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Topic outline
General
Precalculus
Precalculus
- Functions Page
- Which functions pass the VERTICAL LINE TEST?!! Page
- How to find DOMAIN AND RANGE for a function Page
- Finding values and domain and range from a graph Page
- Determining if a function is even, odd or neither Page
- How to classify functions Page
- Equation Modeling Page
- Modeling the equation of a piecewise defined function from its graph Page
- Sketching a graph from a story problem Page
- Equation of a line in point-slope form Page
- Equation of the line in slope-intercept form Page
- Least squares line Page
- Sketch the graph of a parabola Page
- How to find the CENTER AND RADIUS of a circle Page
- Sketch the graph of a circle Page
- Combinations of functions and their domains Page
- Composite functions Page
- Composite functions and their domains Page
- Describing transformations algebraically Page
- Using transformations to sketch a graph Page
- Determine whether a function is 1 to 1 Page
- How to find the INVERSE OF A FUNCTION Page
- Finding the linear function given two points on its inverse Page
- Use laws of logarithms to simplify a logarithmic function Page
- Use the quadratic formula to find roots of the function Page
- Completing the square of a quadratic function Page
- Polynomial long division for rational functions Page
- Hyperbolic identities Page
- How to remember the unit circle Page
Limits & Continuity
Limits & Continuity
- Limits and Continuity Page
- Solving limits with substitution Page
- How to solve LIMITS BY FACTORING Page
- CONJUGATE METHOD for solving limits Page
- Use limit laws to evaluate limits of combination functions Page
- How to find limits on CRAZY GRAPHS Page
- Limits at infinity Page
- Infinite limits Page
- Limits of trig functions: Everything you need to know! Page
- How to find the ONE-SIDED LIMITS of a function Page
- How to prove that the limit does not exist Page
- The precise definition of the limit EXPLAINED! Page
- Finding delta from a graph and the epsilon-delta definition of the limit Page
- How to find the limit using SQUEEZE THEOREM Page
- Limit of an inequality, with squeeze theorem Page
- Finding the domain by investigating continuity Page
- How to make a function continuous (for a piecewise function) Page
- How to find REMOVABLE DISCONTINUITIES Page
- How to use the Intermediate Value Theorem Page
- Intermediate value theorem to prove a root in an interval Page
- Prove the equation has at least one real root Page
- Limits of composite functions - How to find them? Page
- Jump discontinuities - What are they? Page
Derivatives
Derivatives
- Derivatives Page
- How to calculate the difference quotient Page
- DEFINITION OF THE DERIVATIVE to find the derivative Page
- Power rule for derivatives Page
- PRODUCT RULE for derivatives Page
- Product rule - 3+ functions Page
- Quotient rule Page
- Reciprocal rule Page
- Chain rule combined with power rule Page
- Chain rule for derivatives, with product rule Page
- Chain rule for derivatives, with quotient rule Page
- Chain rule for derivatives, with trig functions Page
- Derivatives of TRIG FUNCTIONS Page
- Derivative of cot^4(x/2) Page
- Derivatives of inverse trig functions - arcsin Page
- Derivatives of inverse trig functions - arccot Page
- Derivatives of HYPERBOLIC functions Page
- Derivatives of inverse hyperbolic functions Page
- Implicit differentiation COMPLETELY EXPLAINED! Page
- Finding the derivative of a function with e^x Page
- Derivatives of logarithms Page
- How to use LOGARITHMIC DIFFERENTIATION to find the derivative Page
- Derivative of x^x Page
- Equation of the tangent line Page
- Value that makes two tangent lines parallel Page
- DIFFERENTIABILITY and horizontal and vertical tangent lines Page
- Equation of the normal line at a point Page
- Average rate of change of a function Page
- Finding HALF LIFE Page
- Continuous compounding interest Page
- SALES DECLINE calculus problems Page
Applications of derivatives
Applications of derivatives
- Linear approximation Page
