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, higher-order 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 in-depth. These video lessons make learning fun and interesting. You get the aid of self-graded quizzes and practice tests to allow you to gauge how much you have learned.

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 anti-derivatives, 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, higher-order 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 point-slope 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 non-differentiable graphs of derivatives.
Integration and Integration Techniques Examine anti-derivatives, 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.

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