Our aim in choosing the sample lessons is to give the student a good idea of the content that will be available in the courses, and also to provide something useful irrespective of whether he / she chooses to join our course.
Therefore in these lessons, we give an introduction to Calculus and Vectors, which we hope will be useful, especially to the Class XI student in his/her study of Physics. In order to keep the content in Calculus brief and still explain the main concepts, we have limited our coverage to algebraic functions.
We have also provided lessons on Kinematics of translational motion and Newton's laws to illustrate the use of calculus and vectors. The content available under subscription will be similar, but will have MORE EXAMPLES, and will completely cover the IIT-JEE syllabus.
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Introduction to Calculus and Vectors
|Functions||Concept of functions; some common functions; sum, difference, product and quotient of functions; composite functions.|
|Limits and Continuity||Concept of limit of a function; right hand and left hand limits; some limit examples; concept of continuity of functions and some examples.|
|Derivatives (Part 1)||Concept of derivative; derivative examples; relationship between continuity and differentiability; sum, product and quotient rule for derivatives; chain rule for composite functions; higher order derivatives.|
|Derivatives (Part 2)||Parametric curves; Implicit differentiation; extreme values of functions; Rolle's theorem and Mean Value theorem; some examples.|
|Integration||Antiderivatives; definite integral and some properties; Fundamental theorem of calculus; Substitution rule; First order differential equation with separable variables.|
|Vectors (Part 1)||Concept of vectors; vectors in component form; addition and subtraction of vectors; multiplication of a vector by a scalar; dot product and cross product of vectors; calculus of vector functions.|
Kinematics of translational motion, and Newton's laws of motion
|Kinematics of translational motion (Part 1)||Motion along a straight line; straight line motion with uniform acceleration; examples; motion in 3D space.|
|Kinematics of translational motion (Part 2)||Projectile motion; examples; uniform circular motion; relative velocity.|
|Newton's laws of motion||Concept of force; Newton's first law and inertial frames; Newton's second law; Newton's third law; common forces like friction, normal force, weight, tension; application of Newton's laws with examples; Newton's 2nd law in a non-inertial frame.|
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