- ESTIMATE THE ROOT with linear approximation Page
- Linearization of a function at a point Page
- Optimization Page
- How to find CRITICAL POINTS Page
- Where is the function INCREASING AND DECREASING? Page
- Inflection points and concavity Page
- FIRST DERIVATIVE TEST to find the max and min Page
- How to use the SECOND DERIVATIVE TEST Page
- How to find VERTICAL ASYMPTOTES Page
- How to find HORIZONTAL ASYMPTOTES Page
- How to find SLANT ASYMPTOTES Page
- All about GRAPH SKETCHING Page
- Maxima and minima on a CLOSED interval Page
- Dimensions that maximize the area of the rectangle Page
- OPTIMIZATION: Dimensions that maximize the volume of a cylinder Page
- OPTIMIZATION: Dimensions of a rectangle that minimize its perimeter Page
- OPTIMIZATION: Dimensions that maximize the volume of a box Page
- Dimensions of the rectangle with largest area inscribed in an equilateral triangle Page
- Largest area of a rectangle inscribed in a semicircle Page
- Points on the cone closest to a point Page
- Max volume of a rectangular box inscribed in a sphere Page
- Maximum volume of a cone shaped cup Page
- Largest possible volume of a cylinder inscribed in a sphere Page
- Dimensions that minimize the surface area of a cylinder Page
- OPTIMIZATION: Dimensions that minimize page size with a given printed area
- OPTIMIZATION: Dimensions that minimize the surface area of an open top box Page
- OPEN-TOP BOX?!! How to find the smallest possible surface area Page
- OPTIMIZATION: Point on the line closest to another point Page
- Minimizing the product of two real numbers Page
- Finding numbers with the smallest sum of squares Page
- OPTIMIZATION: Production level, sale price that maximize profit Page
- OPTIMIZATION: Sales level that maximizes revenue Page
- OPTIMIZATION: Time when velocity is minimum Page
- Related Rates Page
- RELATED RATES: Radius of the balloon Page
- RELATED RATES: Ladder sliding down the wall Page
- RELATED RATES: Distance between the person and the plane Page
- RELATED RATES: Water level in the tank Page
- RELATED RATES: Price of the product Page
- MEAN VALUE THEOREM (MVT) for derivatives Page
- How to use ROLLE'S THEOREM Page
- How to use NEWTON'S METHOD Page
- How to use L'HOSPITAL'S RULE Page
- Position Function Page
- All about a PARTICLE'S POSITION function Page
- Instantaneous velocity Page
- HOW HIGH CAN YOU THROW THE BALL?!! How fast is it going when it hits the ground? Page
- Dropping a coin from the roof (VERTICAL MOTION!) Page
- How to find MARGINAL COST, REVENUE AND PROFIT Page
Integration
Integration
- Integrals Page
- Summation Notation - Finding the Sum Page
- How to find a Riemann sum using LEFT ENDPOINTS Page
- Riemann sums with right endpoints Page
- THE MOST ACCURATE WAY TO DO A RIEMANN SUM (Midpoint rule) Page
- Close only counts in horseshoes, hand grenades, and Riemann sums Page
- Trapezoidal Rule Page
- Simpson's Approximation Page
- Definite Integral Page
- ARE YOU FINDING THE RIGHT AREA?!! Area under vs. area enclosed by a graph Page
- Definite integral of an even function Page
- Definite integral of an odd function Page
- PART 1 OF THE DREADED FUNDAMENTAL THEOREM OF CALCULUS! Page
- PART 2 OF THE FUNDAMENTAL THEOREM OF CALCULUS! Page
- Net change theorem Page
- Indefinite Integrals Page
- Properties of integrals Page
- Find f(x) given f''(x), its second derivative Page
- Find f(x) given f'''(x), its third derivative Page
- Initial Value Problem Page
- Find f given f'' and initial conditions Page
- Solving Integrals Page
- U-Substitution Page
- U-Substitution in Definite Integrals Page
- Integration by Parts Page
- Integration by parts two times Page
- Integration by parts three times Page
- U-substitution with integration by parts Page
- Integration by parts to prove the reduction formula Page
- A TOTALLY DIFFERENT WAY to do integration by parts! Page
- Partial fractions, distinct linear factors Page
- Partial fractions, distinct linear factors, example 2, part 1 of 2 Page
- Partial fractions, distinct linear factors, example 2, part 2 of 2 Page
- Partial fractions, distinct linear factors, example 3 Page
