SMA 2101 Calculus

SMA 2101: CALCULUS I c Francis O. Ochieng Department of Pure and Applied Mathematics Jomo Kenyatta University of Agriculture and Technology Course content • Functions: definition, domain, range, codomain, composition (or composite), inverse. • Limits, continuity and differentiability of a function. • Differentiation by first principle and by rule for x (integral and fractional n). • Other techniques of differentiation, i.e., sums, products, quotients, chain rule; their applications to algebraic, trigonometric, logarithmic, exponential, and inverse trigonometric functions all of a single variable. • Implicit and parametric differentiation. • Applications of differentiation to: rates of change, small changes, stationary points, equations of tangents and normal lines, kinematics, and economics and financial models (cost, revenue and profit). • Introduction to integration and its applications to area and volume. References [1] Calculus: Early Transcendentals (8th Edition) by James Stewart [2] Calculus with Analytic Geometry by Roland E. Larson, Robert P. Hostetler and Bruce H. Edwards; 5th edition [3] Calculus and Analytical Geometry (9th edition) by George B. Thomas and Ross L. Finney [4] Advanced Engineering Mathematics (10th ed.) by Erwin Kreyszig [5] Calculus by Larson Hostellem LECTURE 1 1 Functions To understand the word function, we consider the following scenario and definitions. For example, the growth of a sidling is an instance of a functional relation, since the growth may be affected by variations in temperature, moisture, sunlight, etc. If all these factors remain constant, then the growth is a function of time. Definition 1.1 (Variables). A variable is an object, event, time period, or any other type of category you are trying to measu