MAT 111E - Mathematics I

Course Objectives

1. To provide the concepts of functions, limits, continuity, differentiation and integration.
2. To provide the applications of differentiation and integration
3. To give an ability to apply knowledge of mathematics on engineering problems

Course Description

Preliminaries:Real Numbers and the Real Line, Lines, Circles,and Parabolas, Functions and Their
Graphs, Identifying Functions; Mathematical Models, Combining Functions; Shifting and Scaling
Graphs, Trigonometric Functions.
Limits and Continuity: Rates of Change and Limits, Calculating Limits Using the Limits Law, The
Precise Definition of a Limit, One-Sided Limitsa and Limits at Infinity, Infinite Limits and Vertical
Asymptotes, Continuity, Tangents and Derivatives.
Differentiation: The Derivative as a Function, Differentiation Rules, The Derivative as a Rate of
Change, Derivatives of Trigonometric Functions, The Chain Rule and Parametric Equations, Implicit
Differentiation, Related Rates, Linearization and Differentials.
Applications of Derivatives: Extreme Values of Functions, The Mean Value Theorem, Monotonic
Functions and the First Derivative Test, Concavity and Curve Sketching, Applied Optimization
Problems, Indeterminate Forms and L’Hopital’s Rule, Newton’s Method, Antiderivatives.
Integration: Estimating with Finite Sums, Sigma Notation and Limits of Finite Sums, The Definite
Integral, The Fundamental Theorem of Calculus, Indefinite Integrals and the Substitution Rule,
Substitution and Area Between Curves.
Applications of Definite Integrals: Volumes by Slicing and Rotation About an Axis, Volumes by
Cylindrical Shells, Lengths of Plane Curves, Moments and Centers of Mass, Areas of Surfaces of
Revolution and the Theorems of Pappus.
Transcendental Functions: Inverse Functions and Their Derivatives, Natural Logarithms, The
Exponential Function, Exponential Growth and Decay, Inverse Trigonometric
Functions, Hyperbolic Functions.