معلومات المقرر

In this course we will learn about the following:
- Before calculus(Functions-Definition of function - Independent and Dependent Variables - The vertical line test
The absolute value function- Piece wise -Defined functions - Domain and range - New functions from old
-Arithmetic operations functions - Composition of functions - Expressing a function as a composition
Symmetry-Even and odd functions-Inverse functions-Changing the independent variable
(Domain and range of inverse functions-A method for finding inverse functions-Existence of inverse functions
Limits and continuity(Limits (An intuitive approach)-One-sided limits-The relationship between one- sided and
two-sided limits-Infinite limits-Vertical asymptotic -Computing limits-Some basic limits-Limits of polynomial
and rational functions-Limits of piece wise-defined functions-Limits at infinity, end behavior of a function-
Limits at infinity and horizontal asymptotes-Limit laws for limits at infinity-Infinite limits at infinity-Limits of x^n
Limits of polynomials as x ….-Limits of rational functions as x …-A quick method for finding limits of
rational functions as …-Limits involving radicals- Continuity-Continuity on an interval-Some properties of
continuity functions-Continuity of polynomials and rational functions-Continuity of compositions-Continuity
( of trigonometric functions
The Derivative(Tangent line and rates of change-The Derivative Function-Differentiability-The relation
between differentiability and continuity-Other Derivative Notation-Introduction to Techniques of Differentiation
Derivative of a constant-Derivatives of power functions-Derivative of a constant times a function-Derivative of
sums and differences-Higher derivatives-The Product and Quotient Rules-Summary of Differentiation Rules-
Derivative of Trigonometric Functions-The Chain Rule-Derivatives of compositions-An Alternative version of the
(chain rule-Generalized Derivative Formulas-Implicit Differentiation
The derivative in graphing and applications(Analysis of Functions I: Increase, Decrease, and Concavity-Inflection
points-Analysis of Functions II: Relative Exterma; Graphing Polynomilas-First derivative test-Second derivative test
(Rolle’s Theorem; Mean-Value Theorem
(Integration(Antiderivatives - The Indefinite Integral-Integration formulas-Properties of the indefinite integral

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