MATH 101 DIFFERENTIAL AND INTEGRAL CALCULUS I

Functions of one variable (Lines, Graphs, Combination, Sifting and Scaling, Trigonometric and Hyperbolic Functions, Inverse Functions). Limits and continuity. Differentiation (Derivative at a point and as a function, Differentiation Rules, Chain Rule, Implicit Differentiation, Differentials). Applications of derivatives (Extreme Values, Mean Value Theorem, Monotonicity, Concavity, Antiderivatives). Integration (Indefinite Integrals, Substitution Method, Riemann Sums, Definite Integrals, Fundamental Theorem of Calculus). Applications of Definite Integrals (Areas, Volumes, Arc Length, Surfaces of Revolution, Work). Transcendental Functions (Derivatives and Integration of Logarithmic, Exponential and Hyperbolic Functions and their inverses). Separable First Order Differential Equations. Techniques of Integration (Integration by parts, Trigonometric substitutions, Partial Fractions). Improper Integrals. Infinite Sequences and Series.