This course includes a thorough study of differentiation and integration with many applications. Limits and continuity are investigated in-depth. The course will emphasize the importance of mathematics studied to date. After completion of this course, the student may wish to take the Advanced Placement Test.

**1- Introduction & Review**

1- Welcome to Calculus

2- Course Outline

3- Course Syllabus

4- Completing Math Assessments

5- Calculus On The Web

6- Review — Stuff You Should Already Know

7- Pretest

Assignment: Calculus Pretest

**2- Limits & Continuity**

1- An Introduction to Limits & Continuity

Quiz: Introduction to Limits & Continuity

2- Tangent Lines & Rates of Change

Handout: Tangent Lines & Rates of Change Worksheet

Assignment: Tangent Lines & Rates of Change

3- The Limit

Handout: The Limit Worksheet

Assignment: The Limit

4- One-Sided Limits

Handout: One-Sided Limits Worksheet

Assignment: One-Sided Limits

5- Computing Limits

Handout: Computing Limits Worksheet

Assignment: Computing Limits

6- Infinite Limits

Handout: Infinite Limits Worksheet

Assignment: Infinite Limits

7- Limits at Infinity

Handout: Limits at Infinity Worksheet

Assignment: Limits at Infinity

8- Continuity

Handout: Continuity Worksheet

Assignment: Continuity

9- Additional Resources

Handout: Limits & Continuity Exam

Assignment: Limits & Continuity Exam

**3- Derivatives**

1- Introduction to Derivatives

3- Definition & Interpretation of the Derivative

Handout: Definition & Interpretation of the Derivative Worksheet

Assignment: Definition & Interpretation of the Derivative

4- Differentiation Formulas

Handout: Differentiation Formulas Worksheet

Assignment: Differentiation Formulas

5- Product & Quotient Rule

Handout: Product & Quotient Rule Worksheet

Assignment: Product & Quotient Rule

6- Derivatives of Trig Functions

Handout: Derivatives of Trig Functions Worksheet

Assignment: Derivatives of Trig Functions

7- Derivatives of Exponential & Logarithm Functions

Handout: Derivatives of Exponential & Logarithm Functions Worksheet

Assignment: Derivatives of Exponential & Logarithm Functions

8- The Chain Rule

Handout: The Chain Rule Worksheet

Assignment: The Chain Rule

9- Implicit Differentiation

Handout: Implicit Differentiation Worksheet

Assignment: Implicit Differentiation

10- Related Rates

Handout: Related Rates Worksheet

Assignment: Related Rates

11- Higher Order Derivatives

Handout: Higher Order Derivatives Worksheet

Assignment: Higher Order Derivatives

12- Additional Resources

Handout: Derivatives Exam

Assignment: Derivatives Exam

**4- Applications of Derivatives**

1- What’s the Big Deal About Derivatives, Anyway?

2- Rates of Change

3- Critical Points & Extrema

Handout: Critical Points & Extrema Worksheet

Assignment: Critical Points & Extrema

4- The Shape of a Graph

Handout: The Shape of a Graph Worksheet

Assignment: The Shape of a Graph

5- The Mean Value Theorem

Handout: The Mean Value Theorem Worksheet

Assignment: The Mean Value Theorem

6- Optimization

Handout: Optimization Worksheet

Assignment: Optimization

7- Linear Approximations

Handout: Linear Approximations Worksheet

Assignment: Linear Approximations

8- Midtest

Assignment: Calculus Midtest

Handout: Applications of Derivatives

Assignment: Applications of Derivatives

**5- Integrals**

1- Working Backwards

2- Indefinite Integrals

Handout: Indefinite Integrals Worksheet

Assignment: Indefinite Integrals

3- Computing Indefinite Integrals

Handout: Computing Indefinite Integrals Worksheet

Assignment: Computing Indefinite Integrals

4- Substitution Rule for Indefinite Integrals

Handout: Substitution Rule Worksheet

Assignment: Substitution Rule

5- Area Problem

Handout: Area Problem Worksheet

Assignment: Area Problem

6- Definite Integrals

Handout: Definite Integrals Worksheet

Assignment: Definite Integrals

7- Computing Definite Integrals

Handout: Computing Definite Integrals Worksheet

Assignment: Computing Definite Integrals

8- Substitution Rule for Definite Integrals

Handout: Substitution Rule for Definite Integrals Worksheet

Assignment: Substitution Rule for Definite Integrals

9- Integration by Parts

Handout: Integration by Parts Worksheet

Assignment: Integration by Parts

10- Partial Fractions

Handout: Partial Fractions Worksheet

Assignment: Partial Fractions

11- Improper Integrals

Handout: Improper Integrals Worksheet

Assignment: Improper Integrals

12- Additional Resources

Handout: Integrals Exam

Assignment: Integrals

**6- Applications of Integrals**

1- What’s the Big Deal About Integrals, Anyway?

2- Area Between Curves

Handout: Area Between Curves Worksheet

Assignment: Area Between Curves

3- Volumes of Solids of Revolution (Part 1)

Handout: Method of Rings Worksheet

Assignment: Method of Rings

4- Volumes of Solids of Revolution (Part 2)

Handout: Method of Cylinders Worksheet

Assignment: Method of Cylinders

5- Volume

6- Work

Handout: Work Worksheet

Assignment: Work

Assignment: Applications of Integrals

**7- Sequences & Series**

1- Sequences & Series

2- Sequences

3- Series: The Basics

4- Series: Convergence & Divergence

5- Special Series

6- Integral Test

7- Comparison Test

8- Alternating Series Test

9- Absolute Convergence

10- Ratio & Root Tests

11- Strategy for Series

12- Estimating the Value of a Series

13- Power Series

14- Taylor Series

15- Additional Resources

16- Post-Test

Assignment: Sequences & Series

**8- Course Survey**

Handout: Course Survey

Assignment: Course Survey

Call 800.890.6269 / 561.537.5501