- Partial fractions, repeated linear factors Page
- Using partial fractions with DISTINCT QUADRATIC FACTORS Page
- Partial fractions, distinct quadratic factors, example 2 Page
- Partial fractions, distinct quadratic factors, example 3 Page
- Partial fractions, repeated quadratic factors Page
- Partial fractions, rationalizing substitution Page
- Integrating with partial fractions: how to factor difficult denominators Page
- Partial fractions, two ways to find the constants Page
- Integrating a trig function using u-substitution! Page
- Trigonometric integrals - sin^mcos^n, odd m Page
- Trigonometric integrals - sin^mcos^n, odd n Page
- Trigonometric integrals - sin^mcos^n, m and n even Page
- Integrals of trigonometric functions, tan^msec^n, odd m Page
- Integrals of trigonometric functions, tan^msec^n, even n Page
- Integrals of trigonometric functions, sin(mx)cos(nx) Page
- Integrals of trigonometric functions, sin(mx)sin(nx) Page
- Integrals of trigonometric functions, cos(mx)cos(nx) Page
- Hyperbolic integrals... pretty much just like trig integrals Page
- Integrals of Inverse Hyperbolic Functions Page
- How to solve EVERY trigonometric substitution problem ever! Page
- Trigonometric substitution with secant Page
- Trigonometric substitution with sine Page
- Trigonometric substitution with tangent Page
- Integral of a quadratic function Page
- Improper integrals, case 2 Page
- Improper integrals, case 3 Page
- improper integrals, case 4 Page
- COMPARISON THEOREM WILL FINALLY MAKE SENSE! Page
- Integrals using reduction formulas Page
- How to use inverse hyperbolic functions to evaluate integrals Page
- Partial fractions are SPECIAL! (Repeated linear factors) Page
- PARTIAL FRACTIONS example with distinct linear factors Page
- Trig substitution - How to solve? Page
Applications of integration
Applications of integration
- Applications of Integration Page
- Average Value of a Function Example 1 Page
- Area between curves - dx Page
- Area between curves - dy Page
- Area between curves - sketching Page
- Arc Length Page
- Arc length x=g(y) Page
- Arc length - Simpson's Rule Page
- Surface Area of Revolution Page
- Surface area of revolution - Simpson's Rule Page
- Surface of Revolution Page
- Volume of rotation: disk method about the y-axis or x= Page
- Volume of rotation: disk method about the y-axis or x= Page
- Volume of rotation: disk method about the x-axis or y= Page
- Volume of rotation: washer method about the x-axis or y= Page
- Volume of rotation: washer method about y-axis or x= Page
- Volume of rotation: washer method about x-axis or y= Page
- Volume of rotation: cylindrical shells about the y-axis or x= Page
- Volume of rotation: cylindrical shells about the x-axis or y= Page
- Mean value theorem for integrals Page
- Work done using a rope to lift a weight Page
- Work Done on Elastic Springs Page
- Work Done by a Variable Force Page
- Moments of the system Page
- Moments of the system, x-axis Page
- Center of mass of the system Page
- Center of mass of the system, x-axis Page
- Hydrostatic pressure Page
- Hydrostatic force Page
- Vertical Motion (integration) Page
- Rectilinear Motion Page
- Centroids of Plane Regions Page
- Centroid of the plane - Simpson's Rule Page
- Area of the triangle with the given vertices Page
- Present and Future Value Page
- Present and Future Value Example 2 Page
- Present and Future Value Example 3 Page
- Present and Future Value Example 4 Page
- Present and Future Value Example 5 Page
- Consumer and Producer Surplus Page
- Probability density functions Page
- Cardiac output Page
- Cardiac output - Simpson's Rule Page
- Poiseuille's law Page
- Theorem of Pappus Page
Polar & Parametric
Polar & Parametric
- Eliminating the Parameter Page
- Derivative of a parametric curve Page
- Second Derivative of a Parametric Curve Page
- Sketch the parametric curve by plotting points Page
- Tangent line to the parametric curve Page
- Area under the parametric curve Page
- Parametric area under one arc or loop Page
- Volume of Revolution of a Parametric Curve Page
