Course Resources Math 1910

Chapter 1 – Functions and Models

Knowledge of materials presented in Chapter 1 is essential to be successful in the course. Students may not be prepared to start Calculus I without these basic pre-calculus concepts. If the material in Chapter 1 is unclear, the student may consider taking Math 1710 and Math 1720 instead.

 

Chapter 2 – Limits and Derivative

2.2 The Limit of a function(C1)

• Introduction to Limits (HD)
• Introduction to Limits : Introduction to the intuition behind limits

2.3 Calculating limits Using Limit Laws(C1)

• Introduction to Limits: Introduction to the intuition behind limits
• Squeeze Theorem: Intuition (but not a proof) of the Squeeze Theorem
• Proof: lim (sin x)/x
• Epsilon Delta Limit Definition 2

2.6 Derivatives and Rates of Change(C3)

• Calculus: Derivatives 1
• Calculus: Derivatives 2 (new HD version)
• Calculus: Derivatives 2.5 (new HD version)
• Calculus: Derivatives 1
• Calculus: Derivatives 2

2.7 The Derivative as a Function(C6)

• Derivative Intuition Module --Khan Academy

 

Chapter 3 – Differentiation Rules

3.4 The Chain Rule(C5)

• Product Rule

3.5 Implicit Differentiation(C5)

• Implicit Differentiation

3.7 Derivatives of Logarithmic Functions(C4)

• Calculus: Derivative of x^(x^x)

 

Chapter 4 –Applications of Differentiation

4.2 Maximum and Minimum Values(C6)

• Cylinder Volume and Surface Area
  (review)
• Volume of a Sphere
  (review)
• Calculus: Graphing Using Derivatives
• Calculus Graphing with Derivatives Example

4.3 Derivatives and the Shape of Curves(C6)

• Mean Value Theorem

4.5 Indeterminate Forms and L’Hospital Rule(C1)

• Introduction to L'Hopital's Rule
• L'Hopital's Rule Example 1
• L'Hopital's Rule Example 2
• L'Hopital's Rule Example 3

4.8 Antiderivatives(C8)

• The Indefinite Integral or Anti-derivative
• Indefinite integrals (part II)
• Indefinite Integration (part III)
• Simple Differential Equations

 

Chapter 5 – Integrals

5.1 Area and Distance(C9)

• Introduction to definite integrals
• Definite integrals (part II)
• Definite Integrals (area under a curve) (part III)

5.4 The Fundamental Theorem of Calculus(C10)

• 2011 Calculus AB Free Response #1a
• 2011 Calculus AB Free Response #1 parts b c d
• 2011 Calculus AB Free Response #2 (a & b)
• 2011 Calculus AB Free Response #2 (c & d)
• 2011 Calculus AB Free Response #3 (a & b)
• 2011 Calculus AB Free Response #3 (c)
• 2011 Calculus AB Free Response #4a : Taking derivatives and integrals of strangely defined functions
• 2011 Calculus AB Free Response #4b: Absolute maximum over an interval. Critical points and differentiability
• 2011 Calculus AB Free Response #4c : Finding the points of inflection for a strangely defined function
• 2011 Calculus AB Free Response #4d : Mean Value Theorem and differentiability
• 2011 Calculus AB Free Response #5a : Using a tangent line to extrapolate a function from a known initial condition
• 2011 Calculus AB Free Response #5b : Using the second derivative
• 2011 Calculus AB Free Response #5c: Solving a differential equation using separation of variables
• 2011 Calculus AB Free Response #6a : Continuity of piecewise-defined functions
• 2011 Calculus AB Free Response #6b : Derivative of a piecewise-defined function
• 2011 Calculus AB Free Response #6c : Average value of a piecewise-defined function on an interval