Calculus 12

Our plan ! 

If you miss a class, please go into TEAMS and  work through the lesson at home.

 ₀ PreCalculus skills (4 hours)

Lines

Slope as rate of change

Equations of lines

Functions and graphs

Functions – difference quotient

Domain and range

Piecewise functions

Trigonometric functions

Graphs of basic trigonometric functions

 

1. Limits and Their Properties (5 hours)

1.2 Finding Limits Graphically and Numerically                                                  

1.3 Evaluating Limits Analytically

1.4 Continuity and One-Sided Limits 

• Intermediate Value Theorem
• Removable discontinuities

1.5 Infinite Limits

EXTRA :  l’HOPITAL’S LAW       

 

 

2. Differentiation (11 hours)

 

2.1 The Derivative and the Tangent Line Problem

2.2 Basic Differentiation Rules and Rates of Change

2.2.1 Higher-Order Derivatives

2.3 The Product and Quotient Rules

2.3.1 Velocity and Acceleration Problems

2.4 The Chain Rule

2.5 Implicit Differentiation

2.6 Related Rate

 

 

3. Applications of Differentiation (11 hours)

 

3.1 Extrema on an Interval 

3.2 Rolle's Theorem and the Mean Value Theorem

3.3 Increasing and Decreasing Functions and the First Derivative

3.4 Concavity and the Second Derivative Test Points of Inflection

3.4.b  sketching derivative functions

3.5 Limits at Infinity  -  asymptotes

3.6 A Summary of Curve Sketching

3.7 Optimization Problems

3.8 Newton's Method - Linearization Models

 

4. Integration (12 hours)

 

4.1 Antiderivatives and Indefinite Integration

4.2 Area under the curve

4.3 Riemann Sums and Definite Integrals 

4.3  Trapezoid rule       

4.4 The Fundamental Theorem of Calculus   

• Average Value of a Function on an Interval

4.5 Integration by Substitution ( “U”-substitution )

4.6  Integration  by parts

5. Logarithmic & Exponential Functions (12 hours)

 

5.0 What is a logarithm ?    properties ?

5.1 The Natural Logarithmic Function: Differentiation

5.2 The Natural Logarithmic Function: Integration

5.3 Inverse Functions

5.4 Exponential Functions: Differentiation and Integration

5.5 Bases Other Than e and Applications

5.6 Differential Equations: Growth and Decay

5.7 Differential Equations: Separation of Variables    

• Slope fields

5.8 Inverse Trigonometric Functions: Differentiation

5.9 Inverse Trigonometric Functions: Integration

 

 

 

6. Applications of Integration (8 hours)

 

6.1 Area of a Region between two curves

6.2 Volume: The Disk Method and solids with known Cross-Sections 

6.3 Volume: The Shell Method