MATH104 ENGINEERING MATHEMATICS I

Wishlist

Course Prerequisite(s)

  • Please note that this course has the following prerequisites which must be completed before it can be accessed
  • INTERMEDIATE ALGEBRA

About Course

This course provides a preparation for more advanced study in Algebra and Calculus. Topics include
simplifying algebraic, rational, and radical expressions; solving quadratic, rational, radical, absolute
value, exponential, and logarithmic equations; solving compound and absolute value inequalities, and
graphing functions. Also, it include the concepts of Functions: domain, operations on functions, graphs
of functions; trigonometric functions; limits: meaning of a limit, computational techniques, limits at
infinity, infinite limits; continuity; limits and continuity of trigonometric functions; the derivative:
techniques of differentiation, derivatives of trigonometric functions; the chain rule; implicit
differentiation; differentials; Roll’s Theorem; the mean value theorem; the extended mean value
theorem; L’Hopital’s rule; increasing and decreasing functions; concavity; maximum and minimum
values of a function; graphs of functions including rational functions (asymptotes) and functions with
vertical tangents (cusps); antiderivatives; the indefinite integral; the definite integral; the fundamental
theorem of calculus; area under a curve; area between two curves; transcendental functions: inverse
functions, logarithmic and exponential functions and their derivatives and integrals; limits (the
indeterminate forms); hyperbolic functions and their inverses; inverse trigonometric functions; some
techniques of integration.

Show More

What Will You Learn?

  • Upon successful completion of this course, each student will be able to:
  • 1. Classify a real Number, Order of Operations, Properties of Real Numbers, Evaluate Algebraic
  • Expressions, Simplify Algebraic Expressions;
  • 2. Factor polynomials using the distributive property, reverse foil, grouping, the difference of
  • squares, sum and difference of cubes;
  • 3. Perform operations on rational expressions, radical expressions, and complex numbers; solve rational and radical equations;
  • 4. Solve compound inequalities, absolute value equations and inequalities;
  • 5. Solve quadratic equations by using factoring, the quadratic formula, and completing the square and solve relevant applications;
  • 6. Use function notation, perform operations with functions including composition of functions, find the inverse of a one-to-one function, graph quadratic, exponential, and logarithmic functions, and identify the domain and range of a function; and
  • 7. Use properties of logarithms to solve logarithmic and exponential equations and relevant
  • applications
  • 8. Calculate the limit for various types of functions.
  • 9. Determine whether a given function is continuous at a certain point.
  • 10. Differentiate and integrate various types of functions.
  • 11. Sketch the graph of polynomials, trigonometric and rational functions.
  • 12. Use correctly some famous Theorems in calculus such as: Intermediate Value
  • 13. Theorem, Mean Value Theorem, and Fundamental Theorem of Calculus.

Course Content

Algebra Essentials
This course entails: 1. Operations on Real Numbers System 2. Concept of Exponents and Scientific Notation 3. Introduction to Radicals and Rational Exponents

Function Basics, Polynomial &Rational Functions
This course entails: 1. Polynomial & Rational Expressions Basics 2. Domain and Range of Polynomials and Rationals functions 3. Characteristics of Functions and Their Graphs 4. Methods for Finding Zeros of Polynomials

The Rectangular Coordinate System and Linear Graphs
Introduction to Points and Lines in the Plane Compositions & Transformations of Functions Linear Functions &Inverse Functions Graphs and Modeling of Linear Functions

Equations and Inequalities
Introduction to Equation-Solving Techniques Models and Applications Quadratic Equations Linear Inequalities and Absolute Value Inequalities

Algebraic Operations on Linear and Absolute Value Functions
Compositions & Transformations of Functions Linear Functions &Inverse Functions Graphs and Modeling of Linear Functions

Quadratic Functions
Introduction to Complex Numbers Graphs of Quadratic Functions Introduction to Analysis of Quadratic Functions

Exponential and Logarithmic Functions
Exponential and Logarithmic Equations, Introduction to Logarithmic Functions Introduction to Graphs of Logarithmic Functions

Limits and Continuity
Limits of functions, Indeterminate Forms Limits at Infinity and Infinite Limits, Continuity, Formal Definition of Limits

Techniques of Differentiation
Differentiation Rules Derivatives of Trigonometric Functions Higher-Order Derivatives

Applications of Differentiation-I
Using Differentials and Derivatives Mean-Value Theorem & Implicit Differentiation Antiderivatives, Initial-Value Problems & Velocity and Acceleration

Applications of Differentiation-II
Extreme Values, Concavity and Inflections Sketching the Graph of a Function

Techniques of Integration
The Definite & Indefinite Integral, Properties of the Definite Integral The Method of Substitution, The Fundamental Theorem of Calculus

Applications of Integration
Integration by Parts, Integrals of Rational Functions Arc Length and Surface Area, Mass, Moments, and Centre of Mass Centroids, First-Order Differential Equations