Definition of mathematics given by different mathematicians..

Basic concepts of trigonometry.

Trigonometry, as the name might suggest, is all about triangles.

More specifically, trigonometry is about right-angled triangles, where one of the internal angles is 90°. Trigonometry is a system that helps us to work out missing sides or angles in a triangle.

• The right angle is indicated by the little box in the corner.
• The other angle that we (usually) know is indicated by θ.
• The side opposite the right angle, which is the longest side, is called the hypotenuse.
• The side opposite θ is called the opposite.
• The side next to θ which is not the hypotenuse is called the adjacent.

Introduction on Calculus

There are 2 different fields of calculus. The first subfield is called differential calculus. Using the concept of function derivatives, it studies the behavior and rate on how different quantities change. Using the process of differentiation, the graph of a function can actually be computed, analyzed, and predicted. The second subfield is called integral calculus. Integration is actually the reverse process of differentiation, concerned with the concept of the anti-derivative. Either a concept, or at least semblances of it, has existed for centuries already. Even though these 2 subfields are generally different form each other, these 2 concepts are linked by the fundamental theorem of calculus.

Though it is complicated to use well, calculus does have a lot of practical uses - uses that you probably won't comprehend at first. The most common practical use of calculus is when plotting graphs of certain formulae or functions. Using methods such as the first derivative and the second derivative, a graph and its dimensions can be accurately estimated. These 2 derivatives are used to predict how a graph may look like, the direction that it is taking on a specific point, the shape of the graph at a specific point (if concave or convex), just to name a few.

    * In the field of chemistry, calculus can be used to predict functions such as reaction rates and radioactive decay. 
    * In biology, it is utilized to formulate rates such as birth and death rates. 
    *In economics, calculus is used to compute marginal cost and marginal revenue, enabling economists to predict maximum profit in a specific setting.
    
      In addition, it is used to check answers for different mathematical disciplines such as statistics, analytical geometry, and algebra.

Differential Calculus

COURSE EPC 3:   CRITICAL UNDERSTANDING OFINFORMATION AND  COMMUNICATIONTECHNOLOGY (ICT)

The aim of this course is to enhance the professional capacities of astudent teacher in integrating Information and CommunicationTechnologies (ICTs) with effective teaching and learning in a classroom.

Course objectives:  To enable the student-teachers:

1.  To  teach  effectively  in  a  “technology  enhanced  classroom” (previously referred to as “smart classroom”).

2.  To achieve knowledge-comprehension, practice skills andpresentation skills in ICT.

How to prepare a student teacher for a technology enhanced classroom?

The teachers in Colleges of Education should train the student- teachers:

1. To operate /use various ICT tools such as computer,laptop/Internet, Interactive whiteboard, Tablet PC, iPad, iPhone,Mobile phones, Digital cameras,    Multimedia   equipments   (audio/video),  Skype     and    video     - conferencing.

2.  To  browse  the  Internet,  using  a  computer  /laptop,  identify and  use education related websites and video/audio resources inteaching- learning.

3.  To     prepare    teaching    material/learning    resource     materials:   e-content, e-booklet for selected school subject areas and to createedu(cational) blogs for individual/ group students forstrengthening sharing and learning.

4.  To use a laptop /PC for preparing slides for PowerPointpresentations/ lectures and also download the video resourcesavailable on the internet and use them embedded with slidepresentations.

5.  To teach a content /lesson using an Interactive whiteboard (byconnecting a desktop computer to a whiteboard and project Googleimages onto it).

6.  To use a visualizer/document camera (visual projector) to displayand share an information to the whole class.

7.  To use a mobile device/a camera phone to take a series ofsnapshots of children’s   actions     events/     scenes/     activities    and    prepare    a    photo documentary or photo album withexplanatory notes/ descriptions.

8.  Prepare videos on different teaching styles of experiencedteachers/ peers and keep them available for viewing as a stream ona computer.

9. Organize a few video-conferencing classes (organize Skype-basedvideo conferencing) inviting experts in school subjects andencourage the students to share the learning experiences throughWhatsapp with their classmates and others.

10. To create educational blogs (edublogs) for individual/groupstudents for sharing and learning articles/ class notes/assignments and participating in active blogging community.

Tasks and Assignments:

1.  Write a report based on your preparation of e-content andpresentation of it to the class with different ICT tools.

2.  Write   a    report    on     the   organization    of    video-conferencing   with   an educational expert