# Guide Calculus I

Such requests will routinely be denied, and a student who wishes to take Calculus I for a third time must demonstrate that there was a compelling excuse for at least one of their two F's. Engineering students must take Math Schedule of Sections: This option will not work correctly.

## Calculus I - National University

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Contact Us. Mean value theorem : Analyzing functions Extreme value theorem and critical points : Analyzing functions Intervals on which a function is increasing or decreasing : Analyzing functions Relative local extrema : Analyzing functions Absolute global extrema : Analyzing functions Concavity and inflection points intro : Analyzing functions. Analyzing concavity and inflection points : Analyzing functions Second derivative test : Analyzing functions Sketching curves : Analyzing functions Connecting f, f', and f'' : Analyzing functions Solving optimization problems : Analyzing functions Analyzing implicit relations : Analyzing functions Calculator-active practice : Analyzing functions.

Accumulations of change introduction : Integrals Approximation with Riemann sums : Integrals Summation notation review : Integrals Riemann sums in summation notation : Integrals Defining integrals with Riemann sums : Integrals Fundamental theorem of calculus and accumulation functions : Integrals Interpreting the behavior of accumulation functions : Integrals Properties of definite integrals : Integrals. Fundamental theorem of calculus and definite integrals : Integrals Reverse power rule : Integrals Indefinite integrals of common functions : Integrals Definite integrals of common functions : Integrals Integrating with u-substitution : Integrals Integrating using long division and completing the square : Integrals Integrating using trigonometric identities : Integrals Proof videos : Integrals.

Differential equations. Differential equations introduction : Differential equations Verifying solutions for differential equations : Differential equations Sketching slope fields : Differential equations. Reasoning using slope fields : Differential equations Separation of variables : Differential equations Particular solutions to differential equations : Differential equations Exponential models : Differential equations.

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Applications of integrals. Average value of a function : Applications of integrals Straight-line motion : Applications of integrals Non-motion applications of integrals : Applications of integrals Area: vertical area between curves : Applications of integrals Area: horizontal area between curves : Applications of integrals Area: curves that intersect at more than two points : Applications of integrals. Volume: squares and rectangles cross sections : Applications of integrals Volume: triangles and semicircles cross sections : Applications of integrals Volume: disc method revolving around x- and y-axes : Applications of integrals Volume: disc method revolving around other axes : Applications of integrals Volume: washer method revolving around x- and y-axes : Applications of integrals Volume: washer method revolving around other axes : Applications of integrals Calculator active practice : Applications of integrals.

Apply derivative rules to the inverse trigonometric functions.

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Solve related rates problems. To use the derivative in applications.

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Define local and absolute maxima and minima. Analyze the graph of a function through its first and second derivatives.

Create an accurate graph of a function through the use of limits and derivatives. Solve optimization problems.

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## Calculus I

Use linear approximation to approximate the value of a function, and to define the relationship between differentials dy and dx. Apply the Mean Value Theorem. To set up, compute and evaluate integrals. Approximate the area under the curve using left, right and midpoint Riemann sums.

## MATH230G - Calculus I

Evaluate definite integrals. Apply the Fundamental Theorem of Calculus. Evaluate definite integrals using symmetry. Apply the substitution rule. Calculate the position, velocity, displacement and distance travelled by an object as well as the net change and future value of an object. Compute the area of a region bounded by two or more curves.

To be completed by instructor.

Methods of presentation can include lectures, discussion, demonstration, experimentation, audio-visual aids, group work, and regularly assigned homework. Use of a computer algebra system is recommended. Mathematica is available for use at the College at no charge. Course may be taught as face-to-face, hybrid or online course. Note: Current textbook information for each course and section is available on Oakton's Schedule of Classes. If you have a documented learning, psychological, or physical disability you may be entitled to reasonable academic accommodations or services.

All students are expected to fulfill essential course requirements. The College will not waive any essential skill or requirement of a course or degree program.