YAKILI | UPPER SIXTH PURE MATHEMATICS WITH MECHANICS

Course / Course Details

UPPER SIXTH PURE MATHEMATICS WITH MECHANICS

By - High School Mathematics
0 students
50 Min
(0)

Course Requirements

Upper-Sixth Mathematics with Mechanics is a rigorous and comprehensive course designed to provide students with a deep understanding of advanced mathematical concepts and their applications in mechanics. This course is intended for students who have successfully completed Lower-Sixth Mathematics and are seeking to further develop their mathematical skills and knowledge. Throughout the course, students will explore various topics such as advanced calculus, differential equations, vectors, kinematics, dynamics, and statics. Emphasis will be placed on developing problem-solving skills and applying mathematical principles to real-world scenarios. To successfully complete Upper-Sixth Mathematics with Mechanics, students are required to attend all lectures, actively participate in class discussions, complete assigned readings, and engage in regular problem-solving exercises.

Course Description

UPPER-SIXTH MATHEMATICS WITH MECHANICS course is designed to provide students with an advanced understanding of mathematics and mechanics at the upper-sixth level. Through a comprehensive curriculum, students will delve into the intricate world of mathematical principles and their application in the field of mechanics. This course aims to equip students with the necessary skills and knowledge to excel in higher-level mathematics and mechanics, preparing them for further studies in engineering, physics, or related disciplines.

Course Outcomes

Course Outline: UPPER-SIXTH MATHEMATICS WITH MECHANICS I. Introduction - Overview of the course - Importance of studying Upper-Sixth Mathematics with Mechanics - Goals and objectives II. Mechanics Fundamentals - Introduction to mechanics - Newton's laws of motion - Forces and motion - Equilibrium of particles - Work, energy, and power - Linear momentum and collisions III. Kinematics - One-dimensional motion - Projectile motion - Circular motion - Relative motion IV. Dynamics - Newton's second law - Frictional forces - Uniform circular motion - Centripetal force - Gravitational forces V. Statics - Equilibrium of rigid bodies - Moments and couples - Center of mass and centroid - Stability of equilibrium VI. Linear Motion - Linear motion with constant acceleration - Free fall and terminal velocity - Motion in a vertical circle VII. Circular Motion - Angular velocity and acceleration - Torque and rotational equilibrium - Rotational dynamics - Moment of inertia VIII. Oscillations and Waves - Simple harmonic motion - Damped and forced oscillations - Wave motion - Standing waves IX. Mathematical Methods - Vectors and vector algebra - Differentiation and integration techniques - Differential equations in mechanics X. Practical Applications - Application of mechanics principles in real-life scenarios - Engineering applications - Case studies and problem-solving exercises XI. Assessment and Evaluation - Grading criteria - Types of assessments (exams, quizzes, projects) - Weightage of each assessment - Evaluation methods XII. Resources and References - Recommended textbooks and study materials - Online resources and references - Additional reading materials and references Please note that this is a general course outline and may be subject to modifications based on specific curriculum requirements and teaching methodology.

Course Curriculum

2 chapters
52 lectures
26 quizzes
50 Min total length

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1 Equations of the circle: -Given centre and radius

5 Min

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3 Given coordinates of the ends of a diameter

5 Min

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5 Passing through three given points.

5 Min

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7 Intersection of a straight line with a circle

5 Min

N/A

9 Equation of a tangent to a circle

5 Min

N/A

11 Length of a tangent from external point to a circle

5 Min

N/A

13 Intersecting circles

5 Min

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15 Condition for two circles to touch

5 Min

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17 Orthogonal circles

5 Min

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19 Radical axis of two circles.

5 Min

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21 The equation of a circle through the points of intersection of two given circles and a given point.

5 Min

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1 Introduction to the Complex Number System

5 Min

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3 The imaginary number i and its algebra -Complex Numbers

5 Min

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5 Complex Numbers

5 Min

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7 Complex conjugate

5 Min

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9 The Argand Diagram

5 Min

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11 Geometrical representation of a complex numbers

5 Min

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13 Addition and subtraction of complex numbers

5 Min

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15 Product and Quotient of Complex Numbers

5 Min

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17 Equality of Complex Numbers

5 Min

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20 Multiplication and Division in Polar form

5 Min

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22 Simple equations and expansions

5 Min

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24 Modulus-Argument (Polar) form of a complex Number

5 Min

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26 Modulus and Argument of a Complex Number.

5 Min

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28 Complex roots of a polynomial equation

5 Min

N/A

30 Square root of complex Numbers:

5 Min

Instructor

High School Mathematics

Our High school mathematics Tutors plays a crucial role in equipping students with essential mathematical knowledge, problem-solving skills, and critical thinking abilities.

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