Lesson Description:

Our calculus lesson starts with reviewing the exact definition of what it means to be a function. We then explore different types of algebraic and transcendental functions and their properties. We explore limits and use them to develop and formulate the derivative of a function. We then investigate the derivative and use its properties to solve real life scientific problems using related rates and differentials. We then move into antiderivatives and investigate limits of infinite sums to define the concept of the integral. We then end the course with integration and its applications. For information on how our lesson meets the standards established by the California Department of Education, click here.

Lesson Syllabus:

• Chapter 1: Functions

• Functions defined.
• Algebraic Functions.
• Transcendental Functions
• Function Transformations
• Inverse Functions
• Chapter Test

• Chapter 2: Limits and Rates of Change

• Limits of Functions
• Continuity
• Rates of Change
• Chapter Test

• Chapter 3: The Derivative

• The Derivative Defined
• Differentiation of Algebraic Functions
• Differentiation of Trigonometric Functions
• The Chain Rule
• Implicit Differentiation
• Exponential and Logarithmic Differentiation
• Derivatives of Higher Order
• Antiderivatives
• Chapter Test

• Chapter 4: The Derivative Applied

• Rates of Change
• Related Rates
• Absolute and Local Extrema
• The Mean Value Theorem
• Graphing
• Optimization
• L'Hospitale's Rule
• Newton's Method
• Linear Approximations and differentials
• Chapter Test

• Chapter 5: Integrals

• Area and Distance
• Definite Integrals
• The Fundamental Theorem of Calculus
• Indefinite Integrals
• The Substitution Rule
• Chapter Test

• Chapter 6: Techniques of Integration

• The Substitution Rule
• Integration by Parts
• Partial Fractions
• Improper Integrals
• Chapter Test

• Chapter 7: Integration Applied

• Work
• Area Between Curves
• Arc Length
• Area of a Surface of Revolution
• Applications to Physics and Economics
• Growth and Decay
• Chapter Test

• Chapter 8: Sequences and Series

• Sequences
• Series
• The Comparison Test
• The Alternating Series Test
• The Ratio Test
• Power Series
• Representations of Functions as Power Series
• Taylor and Maclaurin Series
• Chapter Test

• Final Exam

Calculus Sample Lesson
The sample lesson above is exactly the first section in our calculus lesson.

Free Math Support

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Pricing

The price of taking this course along with free math support is $59.95.
Note: You have 18 weeks (the length of a college semester) to complete the course. If you feel that 18 weeks is not enough time, contact us and let us know your reason and we will see if we can make an extension.

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