Index for Calculus Notes. These are notes for a first semester first year calculus course. The notes refer to Adams: Calculus - A Complete Course, Addison Wesley Fourth edition ApproxFixed.doc Fixed point iteration through examples. Cobweb diagram ApproxFunctions.doc Linear and quadratic approximations to a function near a point ApproxNewton.doc Newton-Raphson approximation. Examples. No error analysis ApproxPoly.doc Polynomial approximations - examples Composite Functions.doc Definition and examples of composite functions. Graph sketching using composition DiffInverse.doc Differentiation of inverse functions. Choice of domain for inverse trig functions Differentiation.doc Mainly revision of differentiating composite functions, using the one variable chain rule ExpLogFns.doc Discussion of exponential and logarithm as inverses. relationship between laws of logarithms and indices. General powers Fn2Var.doc Plotting functions of two variables, cross sections and contours. Examples with MAPLE plots Fn2VarLim.doc Examples where limiting properties are more complicated than for one variable Functions.doc Basic properties of functions. Domain & Range. Modulus, square root, odd & even, increasing & decreasing HigherPDiff.doc Second partial derivatives, verifying Laplace's equation as an example HyperbolicFns.doc Definition and basic properties of hyperbolic functions. Logarithmic form of inverses ImplicitDiff.doc Introduction to the technique of implicit differentiation IntApplic.doc Volume of revolution (disc and shell methods). Arc length, surface of revolution IntLog.doc A discussion of the integral of 1/x, explaining what happens when x is negative, and the reasons for ln|x| IntParts.doc Revision of basic integration by parts. Example giving an equation for the integral on integration by parts twice IntRational.doc Step-by step method for integrating rational functions, with examples IntReduction.doc Integration by parts giving reduction formulae IntRevision.doc Revision of basic integration. Using odd and even properties with definite integrals. Example with trig identities for a product of trig functions IntSub.doc Revision of basic integration by substitution IntSubFurther.doc Particular types. Square roots of quadratics, square roots of sums and differences of squares, square root of linear function, rational functions of cos and sin (half-angle substitution) InverseFns.doc Inverse functions, domain and range, graphical properties, restricting domains to obtain 1-1 functions. InverseTrigFns.doc Discussion of restricting domain for inverse trig functions. LeibnizThm.doc Proof and example of Leibniz theorem for the n-th derivative of a product LimitTechniques.doc Finding limits by squeezing, algebraic manipulation, change of variable and l'Hopital's rule Limits.doc Brief discussion of intuitive ideas about limits, introducing terminology LogarithmicDiff.doc The technique of logarithmic differentiation through examples PDiff.doc Basic partial differentiation PDiffChRule.doc The chain rule. Proof (not completely rigorous). Examples. using tree diagrams as an aid. ParametricDiff.doc Discussion and example of parametric differentiation, including the second derivative Polynomialdivision.doc A worked example of polynomial division needed as the first step for integrating rational functions TaylorPoly.doc Derivation of Taylor polynomials with examples TaylorTheorem.doc Statement of Taylor's Theorem (no proof) and an example on approximation Tplanes.doc Deriving equations of tangent plane and normal line to a surface z=f(x,y) Trig.doc Very brief revision of some properties of trig functions