Inequalities Includes Absolute Value

Transcription

1 CALCULUS WEBSITES ALGEBRA TOPICS & SKILLS Inequalities Includes Absolute Value Slopes & Equations of Lines Notes & Practice Parallel & Perpendicular Lines Notes & Practice Factoring Polynomials Notes & Practice Rational Expressions Notes & Practice Complex Fractions Notes & Practice Completing the Square Notes & Practice Quadratic Equations & the Quadratic Formula Notes & Practice Linear Systems Notes & Practice Quadratic Systems Notes & Practice Radicals Notes & Practice Negative & Rational Exponents Notes & Practice MPH 8/09 1

2 ALGEBRA TOPICS & SKILLS Exponential Expressions & Equations Notes & Practice Logarithmic Expressions & Equations Notes & Practice FUNCTIONS & THEIR GRAPHS Functions & Function Notation Includes Domain & Range Is It a Function? Quiz Absolute Value & Piecewise-Defined Functions Composition & Combinations of Functions Includes Inverse Functions Exponential & Logarithmic Functions Includes Solving Equations Transformations of Functions Trigonometric Functions Includes Inverse Functions & Identities Power, Polynomial, & Rational Functions Symmetry & Even/Odd Functions Notes & Practice MPH 8/09 2

3 FUNCTIONS & THEIR GRAPHS Symmetry & Graphing Notes & Practice Even & Odd Functions Quiz LIMITS & CONTINUITY Intuitive Definition of a Limit Includes Tables & Graphs Evaluating Limits Graphically Algebraic Techniques for Finding Limits One-Sided Limits Infinite Limits Includes Vertical Asymptotes Limits at Infinity Includes Horizontal & Oblique Asymptotes Limits of Special Trigonometric Functions Continuity Includes Intermediate Value Theorem Continuity Is the Function Continuous? Quiz MPH 8/09 3

4 LIMITS & CONTINUITY Continuity Quiz on Continuous Functions DERIVATIVES Definition of the Derivative Definition of the Derivative The Moving Secant Line Animation Visualization of the Tangent Line - Animation Plotting a Derivative from a Function Animation Differentiability & Continuity Differentiation Rules Includes Product & Quotient Rules & Trigonometric Functions The Chain Rule Includes Higher-Order Derivatives Implicit Differentiation Derivatives of Inverse Trigonometric Functions Derivatives of Exponential Functions MPH 8/09 4

5 DERIVATIVES Derivatives of Logarithmic Functions Logarithmic Differentiation Differentiating Functions Quiz APPLICATIONS OF DERIVATIVES Tangent & Normal Lines Position, Velocity, & Acceleration Related Rates Related Rates Demos Related Rates Examples with Animation Related Rates Examples & Practice Related Rates An Interactive Tutorial Related Rates The Melting Snowball MPH 8/09 5

6 APPLICATIONS OF DERIVATIVES The Graphs of f(x) & f (x) Increasing & Decreasing Functions Relative Extrema & the First Derivative Test Increasing & Decreasing Functions Concavity & the Second Derivative Test Maxima & Minima An Interactive Tutorial Absolute Extrema & Optimization Includes Extreme Value Theorem Derivatives & Graphing Extrema & Inflection Points Quiz Determining Information about a Graph Based on the Derivative Quiz Distinguishing among f, f, and f Quiz Rolle s Theorem & the Mean Value Theorem for Derivatives The Mean Value Theorem for Derivatives Differentials Optimization A Square Inscribed in a Semicircle Animation MPH 8/09 6

7 ANTIDERIVATIVES & INDEFINITE INTEGRALS Area under the Curve LRAM and RRAM for the Sine Function Animation Area under the Curve LRAM and RRAM for a Polynomial Animation Area under the Curve Trapezoidal Rule Animation Antiderivatives Includes Trigonometric Functions Integration by Substitution Antiderivatives of Exponentials Antiderivatives of Logarithms Antiderivatives of Inverse Trigonometric Functions Integration by Trigonometric Substitution Elementary Integrals & Integration by Substitution Quiz The Definite Integral Includes Riemann Sums & Area Between Curves The Fundamental Theorem of Calculus Includes Properties of Definite Integrals & The Mean Value Theorem for Integrals MPH 8/09 7

8 ANTIDERIVATIVES & INDEFINITE INTEGRALS The Fundamental Theorem of Calculus Animation The Fundamental Theorem of Calculus Animation Integration by Parts Integration by Partial Fractions APPLICATIONS OF INTEGRALS Net Change & Displacement Volume Volume The Disk & Washer Method Volume Animation Volume of Revolution: About the x-axis Animations Volume of Revolution: About the y-axis Animation MPH 8/09 8

9 APPLICATIONS OF INTEGRALS Volume Disk Method Animation Volume The Shell Method Differential Equations & Slope Fields Slope Field Plotter Separable Differential Equations Work Numerical Solutions to Differential Equations Includes Slope Field s & Euler s Method Logistics Growth Arc Length & Surface of Revolution Surface of Revolution Animation IMPROPER INTEGRALS L Hopital s Rule MPH 8/09 9

10 IMPROPER INTEGRALS Improper Integrals SERIES Sequences Series Estimating Sums DCT, LCT, & Integral Tests Other Tests for Convergence Includes Absolute Convergence Convergence Tests for Infinite Series Notes Power Series Taylor & Maclaurin Series PARAMETRIC, VECTOR, & POLAR FUNCTIONS Parametric Equations MPH 8/09 10

11 PARAMETRIC, VECTOR, & POLAR FUNCTIONS Parametric Derivatives Parametric Integrals Includes Area & Arc Length Vectors Includes Vector Operations Differentiation of Vector-Valued Functions Integration of Vector-Valued Functions Polar Coordinates & Graphs Differentiation with Polar Curves Polar Integrals Includes Area & Arc Length Polar Area Animation Polar Area between Two Curves Animation Polar Area Inside One Curve & Outside Another Animation MPH 8/09 11