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Core Content and Skills
Math Calculus 2/SUPA 296 
2007-2008
BOE Approved

Exponential And Logarithmic Functions  Content   Skills  Natural Logarithms Logarithm Laws Review Trigonometric Derivatives Implicit Differentiation Laws of Exponents Integrals of Exponential Functions General Power Functions General Logarithm Functions Indeterminate Forms L’Hopital’s Rule Indeterminate Forms Involving Infinity   graph the natural logarithm function use logarithm laws to evaluate functions find the derivatives of trigonometric functions find derivatives implicitly find the integral of exponential functions find the antiderivative of indeterminate functions use L'Hopital's Rule to find limits evaluate limits where we have 0/0 or infinity/infinity     Differential Equations / Exponential Growth and Decay  Content   Skills  Separable Differential Equations Slope Fields Solution Curves Population Growth Torricelli’s Laws Applications of Differential Equations Natural Growth and Decay   solutions of basic differential equations solution of 1st order linear differential equations with constant coefficients evaluation of the constant of integration in an initial value problem use differential equations to solve natural growth equations, radioactive decay and radiocarbon dating solution of separable first-order differential equations

Diff. EQs. Continued  Content   Skills  Linear 1st-Order Equations Applications Inverse Trigonometric Functions   examine the uses of differential equations in the real-world solve differential equations with inverse trig functions     Techniques of Integration  Content   Skills  Substitution Integration by Parts Reduction Formulas Trigonometric Integrals Rational Functions Partial Fractions   integrate using u-substitution integrate by parts integrate using reduction formulas integrate using trig. substitutions integrating rational functions integrate using partial fractions

Techniques of Integration continued  Content   Skills  Quadratic Factors Applications to Differential Equations Trigonometric Substitution Integrals containing Quadratic Polynomials   use differential equations to solve real-life problems solve integrals containing Quadratic polynomials     Improper Integrals / Indeterminate Forms / Area  Content   Skills  Improper Integrals Applications of Improper Integrals   evaluate improper integrals solve real-life problems that require the use of improper integrals

Indeterminate Forms / Area continued  Content   Skills  Algebraic Manipulations of Indeterminate Forms Area Computations in Polar Form   evaluate indeterminate forms of integrals by algebraic manipulations compute the area using polar forms     Infinite Series  Content   Skills  Infinite Sequences and Series Limits of Sequences Bounded Monotonic Sequences   find the limit of a sequence find the sum of an infinite series

Infinite Series continued  Content   Skills  Convergence Geometric Series Nth Term Harmonic series Taylor Series Taylor Polynomials The Integral Test   find the sum of a geometric series use the nth term test to test for divergence find an nth term Taylor polynomial for a function at a specific point use the integral test to test for convergence

More Infinite Series and Tests for Convergence  Content   Skills  Comparison Test Limit Comparison Test Alternating Series Test Ratio Test Root Test Power Series   use the comparison test and the limit comparison test to test for convergence test for convergence by using the alternating series test, the ratio test, and the root test find the radius of convergence and intervals of convergence of power series

Plane Curves, Vectors, Curves, and Surfaces in Space  Content   Skills  Parametric Equations Vectors in the Plane 3-Dimensional Vectors Direction Angles and Projections Cross Product   solve problems using parametric equations find the magnitude of vectors use the dot product to test perpendicularity of vectors and find the angle between two vectors find the cross product of two vectors find the parametric and symmetric equations of a straight line that passes through a given point and is parallel to a given point

More Surfaces in Space  Content   Skills  Algebraic Properties and Applications Lines in Space Planes in Space Vector-Valued Functions Velocity and Acceleration Vectors Integration of Vector-Valued Functions Quadric Surfaces   find vector-valued functions, velocity vectors, and acceleration vectors find the equations of motion of a projectile find the arc length of a parametric space curve find the curvature, unit tangent vector, and principal unit normal vector of a parametric curve in the plane or in space use Kepler's three laws of planetary motion to solve problems

Partial Differentiation  Content   Skills  Level Curves Limits and Continuity Partial Derivatives Higher Partial Derivatives Tangent Planes Maximum/Minimum Problems   find the level curves of functions of two variables find the limits and continuity of functions of two or three variables compute partial derivatives find the absolute and local maxima and minima for 3-D curves find the necessary conditions for local extrema     More Partial Derivatives  Content   Skills  Differentials Linear Approximation The Chain Rule Implicit Partial Differentiation   apply the linear approximation theorem for functions of 3 variables use the chain rule for functions of several variables

More Partial Derivatives continued  Content   Skills  Directional Derivatives Interpretation of the Gradient LaGrange Multipliers   compute the directional derivatives find the gradient vector solve constrained max/min problems using the LaGrange multiplier method