The gif files and .mov files were developed by David R. Hill, Department of Mathematics,Temple University and are included with his permission. These resources from the Demos with Positive Impact project. The current link is www.mathdemos.org/mathdemos/

[ Tools ] [ Prerequisites for Calculus ] [ Limits and Continuity of Functions ] [ Derivatives ] [ Related Rates ] [ Curve Sketching ] [Optimization Problems ] [ Definite Integral ] [ Integration ] [ Applications of Integration ] [ Review ]

Prerequisites for Calculus

Reference Material

• Introductory Material (123 kb pdf file) - Properities of real numbers, inequalities, intervals, infinity, absolute value, distance/midpoint/slope formula, intercepts, symmetry
• Functions ( kb pdf file) - definitions, examples of domian/range, function notation, odd/even/periodic and composite functions, algebraic functions, transcendental functions, special functions
• Formulas (57.5 kb pdf file) - Areas, volumes and lateral surface areas of triangles, parallelograms, trapezoids, ellipses, circles, sectors, rings, cylinders, cones, spheres amd wedges.
• Trigonometry Formulas -Formulas and Identities
• Algebra Rules - Operations, radicals, exponents,factors, binomial theorem, logs and natural logs

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Exams

Limits and Continuity of Functions

Reference Material

• Limits (html format)- tangent problem, formal definition, informal definition, animation
• Limits (977 kb pdf file)-- tangent problem, formal definition, informal definition

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Exams

Derivatives

Reference Material

Quizzes/Assignments/Labs

Exams

Related Rates

Reference Material

• Related Rates - categories of problems are defined and a series of problems with solutions are provided
•  Problem Defined GIF File Mov File Problem Defined GIF File Mov File Airplane Baseball Conical tank Ellipse Ladder Oil Paint Sand Pile Search Light Shadow Snow Ball Tank

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Exams

Curve Sketching

Reference Material

• Curve Sketching - Concepts of intercetps, symmetry, domain and range, continuity, vertical and horizontal asymptotes, differentiability, increasing and decreasing functions, maximum and minimum values, concavity, points of inflecton, and examples of polynomial, rational, radical and trig function

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Exams

Optimization Problems

Reference Material

• Optimization Problems - derivative tests, rules for solving problems, and a series of problems involving maximum and minimum values
•  Problem Defined Gif File Mov File Problem Defined Gif File Mov File Max Volume Cardboard Box Max Volume of a Cone Minimize Distance between a Curve and a Point Max Area of an Enclosure Maximum Volume Inscribed Cylinder Max Area of an Inscribed Rectangle under a Curve. Max Area of an Inscribed Rectangle in an Isoceles Triangle. Max Area of Printable Surface Walk and Row shortest possible Time Max Viewing Angle Max Enclosed Area

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Exams

Definite Integral

Reference Material

• Definite Integral - Reimann Sums, rules for definite integrals, Fundamental Theorem of Calculus, evaluating integrals, Mean Value Theorem

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Exams

Integration

Reference Material

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Exams

Applications of Integration

Reference Material

•  Disk Method Wire Slice Washer Region Shell Region f(x) = x^2 Pyramid Pyramid x = 0, y = x, y = (x - 1)^2 + 1 y = 0, x = 0, y = 1, y = x^2 + 1 f(x) = sqrtx Semicircular Semicircular y = 1, y = (x - 1)^2 + 1, x = 1 y = 0, y = sinx, x = 0, x = pi f(x) = sinx Square Cross Square Cross y = (x - 1)^2, y = 1, x = 1 y = 0, y = -12+8x-x^2, x = 2, x = 6 Polynomial Equilateral Cross Equilateral Cross y = 1,x = 0, y = x^2 y = 0, x = 0, y = -2x+3 f(x) = x^2sinx Isosceles Cross Isosceles Cross x = y^2, y = x^2 y = =, y = sinx, x = pi/2. x = pi y = sinx, y = 0 y = sqrtx, y = x^2 x = 0, y = 0, x = 1, y = x^2 + 1 y = 1/2 x, y = (x - 1)^2 x = y^2, y = x^2

Quizzes/Assignments/Labs

Exams

Review

Final Exam Review,(80kb pdf file), Answer key (108kb pdf file)