تفاضل و تكامل 1 - CALCULUS I

Calculus I of Mandatory course in the second level of the common first year and serves other programs that are physics, chemistry, engineering, and Computer Science. The course is concerned with the study of Functions (domain- codomain – range), operations on functions (sum – difference – product – quotient) types of functions (odd – even - one to one – onto – one to one correspondence) Inverse function. Standard functions and their properties (polynomials – rational – exponential -logarithmic- trigonometric functions)., Limits (Definition of the limit, Calculating limits using the limits laws, Limits at Infinity), continuity (continuous and discontinuous functions, theorems of continuity, Vertical and Horizontal Asymptotes), derivation of one-variable functions (Derivatives and Rates of Change, Derivatives of polynomials and Exponential Function, The Product and Quotient Rules, Derivatives of Trigonometric Function, The Chain Rule, Implicit Differentiation, Derivatives of Logarithmic Functions, Hyperbolic Function) and applications of differentiation (Maximum and Minimum Values, The Mean Value Theorem, Graph Sketching, Indeterminate forms, and L’Hospital’s Rule, Taylor and Maclaurin expansions).