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Calculus R




A REVIEW OF PRECALCULUS AND OTHER PREVIOUSLY STUDIED MATERIAL:                                                 Coordinates, graphs and lines; Functions,  limits and continuity;Domain; range; absolute value; rational functions; composition of functions; inverse; even and odd; zeros; intercepts; transformations; basic limits; continuous functions

DERIVATIVES AND DIFFERENTIATION:                      Definitions; derivatives of algebraic functions; rules of differentiation; derivatives of trigonometric functions; proofs;  implicit differentiation; differentials

APPLICATIONS OF DERIVATIVES:                                    Slope of tangent lines; related rates; concavity and points of inflection; relative and absolute maxima and minima; rectilinear motion; mean value theorem

INTEGRATION:                                                                           All basic formulas and functions including  u  substitution; definite and indefinite integrals;      1st and 2nd Fundamental Theorems of Calculus; indeterminate forms

APPLICATIONS OF THE INTEGRAL:                                   Area under a curve; area between two curves; volumes of solids of revolution; inverse trigonometric functions; rectilinear motion; average value

***Exponential and logarithmic functions will be included, as appropriate, as each topic is studied rather than as separate topics (see textbook).  Thus their applications will be included at the appropriate time as each topic is studied. ***




Calculus (2nd ed.):  Finney, Demana, Waits, Kennedy


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As the time available is limited and the material to be studied extensive, it is possible that not all your questions will be answered in the class time available. It is the student's responsibility to ensure that he understands the fundamentals of each topic covered. This will mean that the student must have the conscientiousness and perseverance to work on his own and with others (students and teacher) to find solutions to the problems he has been assigned. Please ASK me for help if you are having difficulties and cannot proceed. We will arrange a time to discuss the situation.


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Calculus R

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