Differentiation, Limits, Application of derivatives
Description
This course has been designed for class 11 and 12 students. All the concepts of differentiation are explained along with solved examples. Lots of problems are solved to make the students confident to solve the problems. Questions of all levels of difficulties are solved. Efforts have been made to make the complex concepts simple and easy for students. Concepts of differentiation not only form a major portion of mathematics but also have applications in physics
The following topics are covered in this course:
1. Limits: Basic concepts, trigonometric limits, limits at infinity, existence of limit of a function.
2. Continuity: Continuity at a point, Continuous functions
3. Differentiability: Right hand derivative and left hand derivative, differentiability of a function.
4. Differentiation: Differentiation from first principles, derivative of functions, derivative of the product of functions. Derivative of quotient of two functions, derivative of a function of a function. Differentiation of implicit functions, differentiation of logarithmic functions, differentiation of infinite series. Differentiation of parametric functions, derivative of one function w.r.t. another function, derivatives of higher order.
5. Application of derivatives
6. Rolle’s and Lagrange’s theorems
7. Tangents and normals.
8. Monotonic functions: Increasing and decreasing functions
9. Local maxima and local minima: first derivative test, second derivative test, applications of the concept of local maxima and minima
Course Title: Differential calculus from scratch(For grade 11 and 12)
Prerequisite: Basic Algebra and trigonometry of grade 10
Duration of course : 23hr 15 min
Who this course is for:
- Grade 11 and Grade 12 students
