Math 104: Calculus
About this Course
Math 104: Calculus is designed to prepare you to earn real college credit by passing the Calculus CLEP and Calculus Excelsior exams. This course covers topics that are included on the exams, such as polynomials, factoring, higherorder derivative and intermediate value theorem. Use it to help you learn what you need to know about calculus topics to help you succeed on the exams.
The calculus instructors are experienced and knowledgeable educators who have put together comprehensive video lessons in categories ranging from breaking a complex concept down into its basic components to calculating velocity. Each category is broken down into smaller chapters that will cover topics more indepth. These video lessons make learning fun and interesting. You get the aid of selfgraded quizzes and practice tests to allow you to gauge how much you have learned.
Category  Objectives 

Applications of Derivatives  Learn how to estimate function values using linearization and how to use Newton's method to find roots of equations. Also, study linearization of functions, optimization and differentiation, optimizing complex systems and optimizing simple systems. 
Area Under the Curve and Integrals  Take a look at average value theorem, definite integrals, indefinite integrals as antiderivatives, linear properties of definite integrals, the fundamental theorem of calculus, sum notation and the trapezoid rule. Learn how to find the arc length of a function, find the limits of Riemann sums, to identify and draw left, right and middle sums, use Riemann sums for functions and graphs and use Riemann sums to calculate integrals. 
Calculating Derivatives and Derivative Rules  Discover how to apply the rules of differentiation to calculate derivatives, calculate derivatives of exponential equations and find derivatives of implicit functions. Additionally, take a look at derivatives of polynomial equations, derivatives of trigonometric functions, higherorder derivatives, derivatives of inverse trigonometric functions and linear properties of a derivative. 
Continuity  Study continuity in a function, discontinuities in functions and graphs, intermediate value theorem and regions of continuity in a function. 
Differential Equations  Find out about differential notation in physics, separation of variables to solve system differential equations and calculating rate and exponential growth. 
Geometry and Trigonometry in Calculus  Learn to find distance with the Pythagorean theorem, calculate the volumes of basic shapes and solve visualizing geometry problems. Also study sine and cosine. 
Graphing and Functions  Discover concepts that include compounding functions and graphing functions of functions, figuring the equation of a line using pointslope formula, graphing exponentials and logarithms and graphing basic functions. Additionally, study horizontal and vertical asymptotes, implicit functions, exponents, slopes and tangents. 
Graphing Derivatives and L'Hopital's Rule  Learn to apply L'Hopital's Rule and about concavity and inflection points on graphs, function properties from derivatives, identifying functions from derivative graphs, graphing the derivative from any function, determining maximum and minimum values of a graph and nondifferentiable graphs of derivatives. 
Integration and Integration Techniques  Examine antiderivatives, integrals of simple shapes, integrals of exponential functions, integrals of trigonometric functions and improper integrals. Also take a look at how to solve integrals using substitution, how to use trigonometric substitution to solve integrals and how to factorize fractions with quadratic denominators. 
Integration Applications  Learn how to calculate volumes using single intervals, find area between functions with integration, find simple areas with root finding and integration and find volumes of revolution with integration. 
Limits  Study concepts including asymptotes, infinity, limits, continuity and the squeeze theorem, Also learn to determine the limits of functions and use a graph to define limits. 
Rate of Change  Examine derivatives, Rolle's theorem, velocity and the rate of change. Additionally, look at the definition of mean value theorem and 'differentiable.' 
Using Scientific Calculators for Calculus  Discover how to use a scientific calculator, solve equations on a scientific calculator and understand radians and degrees on a scientific calculator. Also study trigonometry functions and exponentials on a calculator. 
100% developed
Course Chapters
Graphing and Functions
All Videos in Graphing and Functions
 1. What is a Function: Basics and Key Terms
 2. Graphing Basic Functions
 3. Compounding Functions and Graphing Functions of Functions
 4. Understanding and Graphing the Inverse Function
 5. Polynomials Functions: Properties and Factoring
 6. Polynomials Functions: Exponentials and Simplifying
 7. Exponentials, Logarithms & the Natural Log
 8. Slopes and Tangents on a Graph
 9. Equation of a Line Using PointSlope Formula
 10. Horizontal and Vertical Asymptotes
 11. Implicit Functions
Limits
All Videos in Limits
Rate of Change
All Videos in Rate of Change
Calculating Derivatives and Derivative Rules
All Videos in Calculating Derivatives and Derivative Rules
 1. Using Limits to Calculate the Derivative
 2. The Linear Properties of a Derivative
 3. Calculating Derivatives of Trigonometric Functions
 4. Calculating Derivatives of Polynomial Equations
 5. Calculating Derivatives of Exponential Equations
 6. Using the Chain Rule to Differentiate Complex Functions
 7. Differentiating Factored Polynomials: Product Rule and Expansion
 8. When to Use the Quotient Rule for Differentiation
 9. Understanding Higher Order Derivatives Using Graphs
 10. Calculating Higher Order Derivatives
 11. How to Find Derivatives of Implicit Functions
 12. How to Calculate Derivatives of Inverse Trigonometric Functions
 13. Applying the Rules of Differentiation to Calculate Derivatives
Graphing Derivatives and L'Hopital's Rule
All Videos in Graphing Derivatives and L'Hopital's Rule
 1. Graphing the Derivative from Any Function
 2. Non Differentiable Graphs of Derivatives
 3. How to Determine Maximum and Minimum Values of a Graph
 4. Using Differentiation to Find Maximum and Minimum Values
 5. Concavity and Inflection Points on Graphs
 6. Understanding Concavity and Inflection Points with Differentiation
 7. Data Mining: Function Properties From Derivatives
 8. Data Mining: Identifying Functions From Derivative Graphs
 9. What is L'Hopital's Rule?
 10. Applying L'Hopital's Rule in Simple Cases
 11. Applying L'Hopital's Rule in Complex Cases
Applications of Derivatives
All Videos in Applications of Derivatives
Area Under the Curve and Integrals
All Videos in Area Under the Curve and Integrals
 1. Summation Notation and Mathematical Series
 2. How to Use Riemann Sums for Functions and Graphs
 3. How to Identify and Draw Left, Right and Middle Riemann Sums
 4. What is the Trapezoid Rule?
 5. How to Find the Limits of Riemann Sums
 6. Definite Integrals: Definition
 7. How to Use Riemann Sums to Calculate Integrals
 8. Linear Properties of Definite Integrals
 9. Average Value Theorem
 10. The Fundamental Theorem of Calculus
 11. Indefinite Integrals as Anti Derivatives
 12. How to Find the Arc Length of a Function
Integration and Integration Techniques
All Videos in Integration and Integration Techniques
 1. Calculating Integrals of Simple Shapes
 2. AntiDerivatives: Calculating Indefinite Integrals of Polynomials
 3. How to Calculate Integrals of Trigonometric Functions
 4. How to Calculate Integrals of Exponential Functions
 5. How to Solve Integrals Using Substitution
 6. Substitution Techniques for Difficult Integrals
 7. Using Integration By Parts
 8. Partial Fractions: How to Factorize Fractions with Quadratic Denominators
 9. How to Integrate Functions With Partial Fractions
 10. Understanding Trigonometric Substitution
 11. How to Use Trigonometric Substitution to Solve Integrals
 12. How to Solve Improper Integrals
Differential Equations
All Videos in Differential Equations

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