1 Ex 2
With Quotient Rule
Mixed Derivatives: Ex 1 Ex 2 Ex 3
7.5 The Derivative and Kinematics
Position, Velocity, and Acceleration
Various Examples
7.6 The Derivative and Graphing
Critical Numbers Definition Ex 1 Ex 2
Local Max/Min, Inc/Dec: From a Function
Local Max/Min – Second Derivative Test
Concavity and Second Derivatives
Sketching the Curve Using Calculus Part 1 Part 2
Sketching the Curve Summary Part 1 Part 2
Part 3 Part 4
7.7 Optimization
Optimization Problem #1
Optimization Problem #2
Optimization Problem #3 – Making a Rain Gutter!
Chapter 9a: Integration Rules9.1 Antiderivatives and Indefinite Integration
Basic Integration Rules
Basic Integration examples
9.2 More on Indefinite Integrals
Integral of 1/x (watch only until 2:30)
Integral of ex
Integrals: Exponential Functions – Ex 1 and 2
Integrals: Exponential Functions – Ex 3 and 4
9.2 Integration by Substitution
Simple examples (ignore the third example...)
Another 2 Examples
Multiply / divide by a constant
Multiply / divide by a constant
Example with ex
Example with 1/x
More Complicated
Chapter 14: Calculus with Trigonometric Functions14.1 Derivatives of Sine, Cosine, and Tangent
Example 1 Example 2
14.2 More Practice with Derivatives
14.3 Integrals of Sine and Cosine
Trigonometric integrals - Basic examples
14.4 Revisiting Linear Motion
Chapter 9b: Applications of Integration9.3 Area and Definite Integrals
Definite Integral – Understanding the Definition
Approximating a Definite Integral Using Rectangles
9.4 The Fundamental Theorem of Calculus
Properties of Integrals
9.5 Area Between Curves
Areas Between Curves
9.6 Volumes of Revolution
Example 1 Example 2
9.7 Integrals and Kinematics
Example 1 Example 2
Chapter 12: Vectors12.1 Vectors: Basic Concepts
12.2 Addition and Subtraction of Vectors
Introduction to Vectors
Adding vectors
Subtracting vectors
Scalar multiplication
Magnitude and unit vector
Finding a Unit Vector
Vector algebra
Vectors in 3D
Magnitude and Direction of a Vector
Components of a Vector
12.3 Scalar Product
Intro to the Scalar Product
Perpendicular vectors
Exam Question
Perpendicular to two vectors
12.4 Vector Equation of a Line
Vector Equation of a Line: Introduction
Example 1 Example 2
Vector Equations to Cartesian Equations
Parallel Lines
Intersecting and Skew Lines
Exam Question 1 Exam Question 2
Exam Question 3 Exam Question 4
12.5 Applications of Vectors
Position and Time
Constant Velocity
Exam Question 1 Exam Question 2
Exam Question 3