Things to know for 10560 final ====================== 7.1 Definition of inverse function Derivative of an inverse function 7.2* Definition of logarithm via integral Derivative of logarithm Laws of logarithms Graph of logarithm function Logarithmic differentiation 7.3* Definition of exponential as inverse of logarithm Derivative and integral of exponential Laws of exponents Graph of exponential conference 7.4* Definition of general logarithm and exponential functions 7.5 The law of natural growth (and decay) Solution to differential equation dy/dx=ky 7.6 Definition of arcsin, arccos and arctan Domains on which each is defined Graphs of each Derivatives of each 7.7 Definition of sinh, cosh and tanh 7.8 L'Hospital's rule Dealing with indeterminate products of the form 0 times infinity Dealing with indeterminate powers 8.1 Integration by parts formula 8.2 Dealing with integrals of the form sin^n x cos^m x Dealing with integrals of the form tan^n x sec^m x 8.3 The three basic trigonometric substitutions 8.4 Partial fractions method to integral rational functions Difference between the four cases 8.5 General approach to integration problems 8.7 Midpoint rule Trapezoidal rule Simpson's rule (No error bounds) 8.8 Integrals over infinite integrals Integrals where function is discontinuous at some point 9.1 Arc length formula 9.2 Area of surface of revolution around x-axis Area of surface of revolution around y-axis 9.3 Center of mass of region in the plane 10.2 What a direction field is Euler's method to approximate the solution of initial value differential equation 10.3 Identifying a separable equation Solving a separable equation 10.4 Identifying a linear equation Finding integrating factor Solving linear equation using integrating factor 11.1 Defining a curve parametrically 11.2 Slopes of parametric curves Arc length of parametric curves 11.3 Definition of polar coordinates Moving back and forth between polar and cartesian points Graphing curves in polar coordinates Slopes in polar coordinates 11.4 Area swept out of polar curves Arc length in polar coordinates 12.1 Definition of a sequence Limit of a sequence Squeeze theorem The sequence {r^n} 12.2 Definition of series What it means for sequence to converge The geometric series The harmonic series The divergence test 12.3 The integral test The p-series (no remainder estimate) 12.4 The comparison test The limit comparison test 12.5 The alternating series test The alternating series test error estimate 12.6 Definition of absolute convergence Definition of conditional convergence Ratio test Root test 12.7 General approach to testing series for convergence and divergence 12.8 Definition of a power series Power series centered at 0 and centered at a Radius of convergence Interval of convergence 12.9 The geometric series as a power series Integrating and differentiating series term-by-term Obtaining power series by integration and differentiation 12.10 Definition of Taylor series Definition of Maclaurin series The Maclaurin series of e^x, sin x and cos x Binomial series Multiplying power series Using series to evaluate limits (No error estimates) 12.11 The nth order Taylor polynomial