- Parametric arc length Page
- Parametric arc length and the distance traveled by the particle Page
- Parametric arc length, simpson's rule Page
- Parametric Curve - Surface Area of Revolution Page
- Polar coordinates Page
- Converting Polar Coordinates Page
- Converting Rectangular Equations to Polar Equations Page
- Converting Polar Equations to Rectangular Equations Page
- Distance between two polar points Page
- Sketching Polar Curves Page
- Sketching Polar Curves - 2 Examples Page
- Sketching polar curves from cartesian curves Page
- Tangent line to the polar curve Page
- Vertical and horizontal tangent lines to the polar curve Page
- Polar Area Page
- Polar Area Bounded by One Loop Page
- Points of intersection of two polar curves Page
- Area Between Polar Curves Page
- Polar area inside both curves Page
- Arc Length of a Polar Curve Page
- Polar Parametric Curve - Arc Length Page
- Polar Parametric Curve - Surface Area of Revolution Page
- Taking a look at complex numbers in polar form Page
- Let's multiply some complex numbers! Page
- Analytic Geometry - Graph of a Single Point or of No Points Page
- Analytic Geometry - Set of Points Equally Distant from Two Points Page
- Analytic Geometry- Set of Points Unequally Distant from Two Points Page
- Eccentricity and directrix of the conic section Page
- Parabolas -Vertex, Axis, Focus, Directrix Page
- Equation of a parabola (conic section) Page
- Polar equation of the parabola (conic section) Page
- Vertex axis focus directrix of an ellipse Page
- Equation of an ellipse (conic section) Page
- Polar equation of the ellipse (conic section) Page
- Vertex axis focus directrix asymptotes of a hyperbola Page
- Equation of a hyperbola (conic section) Page
- Polar equation of the hyperbola (conic section) Page
Sequences and series
Sequences and series
- Listing the first terms of the sequence Page
- Calculating the first terms of the sequence Page
- Finding a formula for the general term of the sequence (a_n) Page
- Does the sequence converge or diverge? Page
- Finding the limit of a convergent sequence Page
- Increasing, decreasing and not monotonic sequences Page
- Bounded sequences Page
- Calculating the first terms in a series of partial sums Page
- Sum of the series of partial sums Page
- nth term test, divergence test, zero test Page
- Convergence of a geometric series Page
- Convergence and sum of a geometric series, example 1 Page
- Convergence and sum of a geometric series, example 2 Page
- Convergence and sum of a geometric series, example 3 Page
- Values for which the geometric series converges Page
- Repeating decimal expressed as a ratio of integers Page
- Convergence of a telescoping series Page
- Sum of Telescoping Series Page
- p-Series test for convergence Page
- How to use the INTEGRAL TEST for series Page
- Comparison Test Page
- Limit Comparison Test Page
- Estimating error/remainder of a series Page
- Alternating Series Test - Calculus Page
- Alternating series estimation theorem Page
- Ratio Test Page
- Ratio Test with Factorials Page
- Root Test Page
- Absolute and conditional convergence Page
- Difference Between Limit and Sum of the Series Page
- Radius of convergence Page
- Interval of Convergence Page
- Interval of Convergence Example 2 Page
- Power series representation, radius and interval of convergence Page
- Power series multiplication Page
- Power series division Page
- Power series differentiation Page
- Using power series to estimate a definite integral Page
- Binomial series Page
- Taylor Polynomial Example 1 PART 1/2 Page
- Taylor Polynomial Example 1 PART 2/2 Page
- Taylor Polynomial Example 2 PART 1/2 Page
- Taylor Polynomial Example 2 PART 2/2 Page
- Finding radius of convergence of a Taylor series Page
- Taylor's inequality Page
- Maclaurin Series Page
- Sum of the maclaurin series Page
- Maclaurin series radius of convergence Page
- Expressing the integral as a power series Page
- Using maclaurin series to estimate an indefinite integral Page
- Maclaurin series to estimate a definite integral Page
- Maclaurin series to evaluate a limit Page