MAT 111 Foundations of Mathematics
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- ItemMAT 111 Module 8: Conics Sections(2023-04-22) Michael ObieroIn this module, you will learn about the two-dimensional figures that are formed when a right circular cone is intersected by a plane. These include the ellipse, the parabola and the hyperbola. You will learn how to develop defining equations for each figure and then learn how to use these equations to solve a variety of problems.
- ItemMAT 111 Module 1: Sets(2023-04-22) Michael ObieroThis module introduces the concepts of sets, which are the building blocks of almost all mathematical concepts and statements. Once we have a well defined set, we can construct relations on elements of that set, or between sets, and functions between sets. In this module you will be introduced to operations between sets, cardinality of sets and classification of sets.
- ItemMAT 111 Module 2: Relations and functions(2023-04-22) Michael ObieroThis module introduces the concepts of relations on sets and between sets. You will be presented with different types of relations. A very important relation is the equivalence relations which is related to partitions of sets. Another important relation is a `function' which is a special relation between elements of two sets that maps all elements of the domain to unique elements in the range. Functions are important in many ways and here, you will be introduced to the basics of what a function is and some properties and examples of functions that are common in mathematics.
- ItemMAT 111 Module 3: Trigonometry(2023-04-22) Michael ObieroIn the previous lesson on "Relations and functions" we defined and looked at examples of functions. Some of the most important functions with wide applications in engineering, computing, finance e.t.c. are trigonometric functions. Trigonometric functions are used to model many phenomena, including sound waves, vibrations of strings, alternating electrical current, and the motion of pendulums, motion of objects, population dynamics. In fact, almost any repetitive, or cyclical, motion can be modeled by some combination of trigonometric functions. In this lesson,you will be introduced to trigonometric functions like \(\sin(x)\), \(\cos(x)\), \(\tan(x)\) from the right angled triangle their use in calculating angles and lengths. You will then be introduced to trigonometric identities and their applications in solving trigonometric equations. Lastly, you will learn about graphs and periods of trigonometric functions, and shifted graphs of sine and cosine functions.
- ItemMAT 111 Module 4: Polynomials(2023-04-22) Michael ObieroIn this module you will be introduced to polynomials, different types and properties of polynomials depending on their degree, factorization of polynomial functions, techniques of finding roots of polynomial functions, factorization of polynomials of degree 2 also called the quadratic functions. You also study methods of solving quadratic equations and inequalities.